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# http://pyrocko.org - GPLv3 

# 

# The Pyrocko Developers, 21st Century 

# ---|P------/S----------~Lg---------- 

 

'''Classical seismic ray theory for layered earth models (*layer cake* models). 

 

This module can be used to e.g. calculate arrival times, ray paths, reflection 

and transmission coefficients, take-off and incidence angles and geometrical 

spreading factors for arbitrary seismic phases. Computations are done for a 

spherical earth, even though the module name may suggests something flat. 

 

The main classes defined in this module are: 

 

* :py:class:`Material` - Defines an isotropic elastic material. 

* :py:class:`PhaseDef` - Defines a seismic phase arrival / wave propagation 

history. 

* :py:class:`Leg` - Continuous propagation in a :py:class:`PhaseDef`. 

* :py:class:`Knee` - Conversion/reflection in a :py:class:`PhaseDef`. 

* :py:class:`LayeredModel` - Representation of a layer cake model. 

* :py:class:`Layer` - A layer in a :py:class:`LayeredModel`. 

 

* :py:class:`HomogeneousLayer` - A homogeneous :py:class:`Layer`. 

* :py:class:`GradientLayer` - A gradient :py:class:`Layer`. 

 

* :py:class:`Discontinuity` - A discontinuity in a :py:class:`LayeredModel`. 

 

* :py:class:`Interface` - A :py:class:`Discontinuity` between two 

:py:class:`Layer` instances. 

* :py:class:`Surface` - The surface :py:class:`Discontinuity` on top of 

a :py:class:`LayeredModel`. 

 

* :py:class:`RayPath` - A fan of rays running through a common sequence of 

layers / interfaces. 

* :py:class:`Ray` - A specific ray with a specific (ray parameter, distance, 

arrival time) choice. 

* :py:class:`RayElement` - An element of a :py:class:`RayPath`. 

 

* :py:class:`Straight` - A ray segment representing propagation through 

one :py:class:`Layer`. 

* :py:class:`Kink` - An interaction of a ray with a 

:py:class:`Discontinuity`. 

''' 

 

from __future__ import absolute_import 

from functools import reduce 

from future import standard_library 

standard_library.install_aliases() # noqa 

from builtins import range, zip, str as newstr 

 

import os 

import logging 

import copy 

import math 

import cmath 

import operator 

try: 

from StringIO import StringIO 

except ImportError: 

from io import StringIO 

 

import glob 

import numpy as num 

from scipy.optimize import bisect, brentq 

 

from . import util, config 

 

logger = logging.getLogger('cake') 

 

ZEPS = 0.01 

P = 1 

S = 2 

DOWN = 4 

UP = -4 

 

DEFAULT_BURGERS = (0., 0., 1.) 

 

earthradius = config.config().earthradius 

 

r2d = 180./math.pi 

d2r = 1./r2d 

km = 1000. 

d2m = d2r*earthradius 

m2d = 1./d2m 

sprad2spm = 1.0/(r2d*d2m) 

sprad2spkm = 1.0/(r2d*d2m/km) 

spm2sprad = 1.0/sprad2spm 

spkm2sprad = 1.0/sprad2spkm 

 

 

class CakeError(Exception): 

pass 

 

 

class InvalidArguments(CakeError): 

pass 

 

 

class Material(object): 

'''Isotropic elastic material. 

 

:param vp: P-wave velocity [m/s] 

:param vs: S-wave velocity [m/s] 

:param rho: density [kg/m^3] 

:param qp: P-wave attenuation Qp 

:param qs: S-wave attenuation Qs 

:param poisson: Poisson ratio 

:param lame: tuple with Lame parameter `lambda` and `shear modulus` [Pa] 

:param qk: bulk attenuation Qk 

:param qmu: shear attenuation Qmu 

 

:param burgers: Burgers rheology paramerters as `tuple`. 

`transient viscosity` [Pa], <= 0 means infinite value, 

`steady-state viscosity` [Pa] and `alpha`, the ratio between the 

effective and unreleaxed shear modulus, mu1/(mu1 + mu2). 

:type burgers: tuple 

 

If no velocities and no lame parameters are given, standard crustal values 

of vp = 5800 m/s and vs = 3200 m/s are used. If no Q values are given, 

standard crustal values of qp = 1456 and qs = 600 are used. If no Burgers 

material parameters are given, transient and steady-state viscosities are 

0 and alpha=1. 

 

Everything is in SI units (m/s, Pa, kg/m^3) unless explicitly stated. 

 

The main material properties are considered independant and are accessible 

as attributes (it is allowed to assign to these): 

 

.. py:attribute:: vp, vs, rho, qp, qs 

 

Other material properties are considered dependant and can be queried by 

instance methods. 

''' 

 

def __init__( 

self, vp=None, vs=None, rho=2600., qp=None, qs=None, poisson=None, 

lame=None, qk=None, qmu=None, burgers=None): 

 

parstore_float(locals(), self, 'vp', 'vs', 'rho', 'qp', 'qs') 

 

if vp is not None and vs is not None: 

if poisson is not None or lame is not None: 

raise InvalidArguments( 

'If vp and vs are given, poisson ratio and lame paramters ' 

'should not be given.') 

 

elif vp is None and vs is None and lame is None: 

self.vp = 5800. 

if poisson is None: 

poisson = 0.25 

self.vs = self.vp / math.sqrt(2.0*(1.0-poisson)/(1.0-2.0*poisson)) 

 

elif vp is None and vs is None and lame is not None: 

if poisson is not None: 

raise InvalidArguments( 

'Poisson ratio should not be given, when lame parameters ' 

'are given.') 

 

lam, mu = float(lame[0]), float(lame[1]) 

self.vp = math.sqrt((lam + 2.0*mu)/rho) 

self.vs = math.sqrt(mu/rho) 

 

elif vp is not None and vs is None: 

if poisson is None: 

poisson = 0.25 

 

if lame is not None: 

raise InvalidArguments( 

'If vp is given, Lame parameters should not be given.') 

 

poisson = float(poisson) 

self.vs = vp / math.sqrt(2.0*(1.0-poisson)/(1.0-2.0*poisson)) 

 

elif vp is None and vs is not None: 

if poisson is None: 

poisson = 0.25 

if lame is not None: 

raise InvalidArguments( 

'If vs is given, Lame parameters should not be given.') 

 

poisson = float(poisson) 

self.vp = vs * math.sqrt(2.0*(1.0-poisson)/(1.0-2.0*poisson)) 

 

else: 

raise InvalidArguments( 

'Invalid combination of input parameters in material ' 

'definition.') 

 

if qp is not None or qs is not None: 

if not (qk is None and qmu is None): 

raise InvalidArguments( 

'if qp or qs are given, qk and qmu should not be given.') 

 

if qp is None: 

if self.vs != 0.0: 

s = (4.0/3.0)*(self.vs/self.vp)**2 

self.qp = self.qs / s 

else: 

self.qp = 1456. 

 

if qs is None: 

if self.vs != 0.0: 

s = (4.0/3.0)*(self.vs/self.vp)**2 

self.qs = self.qp * s 

else: 

self.vs = 600. 

 

elif qp is None and qs is None and qk is None and qmu is None: 

if self.vs == 0.: 

self.qs = 0. 

self.qp = 5782e4 

else: 

self.qs = 600. 

s = (4.0/3.0)*(self.vs/self.vp)**2 

self.qp = self.qs/s 

 

elif qp is None and qs is None and qk is not None and qmu is not None: 

s = (4.0/3.0)*(self.vs/self.vp)**2 

if qmu == 0. and self.vs == 0.: 

self.qp = qk 

else: 

if num.isinf(qk): 

self.qp = qmu/s 

else: 

self.qp = 1.0 / (s/qmu + (1.0-s)/qk) 

self.qs = qmu 

else: 

raise InvalidArguments( 

'Invalid combination of input parameters in material ' 

'definition.') 

 

if burgers is None: 

burgers = DEFAULT_BURGERS 

 

self.burger_eta1 = burgers[0] 

self.burger_eta2 = burgers[1] 

self.burger_valpha = burgers[2] 

 

def astuple(self): 

'''Get independant material properties as a tuple. 

 

Returns a tuple with ``(vp, vs, rho, qp, qs)``. 

''' 

return self.vp, self.vs, self.rho, self.qp, self.qs 

 

def __eq__(self, other): 

return self.astuple() == other.astuple() 

 

def lame(self): 

'''Get Lame's parameter lambda and shear modulus.''' 

mu = self.vs**2 * self.rho 

lam = self.vp**2 * self.rho - 2.0*mu 

return lam, mu 

 

def lame_lambda(self): 

'''Get Lame's parameter lambda. 

 

Returned units are [Pa]. 

''' 

lam, _ = self.lame() 

return lam 

 

def shear_modulus(self): 

'''Get shear modulus. 

 

Returned units are [Pa]. 

''' 

return self.vs**2 * self.rho 

 

def poisson(self): 

'''Get Poisson's ratio.''' 

lam, mu = self.lame() 

return lam / (2.0*(lam+mu)) 

 

def bulk(self): 

'''Get bulk modulus.''' 

lam, mu = self.lame() 

return lam + 2.0*mu/3.0 

 

def youngs(self): 

'''Get Young's modulus.''' 

lam, mu = self.lame() 

return mu * (3.0*lam + 2.0*mu) / (lam+mu) 

 

def vp_vs_ratio(self): 

'''Get vp/vs ratio.''' 

return self.vp/self.vs 

 

def qmu(self): 

'''Get shear attenuation coefficient Qmu.''' 

return self.qs 

 

def qk(self): 

'''Get bulk attenuation coefficient Qk.''' 

if self.vs == 0. and self.qs == 0.: 

return self.qp 

else: 

s = (4.0/3.0)*(self.vs/self.vp)**2 

denom = (1/self.qp - s/self.qs) 

if denom <= 0.0: 

return num.inf 

else: 

return (1.-s)/(1.0/self.qp - s/self.qs) 

 

def burgers(self): 

'''Get Burger parameters.''' 

return self.burger_eta1, self.burger_eta2, self.burger_valpha 

 

def _rayleigh_equation(self, cr): 

cr_a = (cr/self.vp)**2 

cr_b = (cr/self.vs)**2 

if cr_a > 1.0 or cr_b > 1.0: 

return None 

 

return (2.0-cr_b)**2 - 4.0 * math.sqrt(1.0-cr_a) * math.sqrt(1.0-cr_b) 

 

def rayleigh(self): 

'''Get rayleigh velocity assuming a homogenous halfspace. 

 

Returned units are [m/s].''' 

return bisect(self._rayleigh_equation, 0.001*self.vs, self.vs) 

 

def _has_default_burgers(self): 

if self.burger_eta1 == DEFAULT_BURGERS[0] and \ 

self.burger_eta2 == DEFAULT_BURGERS[1] and \ 

self.burger_valpha == DEFAULT_BURGERS[2]: 

return True 

return False 

 

def describe(self): 

'''Get a readable listing of the material properties.''' 

template = ''' 

P wave velocity [km/s] : %12g 

S wave velocity [km/s] : %12g 

P/S wave vel. ratio : %12g 

Lame lambda [GPa] : %12g 

Lame shear modulus [GPa] : %12g 

Poisson ratio : %12g 

Bulk modulus [GPa] : %12g 

Young's modulus [GPa] : %12g 

Rayleigh wave vel. [km/s] : %12g 

Density [g/cm**3] : %12g 

Qp P-wave attenuation : %12g 

Qs S-wave attenuation (Qmu) : %12g 

Qk bulk attenuation : %12g 

transient viscos., eta1 [GPa] : %12g 

st.-state viscos., eta2 [GPa] : %12g 

relaxation: valpha : %12g 

'''.strip() 

 

return template % ( 

self.vp/km, 

self.vs/km, 

self.vp/self.vs, 

self.lame_lambda()*1e-9, 

self.shear_modulus()*1e-9, 

self.poisson(), 

self.bulk()*1e-9, 

self.youngs()*1e-9, 

self.rayleigh()/km, 

self.rho/km, 

self.qp, 

self.qs, 

self.qk(), 

self.burger_eta1*1e-9, 

self.burger_eta2*1e-9, 

self.burger_valpha) 

 

def __str__(self): 

vp, vs, rho, qp, qs = self.astuple() 

return '%10g km/s %10g km/s %10g g/cm^3 %10g %10g' % ( 

vp/km, vs/km, rho/km, qp, qs) 

 

def __repr__(self): 

return 'Material(vp=%s, vs=%s, rho=%s, qp=%s, qs=%s)' % \ 

tuple(repr(x) for x in ( 

self.vp, self.vs, self.rho, self.qp, self.qs)) 

 

 

class Leg(object): 

'''Represents a continuous piece of wave propagation in a :py:class:`PhaseDef`. 

 

**Attributes:** 

 

To be considered as read-only. 

 

.. py:attribute:: departure 

 

One of the constants :py:const:`UP` or :py:const:`DOWN` indicating 

upward or downward departure. 

 

.. py:attribute:: mode 

 

One of the constants :py:const:`P` or :py:const:`S`, indicating the 

propagation mode. 

 

.. py:attribute:: depthmin 

 

``None``, a number (a depth in [m]) or a string (an interface name), 

minimum depth. 

 

.. py:attribute:: depthmax 

 

``None``, a number (a depth in [m]) or a string (an interface name), 

maximum depth. 

 

''' 

 

def __init__(self, departure=None, mode=None): 

self.departure = departure 

self.mode = mode 

self.depthmin = None 

self.depthmax = None 

 

def set_depthmin(self, depthmin): 

self.depthmin = depthmin 

 

def set_depthmax(self, depthmax): 

self.depthmax = depthmax 

 

def __str__(self): 

def sd(d): 

if isinstance(d, float): 

return '%g km' % (d/km) 

else: 

return 'interface %s' % d 

 

s = '%s mode propagation, departing %s' % ( 

smode(self.mode).upper(), { 

UP: 'upward', DOWN: 'downward'}[self.departure]) 

 

sc = [] 

if self.depthmax is not None: 

sc.append('deeper than %s' % sd(self.depthmax)) 

if self.depthmin is not None: 

sc.append('shallower than %s' % sd(self.depthmin)) 

 

if sc: 

s = s + ' (may not propagate %s)' % ' or '.join(sc) 

 

return s 

 

 

class InvalidKneeDef(CakeError): 

pass 

 

 

class Knee(object): 

'''Represents a change in wave propagation within a :py:class:`PhaseDef`. 

 

**Attributes:** 

 

To be considered as read-only. 

 

.. py:attribute:: depth 

 

Depth at which the conversion/reflection should happen. this can be 

a string or a number. 

 

.. py:attribute:: direction 

 

One of the constants :py:const:`UP` or :py:const:`DOWN` to indicate 

the incoming direction. 

 

.. py:attribute:: in_mode 

 

One of the constants :py:const:`P` or :py:const:`S` to indicate the 

type of mode of the incoming wave. 

 

.. py:attribute:: out_mode 

 

One of the constants :py:const:`P` or :py:const:`S` to indicate the 

type of mode of the outgoing wave. 

 

.. py:attribute:: conversion 

 

Boolean, whether there is a mode conversion involved. 

 

.. py:attribute:: reflection 

 

Boolean, whether there is a reflection involved. 

 

.. py:attribute:: headwave 

 

Boolean, whether there is headwave propagation involved. 

 

''' 

 

defaults = dict( 

depth='surface', 

direction=UP, 

conversion=True, 

reflection=False, 

headwave=False, 

in_setup_state=True) 

 

defaults_surface = dict( 

depth='surface', 

direction=UP, 

conversion=False, 

reflection=True, 

headwave=False, 

in_setup_state=True) 

 

def __init__(self, *args): 

if args: 

(self.depth, self.direction, self.reflection, self.in_mode, 

self.out_mode) = args 

 

self.conversion = self.in_mode != self.out_mode 

self.in_setup_state = False 

 

def default(self, k): 

depth = self.__dict__.get('depth', 'surface') 

if depth == 'surface': 

return Knee.defaults_surface[k] 

else: 

return Knee.defaults[k] 

 

def __setattr__(self, k, v): 

if self.in_setup_state and k in self.__dict__: 

raise InvalidKneeDef('%s has already been set' % k) 

else: 

self.__dict__[k] = v 

 

def __getattr__(self, k): 

if k.startswith('__'): 

raise AttributeError(k) 

 

if k not in self.__dict__: 

return self.default(k) 

 

def set_modes(self, in_leg, out_leg): 

 

if out_leg.departure == UP and ( 

(self.direction == UP) == self.reflection): 

 

raise InvalidKneeDef( 

'cannot enter %s from %s and emit ray upwards' % ( 

['conversion', 'reflection'][self.reflection], 

{UP: 'below', DOWN: 'above'}[self.direction])) 

 

if out_leg.departure == DOWN and ( 

(self.direction == DOWN) == self.reflection): 

 

raise InvalidKneeDef( 

'cannot enter %s from %s and emit ray downwards' % ( 

['conversion', 'reflection'][self.reflection], 

{UP: 'below', DOWN: 'above'}[self.direction])) 

 

self.in_mode = in_leg.mode 

self.out_mode = out_leg.mode 

 

def at_surface(self): 

return self.depth == 'surface' 

 

def matches(self, discontinuity, mode, direction): 

''' 

Check whether it is relevant to a given combination of interface, 

propagation mode, and direction. 

''' 

 

if isinstance(self.depth, float): 

if abs(self.depth - discontinuity.z) > ZEPS: 

return False 

else: 

if discontinuity.name != self.depth: 

return False 

 

return self.direction == direction and self.in_mode == mode 

 

def out_direction(self): 

'''Get outgoing direction. 

 

Returns one of the constants :py:const:`UP` or :py:const:`DOWN`. 

''' 

 

if self.reflection: 

return - self.direction 

else: 

return self.direction 

 

def __str__(self): 

x = [] 

if self.reflection: 

if self.at_surface(): 

x.append('surface') 

else: 

if not self.headwave: 

if self.direction == UP: 

x.append('underside') 

else: 

x.append('upperside') 

 

if self.headwave: 

x.append('headwave propagation along') 

elif self.reflection and self.conversion: 

x.append('reflection with conversion from %s to %s' % ( 

smode(self.in_mode).upper(), smode(self.out_mode).upper())) 

if not self.at_surface(): 

x.append('at') 

elif self.reflection: 

x.append('reflection') 

if not self.at_surface(): 

x.append('at') 

elif self.conversion: 

x.append('conversion from %s to %s at' % ( 

smode(self.in_mode).upper(), smode(self.out_mode).upper())) 

else: 

x.append('passing through') 

 

if isinstance(self.depth, float): 

x.append('interface in %g km depth' % (self.depth/1000.)) 

else: 

if not self.at_surface(): 

x.append('%s' % self.depth) 

 

if not self.reflection: 

if self.direction == UP: 

x.append('on upgoing path') 

else: 

x.append('on downgoing path') 

 

return ' '.join(x) 

 

 

class Head(Knee): 

def __init__(self, *args): 

if args: 

z, in_direction, mode = args 

Knee.__init__(self, z, in_direction, True, mode, mode) 

else: 

Knee.__init__(self) 

 

def __str__(self): 

x = ['propagation as headwave'] 

if isinstance(self.depth, float): 

x.append('at interface in %g km depth' % (self.depth/1000.)) 

else: 

x.append('at %s' % self.depth) 

 

return ' '.join(x) 

 

 

class UnknownClassicPhase(CakeError): 

def __init__(self, phasename): 

self.phasename = phasename 

 

def __str__(self): 

return 'Unknown classic phase name: %s' % self.phasename 

 

 

class PhaseDefParseError(CakeError): 

''' 

Exception raised when an error occures during parsing of a phase 

definition string. 

''' 

 

def __init__(self, definition, position, exception): 

self.definition = definition 

self.position = position 

self.exception = exception 

 

def __str__(self): 

return 'Invalid phase definition: "%s" (at character %i: %s)' % ( 

self.definition, self.position+1, str(self.exception)) 

 

 

class PhaseDef(object): 

 

'''Definition of a seismic phase arrival, based on ray propagation path. 

 

:param definition: string representation of the phase in Cake's phase 

syntax 

 

Seismic phases are conventionally named e.g. P, Pn, PP, PcP, etc. In Cake, 

a slightly different terminology is adapted, which allows to specify 

arbitrary conversion/reflection histories for seismic ray paths. The 

conventions used here are inspired by those used in the TauP toolkit, but 

are not completely compatible with those. 

 

The definition of a seismic ray propagation path in Cake's phase syntax is 

a string consisting of an alternating sequence of *legs* and *knees*. 

 

A *leg* represents seismic wave propagation without any conversions, 

encountering only super-critical reflections. Legs are denoted by ``P``, 

``p``, ``S``, or ``s``. The capital letters are used when the take-off of 

the *leg* is in downward direction, while the lower case letters indicate a 

take-off in upward direction. 

 

A *knee* is an interaction with an interface. It can be a mode conversion, 

a reflection, or propagation as a headwave or diffracted wave. 

 

* conversion is simply denoted as: ``(INTERFACE)`` or ``DEPTH`` 

* upperside reflection: ``v(INTERFACE)`` or ``vDEPTH`` 

* underside reflection: ``^(INTERFACE)`` or ``^DEPTH`` 

* normal kind headwave or diffracted wave: ``v_(INTERFACE)`` or 

``v_DEPTH`` 

 

The interface may be given by name or by depth: INTERFACE is the name of an 

interface defined in the model, DEPTH is the depth of an interface in 

[km] (the interface closest to that depth is chosen). If two legs appear 

consecutively without an explicit *knee*, surface interaction is assumed. 

 

The phase definition may end with a backslash ``\\``, to indicate that the 

ray should arrive at the receiver from above instead of from below. It is 

possible to restrict the maximum and minimum depth of a *leg* by appending 

``<(INTERFACE)`` or ``<DEPTH`` or ``>(INTERFACE)`` or ``>DEPTH`` after the 

leg character, respectively. 

 

**Examples:** 

 

* ``P`` - like the classical P, but includes PKP, PKIKP, Pg 

* ``P<(moho)`` - like classical Pg, but must leave source downwards 

* ``pP`` - leaves source upward, reflects at surface, then travels as P 

* ``P(moho)s`` - conversion from P to S at the Moho on upgoing path 

* ``P(moho)S`` - conversion from P to S at the Moho on downgoing path 

* ``Pv12p`` - P with reflection at 12 km deep interface (or the 

interface closest to that) 

* ``Pv_(moho)p`` - classical Pn 

* ``Pv_(cmb)p`` - classical Pdiff 

* ``P^(conrad)P`` - underside reflection of P at the Conrad 

discontinuity 

 

**Usage:** 

 

>>> from pyrocko.cake import PhaseDef 

# must escape the backslash 

>>> my_crazy_phase = PhaseDef('pPv(moho)sP\\\\') 

>>> print my_crazy_phase 

Phase definition "pPv(moho)sP\": 

- P mode propagation, departing upward 

- surface reflection 

- P mode propagation, departing downward 

- upperside reflection with conversion from P to S at moho 

- S mode propagation, departing upward 

- surface reflection with conversion from S to P 

- P mode propagation, departing downward 

- arriving at target from above 

 

.. note:: 

 

(1) These conventions might be extended in a way to allow to fix wave 

propagation to SH mode, possibly by specifying SH, or a single 

character (e.g. H) instead of S. This would be benificial for the 

selection of conversion and reflection coefficients, which 

currently only deal with the P-SV case. 

''' 

 

allowed_characters_pattern = r'[0-9a-zA-Z_()<>^v\\.]+' 

allowed_characters_pattern_classic = r'[a-zA-Z0-9]+' 

 

@staticmethod 

def classic_definitions(): 

defs = {} 

# PmP, PmS, PcP, PcS, SmP, ... 

for r in 'mc': 

for a, b in 'PP PS SS SP'.split(): 

defs[a+r+b] = [ 

'%sv(%s)%s' % (a, {'m': 'moho', 'c': 'cmb'}[r], b.lower())] 

 

# Pg, P, S, Sg 

for a in 'PS': 

defs[a+'g'] = ['%s<(moho)' % x for x in (a, a.lower())] 

defs[a] = ['%s<(cmb)(moho)%s' % (x, x.lower()) for x in ( 

a, a.lower())] 

 

defs[a.lower()] = [a.lower()] 

 

for a, b in 'PP PS SS SP'.split(): 

defs[a+'K'+b] = ['%s(cmb)P<(icb)(cmb)%s' % (a, b.lower())] 

defs[a+'KIK'+b] = ['%s(cmb)P(icb)P(icb)p(cmb)%s' % (a, b.lower())] 

defs[a+'KJK'+b] = ['%s(cmb)P(icb)S(icb)p(cmb)%s' % (a, b.lower())] 

defs[a+'KiK'+b] = ['%s(cmb)Pv(icb)p(cmb)%s' % (a, b.lower())] 

 

# PP, SS, PS, SP, PPP, ... 

for a in 'PS': 

for b in 'PS': 

for c in 'PS': 

defs[a+b+c] = [''.join(defs[x][0] for x in a+b+c)] 

 

defs[a+b] = [''.join(defs[x][0] for x in a+b)] 

 

# Pc, Pdiff, Sc, ... 

for x in 'PS': 

defs[x+'c'] = defs[x+'diff'] = [x+'v_(cmb)'+x.lower()] 

defs[x+'n'] = [x+'v_(moho)'+x.lower()] 

 

# depth phases 

for k in list(defs.keys()): 

if k not in 'ps': 

for x in 'ps': 

defs[x+k] = [x + defs[k][0]] 

 

return defs 

 

@staticmethod 

def classic(phasename): 

'''Get phase definitions based on classic phase name. 

 

:param phasename: classic name of a phase 

:returns: list of PhaseDef objects 

 

This returns a list of PhaseDef objects, because some classic phases 

(like e.g. Pg) can only be represented by two Cake style PhaseDef 

objects (one with downgoing and one with upgoing first leg). 

''' 

 

defs = PhaseDef.classic_definitions() 

if phasename not in defs: 

raise UnknownClassicPhase(phasename) 

 

return [PhaseDef(d, classicname=phasename) for d in defs[phasename]] 

 

def __init__(self, definition=None, classicname=None): 

 

state = 0 

sdepth = '' 

sinterface = '' 

depthmax = depthmin = None 

depthlim = None 

depthlimtype = None 

sdepthlim = '' 

events = [] 

direction_stop = UP 

need_leg = True 

ic = 0 

if definition is not None: 

knee = Knee() 

try: 

for ic, c in enumerate(definition): 

 

if state in (0, 1): 

 

if c in '0123456789.': 

need_leg = True 

state = 1 

sdepth += c 

continue 

 

elif state == 1: 

knee.depth = float(sdepth)*1000. 

state = 0 

 

if state == 2: 

if c == ')': 

knee.depth = sinterface 

state = 0 

else: 

sinterface += c 

 

continue 

 

if state in (3, 4): 

 

if state == 3: 

if c in '0123456789.': 

sdepthlim += c 

continue 

elif c == '(': 

state = 4 

continue 

else: 

depthlim = float(sdepthlim)*1000. 

if depthlimtype == '<': 

depthmax = depthlim 

else: 

depthmin = depthlim 

state = 0 

 

elif state == 4: 

if c == ')': 

depthlim = sdepthlim 

if depthlimtype == '<': 

depthmax = depthlim 

else: 

depthmin = depthlim 

state = 0 

continue 

else: 

sdepthlim += c 

continue 

 

if state == 0: 

 

if c == '(': 

need_leg = True 

state = 2 

continue 

 

elif c in '<>': 

state = 3 

depthlim = None 

sdepthlim = '' 

depthlimtype = c 

continue 

 

elif c in 'psPS': 

leg = Leg() 

if c in 'ps': 

leg.departure = UP 

else: 

leg.departure = DOWN 

leg.mode = imode(c) 

 

if events: 

in_leg = events[-1] 

if depthmin is not None: 

in_leg.set_depthmin(depthmin) 

depthmin = None 

if depthmax is not None: 

in_leg.set_depthmax(depthmax) 

depthmax = None 

 

if in_leg.mode != leg.mode: 

knee.conversion = True 

else: 

knee.conversion = False 

 

if not knee.reflection: 

if c in 'ps': 

knee.direction = UP 

else: 

knee.direction = DOWN 

 

knee.set_modes(in_leg, leg) 

knee.in_setup_state = False 

events.append(knee) 

knee = Knee() 

sdepth = '' 

sinterface = '' 

 

events.append(leg) 

need_leg = False 

continue 

 

elif c == '^': 

need_leg = True 

knee.direction = UP 

knee.reflection = True 

continue 

 

elif c == 'v': 

need_leg = True 

knee.direction = DOWN 

knee.reflection = True 

continue 

 

elif c == '_': 

need_leg = True 

knee.headwave = True 

continue 

 

elif c == '\\': 

direction_stop = DOWN 

continue 

 

else: 

raise PhaseDefParseError( 

definition, ic, 'invalid character: "%s"' % c) 

 

if state == 3: 

depthlim = float(sdepthlim)*1000. 

if depthlimtype == '<': 

depthmax = depthlim 

else: 

depthmin = depthlim 

state = 0 

 

except (ValueError, InvalidKneeDef) as e: 

raise PhaseDefParseError(definition, ic, e) 

 

if state != 0 or need_leg: 

raise PhaseDefParseError( 

definition, ic, 'unfinished expression') 

 

if events and depthmin is not None: 

events[-1].set_depthmin(depthmin) 

if events and depthmax is not None: 

events[-1].set_depthmax(depthmax) 

 

self._definition = definition 

self._classicname = classicname 

self._events = events 

self._direction_stop = direction_stop 

 

def __iter__(self): 

for ev in self._events: 

yield ev 

 

def append(self, ev): 

self._events.append(ev) 

 

def first_leg(self): 

'''Get the first leg in phase definition.''' 

return self._events[0] 

 

def last_leg(self): 

'''Get the last leg in phase definition.''' 

return self._events[-1] 

 

def legs(self): 

''' 

Iterate over the continuous pieces of wave propagation (legs) defined 

within this phase definition. 

''' 

 

return (leg for leg in self if isinstance(leg, Leg)) 

 

def knees(self): 

''' 

Iterate over conversions and reflections (knees) defined within this 

phase definition. 

''' 

return (knee for knee in self if isinstance(knee, Knee)) 

 

def definition(self): 

'''Get original definition of the phase.''' 

return self._definition 

 

def given_name(self): 

''' 

Get entered classic name if any, or original definition of the phase. 

''' 

 

if self._classicname: 

return self._classicname 

else: 

return self._definition 

 

def direction_start(self): 

return self.first_leg().departure 

 

def direction_stop(self): 

return self._direction_stop 

 

def headwave_knee(self): 

for el in self: 

if type(el) == Knee and el.headwave: 

return el 

return None 

 

def used_repr(self): 

'''Translate into textual representation (cake phase syntax).''' 

def strdepth(x): 

if isinstance(x, float): 

return '%g' % (x/1000.) 

else: 

return '(%s)' % x 

 

x = [] 

for el in self: 

if type(el) == Leg: 

if el.departure == UP: 

x.append(smode(el.mode).lower()) 

else: 

x.append(smode(el.mode).upper()) 

 

if el.depthmax is not None: 

x.append('<'+strdepth(el.depthmax)) 

 

if el.depthmin is not None: 

x.append('>'+strdepth(el.depthmin)) 

 

elif type(el) == Knee: 

if el.reflection and not el.at_surface(): 

if el.direction == DOWN: 

x.append('v') 

else: 

x.append('^') 

if el.headwave: 

x.append('_') 

if not el.at_surface(): 

x.append(strdepth(el.depth)) 

 

elif type(el) == Head: 

x.append('_') 

x.append(strdepth(el.depth)) 

 

if self._direction_stop == DOWN: 

x.append('\\') 

 

return ''.join(x) 

 

def __repr__(self): 

if self._definition is not None: 

return "PhaseDef('%s')" % self._definition 

else: 

return "PhaseDef('%s')" % self.used_repr() 

 

def __str__(self): 

orig = '' 

used = self.used_repr() 

if self._definition != used: 

orig = ' (entered as "%s")' % self._definition 

 

sarrive = '\n - arriving at target from %s' % ('below', 'above')[ 

self._direction_stop == DOWN] 

 

return 'Phase definition "%s"%s:\n - ' % (used, orig) + \ 

'\n - '.join(str(ev) for ev in self) + sarrive 

 

def copy(self): 

'''Get a deep copy of it.''' 

return copy.deepcopy(self) 

 

 

def to_phase_defs(phases): 

if isinstance(phases, (str, newstr, PhaseDef)): 

phases = [phases] 

 

phases_out = [] 

for phase in phases: 

if isinstance(phase, (str, newstr)): 

phases_out.extend(PhaseDef(x.strip()) for x in phase.split(',')) 

elif isinstance(phase, PhaseDef): 

phases_out.append(phase) 

else: 

raise PhaseDefParseError('invalid phase definition') 

 

return phases_out 

 

 

def csswap(x): 

return cmath.sqrt(1.-x**2) 

 

 

def psv_surface_ind(in_mode, out_mode): 

''' 

Get indices to select the appropriate element from scatter matrix for free 

surface. 

''' 

 

return (int(in_mode == S), int(out_mode == S)) 

 

 

def psv_surface(material, p, energy=False): 

'''Scatter matrix for free surface reflection/conversions. 

 

:param material: material, object of type :py:class:`Material` 

:param p: flat ray parameter [s/m] 

:param energy: bool, when ``True`` energy normalized coefficients are 

returned 

:returns: Scatter matrix 

 

The scatter matrix is ordered as follows:: 

 

[[PP, PS], 

[SP, SS]] 

 

The formulas given in Aki & Richards are used. 

''' 

 

vp, vs, rho = material.vp, material.vs, material.rho 

sinphi = p * vp 

sinlam = p * vs 

cosphi = csswap(sinphi) 

coslam = csswap(sinlam) 

 

if vs == 0.0: 

scatter = num.array([[-1.0, 0.0], [0.0, 1.0]]) 

 

else: 

vsp_term = (1.0/vs**2 - 2.0*p**2) 

pcc_term = 4.0 * p**2 * cosphi/vp * coslam/vs 

denom = vsp_term**2 + pcc_term 

 

scatter = num.array([ 

[- vsp_term**2 + pcc_term, 4.0*p*coslam/vp*vsp_term], 

[4.0*p*cosphi/vs*vsp_term, vsp_term**2 - pcc_term]], 

dtype=num.complex) / denom 

 

if not energy: 

return scatter 

else: 

eps = 1e-16 

normvec = num.array([vp*rho*cosphi+eps, vs*rho*coslam+eps]) 

escatter = scatter*num.conj(scatter) * num.real( 

(normvec[:, num.newaxis]) / (normvec[num.newaxis, :])) 

return num.real(escatter) 

 

 

def psv_solid_ind(in_direction, out_direction, in_mode, out_mode): 

''' 

Get indices to select the appropriate element from scatter matrix for 

solid-solid interface. 

''' 

 

return ( 

(out_direction == DOWN)*2 + (out_mode == S), 

(in_direction == UP)*2 + (in_mode == S)) 

 

 

def psv_solid(material1, material2, p, energy=False): 

'''Scatter matrix for solid-solid interface. 

 

:param material1: material above, object of type :py:class:`Material` 

:param material2: material below, object of type :py:class:`Material` 

:param p: flat ray parameter [s/m] 

:param energy: bool, when ``True`` energy normalized coefficients are 

returned 

:returns: Scatter matrix 

 

The scatter matrix is ordered as follows:: 

 

[[P1P1, S1P1, P2P1, S2P1], 

[P1S1, S1S1, P2S1, S2S1], 

[P1P2, S1P2, P2P2, S2P2], 

[P1S2, S1S2, P2S2, S2S2]] 

 

The formulas given in Aki & Richards are used. 

''' 

 

vp1, vs1, rho1 = material1.vp, material1.vs, material1.rho 

vp2, vs2, rho2 = material2.vp, material2.vs, material2.rho 

 

sinphi1 = p * vp1 

cosphi1 = csswap(sinphi1) 

sinlam1 = p * vs1 

coslam1 = csswap(sinlam1) 

sinphi2 = p * vp2 

cosphi2 = csswap(sinphi2) 

sinlam2 = p * vs2 

coslam2 = csswap(sinlam2) 

 

# from aki and richards 

M = num.array([ 

[-vp1*p, -coslam1, vp2*p, coslam2], 

[cosphi1, -vs1*p, cosphi2, -vs2*p], 

[2.0*rho1*vs1**2*p*cosphi1, rho1*vs1*(1.0-2.0*vs1**2*p**2), 

2.0*rho2*vs2**2*p*cosphi2, rho2*vs2*(1.0-2.0*vs2**2*p**2)], 

[-rho1*vp1*(1.0-2.0*vs1**2*p**2), 2.0*rho1*vs1**2*p*coslam1, 

rho2*vp2*(1.0-2.0*vs2**2*p**2), -2.0*rho2*vs2**2*p*coslam2]], 

dtype=num.complex) 

N = M.copy() 

N[0] *= -1.0 

N[3] *= -1.0 

 

scatter = num.dot(num.linalg.inv(M), N) 

 

if not energy: 

return scatter 

else: 

eps = 1e-16 

if vs1 == 0.: 

vs1 = vp1*1e-16 

if vs2 == 0.: 

vs2 = vp2*1e-16 

normvec = num.array([ 

vp1*rho1*(cosphi1+eps), vs1*rho1*(coslam1+eps), 

vp2*rho2*(cosphi2+eps), vs2*rho2*(coslam2+eps)], dtype=num.complex) 

escatter = scatter*num.conj(scatter) * num.real( 

normvec[:, num.newaxis] / normvec[num.newaxis, :]) 

 

return num.real(escatter) 

 

 

class BadPotIntCoefs(CakeError): 

pass 

 

 

def potint_coefs(c1, c2, r1, r2): # r2 > r1 

eps = r2*1e-9 

if c1 == 0. and c2 == 0.: 

c1c2 = 1. 

else: 

c1c2 = c1/c2 

b = math.log(c1c2)/math.log((r1+eps)/r2) 

if abs(b) > 10.: 

raise BadPotIntCoefs() 

a = c1/(r1+eps)**b 

return a, b 

 

 

def imode(s): 

if s.lower() == 'p': 

return P 

elif s.lower() == 's': 

return S 

 

 

def smode(i): 

if i == P: 

return 'p' 

elif i == S: 

return 's' 

 

 

class PathFailed(CakeError): 

pass 

 

 

class SurfaceReached(PathFailed): 

pass 

 

 

class BottomReached(PathFailed): 

pass 

 

 

class MaxDepthReached(PathFailed): 

pass 

 

 

class MinDepthReached(PathFailed): 

pass 

 

 

class Trapped(PathFailed): 

pass 

 

 

class NotPhaseConform(PathFailed): 

pass 

 

 

class CannotPropagate(PathFailed): 

def __init__(self, direction, ilayer): 

PathFailed.__init__(self) 

self._direction = direction 

self._ilayer = ilayer 

 

def __str__(self): 

return 'Cannot enter layer %i from %s' % ( 

self._ilayer, { 

UP: 'below', 

DOWN: 'above'}[self._direction]) 

 

 

class Layer(object): 

'''Representation of a layer in a layered earth model. 

 

:param ztop: depth of top of layer 

:param zbot: depth of bottom of layer 

:param name: name of layer (optional) 

 

Subclasses are: :py:class:`HomogeneousLayer` and :py:class:`GradientLayer`. 

''' 

 

def __init__(self, ztop, zbot, name=None): 

self.ztop = ztop 

self.zbot = zbot 

self.zmid = (self.ztop + self.zbot) * 0.5 

self.name = name 

self.ilayer = None 

 

def _update_potint_coefs(self): 

potint_p = potint_s = False 

try: 

self._ppic = potint_coefs( 

self.mbot.vp, self.mtop.vp, 

radius(self.zbot), radius(self.ztop)) 

potint_p = True 

except BadPotIntCoefs: 

pass 

 

potint_s = False 

try: 

self._spic = potint_coefs( 

self.mbot.vs, self.mtop.vs, 

radius(self.zbot), radius(self.ztop)) 

potint_s = True 

except BadPotIntCoefs: 

pass 

 

assert P == 1 and S == 2 

self._use_potential_interpolation = (None, potint_p, potint_s) 

 

def potint_coefs(self, mode): 

'''Get coefficients for potential interpolation. 

 

:param mode: mode of wave propagation, :py:const:`P` or :py:const:`S` 

:returns: coefficients ``(a, b)`` 

''' 

 

if mode == P: 

return self._ppic 

else: 

return self._spic 

 

def contains(self, z): 

''' 

Tolerantly check if a given depth is within the layer 

(including boundaries). 

''' 

 

return self.ztop <= z <= self.zbot or \ 

self.at_bottom(z) or self.at_top(z) 

 

def inner(self, z): 

''' 

Tolerantly check if a given depth is within the layer 

(not including boundaries). 

''' 

 

return self.ztop <= z <= self.zbot and not \ 

self.at_bottom(z) and not \ 

self.at_top(z) 

 

def at_bottom(self, z): 

'''Tolerantly check if given depth is at the bottom of the layer.''' 

 

return abs(self.zbot - z) < ZEPS 

 

def at_top(self, z): 

'''Tolerantly check if given depth is at the top of the layer.''' 

return abs(self.ztop - z) < ZEPS 

 

def pflat_top(self, p): 

''' 

Convert spherical ray parameter to local flat ray parameter for top of 

layer. 

''' 

return p / (earthradius-self.ztop) 

 

def pflat_bottom(self, p): 

''' 

Convert spherical ray parameter to local flat ray parameter for bottom 

of layer. 

''' 

return p / (earthradius-self.zbot) 

 

def pflat(self, p, z): 

''' 

Convert spherical ray parameter to local flat ray parameter for 

given depth. 

''' 

return p / (earthradius-z) 

 

def v_potint(self, mode, z): 

a, b = self.potint_coefs(mode) 

return a*(earthradius-z)**b 

 

def u_potint(self, mode, z): 

a, b = self.potint_coefs(mode) 

return 1./(a*(earthradius-z)**b) 

 

def xt_potint(self, p, mode, zpart=None): 

''' 

Get travel time and distance for for traversal with given mode and ray 

parameter. 

 

:param p: ray parameter (spherical) 

:param mode: mode of propagation (:py:const:`P` or :py:const:`S`) 

:param zpart: if given, tuple with two depths to restrict computation 

to a part of the layer 

 

This implementation uses analytic formulas valid for a spherical earth 

in the case where the velocity c within the layer is given by potential 

interpolation of the form 

 

c(z) = a*z^b 

''' 

utop, ubot = self.u_top_bottom(mode) 

a, b = self.potint_coefs(mode) 

ztop = self.ztop 

zbot = self.zbot 

if zpart is not None: 

utop = self.u(mode, zpart[0]) 

ubot = self.u(mode, zpart[1]) 

ztop, zbot = zpart 

utop = 1./(a*(earthradius-ztop)**b) 

ubot = 1./(a*(earthradius-zbot)**b) 

 

r1 = radius(zbot) 

r2 = radius(ztop) 

burger_eta1 = r1 * ubot 

burger_eta2 = r2 * utop 

if b != 1: 

def cpe(eta): 

return num.arccos(num.minimum(p/num.maximum(eta, p/2), 1.0)) 

 

def sep(eta): 

return num.sqrt(num.maximum(eta**2 - p**2, 0.0)) 

 

x = (cpe(burger_eta2)-cpe(burger_eta1))/(1.0-b) 

t = (sep(burger_eta2)-sep(burger_eta1))/(1.0-b) 

else: 

lr = math.log(r2/r1) 

sap = num.sqrt(1.0/a**2 - p**2) 

x = p/sap * lr 

t = 1./(a**2 * sap) 

 

x *= r2d 

 

return x, t 

 

def test(self, p, mode, z): 

''' 

Check if wave mode can exist for given ray parameter at given depth 

within the layer. 

''' 

return (self.u(mode, z)*radius(z) - p) > 0. 

 

def tests(self, p, mode): 

utop, ubot = self.u_top_bottom(mode) 

return ( 

(utop * radius(self.ztop) - p) > 0., 

(ubot * radius(self.zbot) - p) > 0.) 

 

def zturn_potint(self, p, mode): 

'''Get turning depth for given ray parameter and propagation mode.''' 

 

a, b = self.potint_coefs(mode) 

r = num.exp(num.log(a*p)/(1.0-b)) 

return earthradius-r 

 

def propagate(self, p, mode, direction): 

'''Propagate ray through layer. 

 

:param p: ray parameter 

:param mode: propagation mode 

:param direction: in direction (:py:const:`UP` or :py:const:`DOWN`''' 

if direction == DOWN: 

zin, zout = self.ztop, self.zbot 

else: 

zin, zout = self.zbot, self.ztop 

 

if self.v(mode, zin) == 0.0 or not self.test(p, mode, zin): 

raise CannotPropagate(direction, self.ilayer) 

 

if not self.test(p, mode, zout): 

return -direction 

else: 

return direction 

 

def resize(self, depth_min=None, depth_max=None): 

'''Change layer thinkness and interpolate :py:class:`Material` if 

required.''' 

if depth_min: 

mtop = self.material(depth_min) 

 

if depth_max: 

mbot = self.material(depth_max) 

 

self.mtop = mtop if depth_min else self.mtop 

self.mbot = mbot if depth_max else self.mbot 

self.ztop = depth_min if depth_min else self.ztop 

self.zbot = depth_max if depth_max else self.zbot 

self.zmid = self.ztop + (self.zbot - self.ztop)/2. 

 

 

class DoesNotTurn(CakeError): 

pass 

 

 

def radius(z): 

return earthradius - z 

 

 

class HomogeneousLayer(Layer): 

'''Representation of a homogeneous layer in a layered earth model. 

 

Base class: :py:class:`Layer`. 

''' 

 

def __init__(self, ztop, zbot, m, name=None): 

Layer.__init__(self, ztop, zbot, name=name) 

self.m = m 

self.mtop = m 

self.mbot = m 

self._update_potint_coefs() 

 

def copy(self, ztop=None, zbot=None): 

if ztop is None: 

ztop = self.ztop 

 

if zbot is None: 

zbot = self.zbot 

 

return HomogeneousLayer(ztop, zbot, self.m, name=self.name) 

 

def material(self, z): 

return self.m 

 

def u(self, mode, z=None): 

if self._use_potential_interpolation[mode] and z is not None: 

return self.u_potint(mode, z) 

 

if mode == P: 

return 1./self.m.vp 

if mode == S: 

return 1./self.m.vs 

 

def u_top_bottom(self, mode): 

u = self.u(mode) 

return u, u 

 

def v(self, mode, z=None): 

if self._use_potential_interpolation[mode] and z is not None: 

return self.v_potint(mode, z) 

 

if mode == P: 

v = self.m.vp 

if mode == S: 

v = self.m.vs 

 

if num.isscalar(z): 

return v 

else: 

return filled(v, len(z)) 

 

def v_top_bottom(self, mode): 

v = self.v(mode) 

return v, v 

 

def xt(self, p, mode, zpart=None): 

if self._use_potential_interpolation[mode]: 

return self.xt_potint(p, mode, zpart) 

 

u = self.u(mode) 

pflat = self.pflat_bottom(p) 

if zpart is None: 

dz = (self.zbot - self.ztop) 

else: 

dz = abs(zpart[1]-zpart[0]) 

 

u = self.u(mode) 

eps = u*0.001 

denom = num.sqrt(u**2 - pflat**2) + eps 

 

x = r2d*pflat/(earthradius-self.zmid) * dz / denom 

t = u**2 * dz / denom 

return x, t 

 

def zturn(self, p, mode): 

if self._use_potential_interpolation[mode]: 

return self.zturn_potint(p, mode) 

 

raise DoesNotTurn() 

 

def split(self, z): 

upper = HomogeneousLayer(self.ztop, z, self.m, name=self.name) 

lower = HomogeneousLayer(z, self.zbot, self.m, name=self.name) 

upper.ilayer = self.ilayer 

lower.ilayer = self.ilayer 

return upper, lower 

 

def __str__(self): 

if self.name: 

name = self.name + ' ' 

else: 

name = '' 

 

calcmode = ''.join('HP'[self._use_potential_interpolation[mode]] 

for mode in (P, S)) 

 

return ' (%i) homogeneous layer %s(%g km - %g km) [%s]\n %s' % ( 

self.ilayer, name, self.ztop/km, self.zbot/km, calcmode, self.m) 

 

 

class GradientLayer(Layer): 

'''Representation of a gradient layer in a layered earth model. 

 

Base class: :py:class:`Layer`. 

''' 

 

def __init__(self, ztop, zbot, mtop, mbot, name=None): 

Layer.__init__(self, ztop, zbot, name=name) 

self.mtop = mtop 

self.mbot = mbot 

self._update_potint_coefs() 

 

def copy(self, ztop=None, zbot=None): 

if ztop is None: 

ztop = self.ztop 

 

if zbot is None: 

zbot = self.zbot 

 

return GradientLayer(ztop, zbot, self.mtop, self.mbot, name=self.name) 

 

def interpolate(self, z, ptop, pbot): 

return ptop + (z - self.ztop)*(pbot - ptop)/(self.zbot-self.ztop) 

 

def material(self, z): 

dtop = self.mtop.astuple() 

dbot = self.mbot.astuple() 

d = [ 

self.interpolate(z, ptop, pbot) 

for (ptop, pbot) in zip(dtop, dbot)] 

 

return Material(*d) 

 

def u_top_bottom(self, mode): 

if mode == P: 

return 1./self.mtop.vp, 1./self.mbot.vp 

if mode == S: 

return 1./self.mtop.vs, 1./self.mbot.vs 

 

def u(self, mode, z): 

if self._use_potential_interpolation[mode]: 

return self.u_potint(mode, z) 

 

if mode == P: 

return 1./self.interpolate(z, self.mtop.vp, self.mbot.vp) 

if mode == S: 

return 1./self.interpolate(z, self.mtop.vs, self.mbot.vs) 

 

def v_top_bottom(self, mode): 

if mode == P: 

return self.mtop.vp, self.mbot.vp 

if mode == S: 

return self.mtop.vs, self.mbot.vs 

 

def v(self, mode, z): 

if self._use_potential_interpolation[mode]: 

return self.v_potint(mode, z) 

 

if mode == P: 

return self.interpolate(z, self.mtop.vp, self.mbot.vp) 

if mode == S: 

return self.interpolate(z, self.mtop.vs, self.mbot.vs) 

 

def xt(self, p, mode, zpart=None): 

if self._use_potential_interpolation[mode]: 

return self.xt_potint(p, mode, zpart) 

 

utop, ubot = self.u_top_bottom(mode) 

b = (1./ubot - 1./utop)/(self.zbot - self.ztop) 

 

pflat = self.pflat_bottom(p) 

if zpart is not None: 

utop = self.u(mode, zpart[0]) 

ubot = self.u(mode, zpart[1]) 

 

peps = 1e-16 

pdp = pflat + peps 

 

def func(u): 

eta = num.sqrt(num.maximum(u**2 - pflat**2, 0.0)) 

xx = eta/u 

tt = num.where( 

pflat <= u, 

num.log(u+eta) - num.log(pdp) - eta/u, 

0.0) 

 

return xx, tt 

 

xxtop, tttop = func(utop) 

xxbot, ttbot = func(ubot) 

 

x = (xxtop - xxbot) / (b*pdp) 

t = (tttop - ttbot) / b + pflat*x 

 

x *= r2d/(earthradius - self.zmid) 

return x, t 

 

def zturn(self, p, mode): 

if self._use_potential_interpolation[mode]: 

return self.zturn_potint(p, mode) 

pflat = self.pflat_bottom(p) 

vtop, vbot = self.v_top_bottom(mode) 

return (1./pflat - vtop) * (self.zbot - self.ztop) / \ 

(vbot-vtop) + self.ztop 

 

def split(self, z): 

mmid = self.material(z) 

upper = GradientLayer(self.ztop, z, self.mtop, mmid, name=self.name) 

lower = GradientLayer(z, self.zbot, mmid, self.mbot, name=self.name) 

upper.ilayer = self.ilayer 

lower.ilayer = self.ilayer 

return upper, lower 

 

def __str__(self): 

if self.name: 

name = self.name + ' ' 

else: 

name = '' 

 

calcmode = ''.join('HP'[self._use_potential_interpolation[mode]] 

for mode in (P, S)) 

 

return ''' (%i) gradient layer %s(%g km - %g km) [%s] 

%s 

%s''' % ( 

self.ilayer, 

name, 

self.ztop/km, 

self.zbot/km, 

calcmode, 

self.mtop, 

self.mbot) 

 

 

class Discontinuity(object): 

'''Base class for discontinuities in layered earth model. 

 

Subclasses are: :py:class:`Interface` and :py:class:`Surface`. 

''' 

 

def __init__(self, z, name=None): 

self.z = z 

self.zbot = z 

self.ztop = z 

self.name = name 

 

def change_depth(self, z): 

self.z = z 

self.zbot = z 

self.ztop = z 

 

def copy(self): 

return copy.deepcopy(self) 

 

 

class Interface(Discontinuity): 

'''Representation of an interface in a layered earth model. 

 

Base class: :py:class:`Discontinuity`. 

''' 

 

def __init__(self, z, mabove, mbelow, name=None): 

Discontinuity.__init__(self, z, name) 

self.mabove = mabove 

self.mbelow = mbelow 

 

def __str__(self): 

if self.name is None: 

return 'interface' 

else: 

return 'interface "%s"' % self.name 

 

def u_top_bottom(self, mode): 

if mode == P: 

return reci_or_none(self.mabove.vp), reci_or_none(self.mbelow.vp) 

if mode == S: 

return reci_or_none(self.mabove.vs), reci_or_none(self.mbelow.vs) 

 

def critical_ps(self, mode): 

uabove, ubelow = self.u_top_bottom(mode) 

return ( 

mult_or_none(uabove, radius(self.z)), 

mult_or_none(ubelow, radius(self.z))) 

 

def propagate(self, p, mode, direction): 

uabove, ubelow = self.u_top_bottom(mode) 

if direction == DOWN: 

if ubelow is not None and ubelow*radius(self.z) - p >= 0: 

return direction 

else: 

return -direction 

if direction == UP: 

if uabove is not None and uabove*radius(self.z) - p >= 0: 

return direction 

else: 

return -direction 

 

def pflat(self, p): 

return p / (earthradius-self.z) 

 

def efficiency(self, in_direction, out_direction, in_mode, out_mode, p): 

scatter = psv_solid( 

self.mabove, self.mbelow, self.pflat(p), energy=True) 

return scatter[ 

psv_solid_ind(in_direction, out_direction, in_mode, out_mode)] 

 

 

class Surface(Discontinuity): 

'''Representation of the surface discontinuity in a layered earth model. 

 

Base class: :py:class:`Discontinuity`. 

''' 

 

def __init__(self, z, mbelow): 

Discontinuity.__init__(self, z, 'surface') 

self.z = z 

self.mbelow = mbelow 

 

def propagate(self, p, mode, direction): 

return direction # no implicit reflection at surface 

 

def u_top_bottom(self, mode): 

if mode == P: 

return None, reci_or_none(self.mbelow.vp) 

if mode == S: 

return None, reci_or_none(self.mbelow.vs) 

 

def critical_ps(self, mode): 

_, ubelow = self.u_top_bottom(mode) 

return None, mult_or_none(ubelow, radius(self.z)) 

 

def pflat(self, p): 

return p / (earthradius-self.z) 

 

def efficiency(self, in_direction, out_direction, in_mode, out_mode, p): 

if in_direction == DOWN or out_direction == UP: 

return 0.0 

else: 

return psv_surface( 

self.mbelow, self.pflat(p), energy=True)[ 

psv_surface_ind(in_mode, out_mode)] 

 

def __str__(self): 

return 'surface' 

 

 

class Walker(object): 

def __init__(self, elements): 

self._elements = elements 

self._i = 0 

 

def current(self): 

return self._elements[self._i] 

 

def go(self, direction): 

if direction == UP: 

self.up() 

else: 

self.down() 

 

def down(self): 

if self._i < len(self._elements)-1: 

self._i += 1 

else: 

raise BottomReached() 

 

def up(self): 

if self._i > 0: 

self._i -= 1 

else: 

raise SurfaceReached() 

 

def goto_layer(self, layer): 

self._i = self._elements.index(layer) 

 

 

class RayElement(object): 

'''An element of a :py:class:`RayPath`.''' 

 

def __eq__(self, other): 

return type(self) == type(other) and self.__dict__ == other.__dict__ 

 

def is_straight(self): 

return isinstance(self, Straight) 

 

def is_kink(self): 

return isinstance(self, Kink) 

 

 

class Straight(RayElement): 

''' 

A ray segment representing wave propagation through one :py:class:`Layer`. 

''' 

 

def __init__(self, direction_in, direction_out, mode, layer): 

self.mode = mode 

self._direction_in = direction_in 

self._direction_out = direction_out 

self.layer = layer 

 

def angle_in(self, p, endgaps=None): 

z = self.z_in(endgaps) 

dir = self.eff_direction_in(endgaps) 

v = self.layer.v(self.mode, z) 

pf = self.layer.pflat(p, z) 

 

if dir == DOWN: 

return num.arcsin(v*pf)*r2d 

else: 

return 180.-num.arcsin(v*pf)*r2d 

 

def angle_out(self, p, endgaps=None): 

z = self.z_out(endgaps) 

dir = self.eff_direction_out(endgaps) 

v = self.layer.v(self.mode, z) 

pf = self.layer.pflat(p, z) 

 

if dir == DOWN: 

return 180.-num.arcsin(v*pf)*r2d 

else: 

return num.arcsin(v*pf)*r2d 

 

def pflat_in(self, p, endgaps=None): 

return p / (earthradius-self.z_in(endgaps)) 

 

def pflat_out(self, p, endgaps=None): 

return p / (earthradius-self.z_out(endgaps)) 

 

def test(self, p, z): 

return self.layer.test(p, self.mode, z) 

 

def z_in(self, endgaps=None): 

if endgaps is not None: 

return endgaps[0] 

else: 

lyr = self.layer 

return (lyr.ztop, lyr.zbot)[self._direction_in == UP] 

 

def z_out(self, endgaps=None): 

if endgaps is not None: 

return endgaps[1] 

else: 

lyr = self.layer 

return (lyr.ztop, lyr.zbot)[self._direction_out == DOWN] 

 

def turns(self): 

return self._direction_in != self._direction_out 

 

def eff_direction_in(self, endgaps=None): 

if endgaps is None: 

return self._direction_in 

else: 

return endgaps[2] 

 

def eff_direction_out(self, endgaps=None): 

if endgaps is None: 

return self._direction_out 

else: 

return endgaps[3] 

 

def zturn(self, p): 

lyr = self.layer 

return lyr.zturn(p, self.mode) 

 

def u_in(self, endgaps=None): 

return self.layer.u(self.mode, self.z_in(endgaps)) 

 

def u_out(self, endgaps=None): 

return self.layer.u(self.mode, self.z_out(endgaps)) 

 

def critical_p_in(self, endgaps=None): 

z = self.z_in(endgaps) 

return self.layer.u(self.mode, z)*radius(z) 

 

def critical_p_out(self, endgaps=None): 

z = self.z_out(endgaps) 

return self.layer.u(self.mode, z)*radius(z) 

 

def xt(self, p, zpart=None): 

x, t = self.layer.xt(p, self.mode, zpart=zpart) 

if self._direction_in != self._direction_out and zpart is None: 

x *= 2. 

t *= 2. 

return x, t 

 

def xt_gap(self, p, zstart, zstop, samedir): 

z1, z2 = zstart, zstop 

if z1 > z2: 

z1, z2 = z2, z1 

 

x, t = self.layer.xt(p, self.mode, zpart=(z1, z2)) 

 

if samedir: 

return x, t 

else: 

xfull, tfull = self.xt(p) 

return xfull-x, tfull-t 

 

def __hash__(self): 

return hash(( 

self._direction_in, 

self._direction_out, 

self.mode, 

id(self.layer))) 

 

 

class HeadwaveStraight(Straight): 

def __init__(self, direction_in, direction_out, mode, interface): 

Straight.__init__(self, direction_in, direction_out, mode, None) 

 

self.interface = interface 

 

def z_in(self, zpart=None): 

return self.interface.z 

 

def z_out(self, zpart=None): 

return self.interface.z 

 

def zturn(self, p): 

return filled(self.interface.z, len(p)) 

 

def xt(self, p, zpart=None): 

return 0., 0. 

 

def x2t_headwave(self, xstretch): 

xstretch_m = xstretch*d2r*radius(self.interface.z) 

return min_not_none(*self.interface.u_top_bottom(self.mode))*xstretch_m 

 

 

class Kink(RayElement): 

'''An interaction of a ray with a :py:class:`Discontinuity`.''' 

 

def __init__( 

self, 

in_direction, 

out_direction, 

in_mode, 

out_mode, 

discontinuity): 

 

self.in_direction = in_direction 

self.out_direction = out_direction 

self.in_mode = in_mode 

self.out_mode = out_mode 

self.discontinuity = discontinuity 

 

def reflection(self): 

return self.in_direction != self.out_direction 

 

def conversion(self): 

return self.in_mode != self.out_mode 

 

def efficiency(self, p, out_direction=None, out_mode=None): 

 

if out_direction is None: 

out_direction = self.out_direction 

 

if out_mode is None: 

out_mode = self.out_mode 

 

return self.discontinuity.efficiency( 

self.in_direction, out_direction, self.in_mode, out_mode, p) 

 

def __str__(self): 

r, c = self.reflection(), self.conversion() 

if r and c: 

return '|~' 

if r: 

return '|' 

if c: 

return '~' 

return '_' 

 

def __hash__(self): 

return hash(( 

self.in_direction, 

self.out_direction, 

self.in_mode, 

self.out_mode, 

id(self.discontinuity))) 

 

 

class PRangeNotSet(CakeError): 

pass 

 

 

class RayPath(object): 

''' 

Representation of a fan of rays running through a common sequence of 

layers / interfaces. 

''' 

 

def __init__(self, phase): 

self.elements = [] 

self.phase = phase 

self._pmax = None 

self._pmin = None 

self._p = None 

self._is_headwave = False 

 

def set_is_headwave(self, is_headwave): 

self._is_headwave = is_headwave 

 

def copy(self): 

'''Get a copy of it.''' 

 

c = copy.copy(self) 

c.elements = list(self.elements) 

return c 

 

def endgaps(self, zstart, zstop): 

'''Get information needed for end point adjustments.''' 

 

return ( 

zstart, 

zstop, 

self.phase.direction_start(), 

self.phase.direction_stop()) 

 

def append(self, element): 

self.elements.append(element) 

 

def _check_have_prange(self): 

if self._pmax is None: 

raise PRangeNotSet() 

 

def set_prange(self, pmin, pmax, dp): 

self._pmin, self._pmax = pmin, pmax 

self._prange_dp = dp 

 

def used_phase(self, p=None, eps=1.): 

'''Calculate phase definition from ray path.''' 

 

used = PhaseDef() 

fleg = self.phase.first_leg() 

used.append(Leg(fleg.departure, fleg.mode)) 

n_elements_n = [None] + self.elements + [None] 

for before, element, after in zip( 

n_elements_n[:-2], 

n_elements_n[1:-1], 

n_elements_n[2:]): 

 

if element.is_kink() and HeadwaveStraight not in ( 

type(before), 

type(after)): 

 

if element.reflection() or element.conversion(): 

z = element.discontinuity.z 

used.append(Knee( 

z, 

element.in_direction, 

element.out_direction != element.in_direction, 

element.in_mode, 

element.out_mode)) 

 

used.append(Leg(element.out_direction, element.out_mode)) 

 

elif type(element) is HeadwaveStraight: 

z = element.interface.z 

k = Knee( 

z, 

before.in_direction, 

after.out_direction != before.in_direction, 

before.in_mode, 

after.out_mode) 

 

k.headwave = True 

used.append(k) 

used.append(Leg(after.out_direction, after.out_mode)) 

 

if (p is not None and before and after 

and element.is_straight() 

and before.is_kink() 

and after.is_kink() 

and element.turns() 

and not before.reflection() and not before.conversion() 

and not after.reflection() and not after.conversion()): 

 

ai = element.angle_in(p) 

if 90.0-eps < ai and ai < 90+eps: 

used.append( 

Head( 

before.discontinuity.z, 

before.out_direction, 

element.mode)) 

used.append( 

Leg(-before.out_direction, element.mode)) 

 

used._direction_stop = self.phase.direction_stop() 

used._definition = self.phase.definition() 

 

return used 

 

def pmax(self): 

'''Get maximum valid ray parameter.''' 

self._check_have_prange() 

return self._pmax 

 

def pmin(self): 

'''Get minimum valid ray parameter.''' 

self._check_have_prange() 

return self._pmin 

 

def xmin(self): 

'''Get minimal distance.''' 

self._analyse() 

return self._xmin 

 

def xmax(self): 

'''Get maximal distance.''' 

self._analyse() 

return self._xmax 

 

def kinks(self): 

''' 

Iterate over propagation mode changes (reflections/transmissions). 

''' 

return (k for k in self.elements if isinstance(k, Kink)) 

 

def straights(self): 

'''Iterate over ray segments.''' 

return (s for s in self.elements if isinstance(s, Straight)) 

 

def headwave_straight(self): 

for s in self.elements: 

if type(s) is HeadwaveStraight: 

return s 

 

def first_straight(self): 

'''Get first ray segment.''' 

for s in self.elements: 

if isinstance(s, Straight): 

return s 

 

def last_straight(self): 

'''Get last ray segment.''' 

for s in reversed(self.elements): 

if isinstance(s, Straight): 

return s 

 

def efficiency(self, p): 

''' 

Get product of all conversion/reflection coefficients encountered on 

path. 

''' 

return reduce( 

operator.mul, (k.efficiency(p) for k in self.kinks()), 1.) 

 

def spreading(self, p, endgaps): 

'''Get geometrical spreading factor.''' 

if self._is_headwave: 

return 0.0 

 

self._check_have_prange() 

dp = self._prange_dp * 0.01 

assert self._pmax - self._pmin > dp 

 

if p + dp > self._pmax: 

p = p-dp 

 

x0, t = self.xt(p, endgaps) 

x1, t = self.xt(p+dp, endgaps) 

x0 *= d2r 

x1 *= d2r 

if x1 == x0: 

return num.nan 

 

dp_dx = dp/(x1-x0) 

 

x = x0 

if x == 0.: 

x = x1 

p = dp 

 

first = self.first_straight() 

last = self.last_straight() 

return num.abs(dp_dx) * first.pflat_in(p, endgaps) / ( 

4.0 * math.pi * num.sin(x) * 

(earthradius-first.z_in(endgaps)) * 

(earthradius-last.z_out(endgaps))**2 * 

first.u_in(endgaps)**2 * 

num.abs(num.cos(first.angle_in(p, endgaps)*d2r)) * 

num.abs(num.cos(last.angle_out(p, endgaps)*d2r))) 

 

def make_p(self, dp=None, n=None, nmin=None): 

assert dp is None or n is None 

 

if self._pmin == self._pmax: 

return num.array([self._pmin]) 

 

if dp is None: 

dp = self._prange_dp 

 

if n is None: 

n = int(round((self._pmax-self._pmin)/dp)) + 1 

 

if nmin is not None: 

n = max(n, nmin) 

 

ppp = num.linspace(self._pmin, self._pmax, n) 

return ppp 

 

def xt_endgaps(self, p, endgaps, which='both'): 

''' 

Get amount of distance/traveltime to be subtracted at the generic ray 

path's ends. 

''' 

 

zstart, zstop, dirstart, dirstop = endgaps 

firsts = self.first_straight() 

lasts = self.last_straight() 

xs, ts = firsts.xt_gap( 

p, zstart, firsts.z_in(), dirstart == firsts._direction_in) 

xe, te = lasts.xt_gap( 

p, zstop, lasts.z_out(), dirstop == lasts._direction_out) 

 

if which == 'both': 

return xs + xe, ts + te 

elif which == 'left': 

return xs, ts 

elif which == 'right': 

return xe, te 

 

def xt_endgaps_ptest(self, p, endgaps): 

'''Check if ray parameter is valid at source and receiver.''' 

 

zstart, zstop, dirstart, dirstop = endgaps 

firsts = self.first_straight() 

lasts = self.last_straight() 

return num.logical_and(firsts.test(p, zstart), lasts.test(p, zstop)) 

 

def xt(self, p, endgaps): 

'''Calculate distance and traveltime for given ray parameter.''' 

 

if isinstance(p, num.ndarray): 

sx = num.zeros(p.size) 

st = num.zeros(p.size) 

else: 

sx = 0.0 

st = 0.0 

 

for s in self.straights(): 

x, t = s.xt(p) 

sx += x 

st += t 

 

if endgaps: 

dx, dt = self.xt_endgaps(p, endgaps) 

sx -= dx 

st -= dt 

 

return sx, st 

 

def xt_limits(self, p): 

''' 

Calculate limits of distance and traveltime for given ray parameter. 

''' 

 

if isinstance(p, num.ndarray): 

sx = num.zeros(p.size) 

st = num.zeros(p.size) 

sxe = num.zeros(p.size) 

ste = num.zeros(p.size) 

else: 

sx = 0.0 

st = 0.0 

sxe = 0.0 

ste = 0.0 

 

sfirst = self.first_straight() 

slast = self.last_straight() 

 

for s in self.straights(): 

if s is not sfirst and s is not slast: 

x, t = s.xt(p) 

sx += x 

st += t 

 

sends = [sfirst] 

if sfirst is not slast: 

sends.append(slast) 

 

for s in sends: 

x, t = s.xt(p) 

sxe += x 

ste += t 

 

return sx, (sx + sxe), st, (st + ste) 

 

def iter_zxt(self, p): 

''' 

Iterate over (depth, distance, traveltime) at each layer interface on 

ray path. 

''' 

 

sx = num.zeros(p.size) 

st = num.zeros(p.size) 

ok = False 

for s in self.straights(): 

yield s.z_in(), sx.copy(), st.copy() 

 

x, t = s.xt(p) 

sx += x 

st += t 

ok = True 

 

if ok: 

yield s.z_out(), sx.copy(), st.copy() 

 

def zxt_path_subdivided( 

self, p, endgaps, 

points_per_straight=20, 

x_for_headwave=None): 

 

'''Get geometrical representation of ray path.''' 

 

if self._is_headwave: 

assert p.size == 1 

x, t = self.xt(p, endgaps) 

xstretch = x_for_headwave-x 

nout = xstretch.size 

else: 

nout = p.size 

 

dxl, dtl = self.xt_endgaps(p, endgaps, which='left') 

dxr, dtr = self.xt_endgaps(p, endgaps, which='right') 

 

# first create full path including the endgaps 

sx = num.zeros(nout) - dxl 

st = num.zeros(nout) - dtl 

zxt = [] 

for s in self.straights(): 

n = points_per_straight 

 

back = None 

zin, zout = s.z_in(), s.z_out() 

if type(s) is HeadwaveStraight: 

z = zin 

for i in range(n): 

xs = float(i)/(n-1) * xstretch 

ts = s.x2t_headwave(xs) 

zxt.append((filled(z, xstretch.size), sx+xs, st+ts)) 

else: 

if zin != zout: # normal traversal 

zs = num.linspace(zin, zout, n).tolist() 

for z in zs: 

x, t = s.xt(p, zpart=sorted([zin, z])) 

zxt.append((filled(z, nout), sx + x, st + t)) 

 

else: # ray turns in layer 

zturn = s.zturn(p) 

back = [] 

for i in range(n): 

z = zin + (zturn - zin) * num.sin( 

float(i)/(n-1)*math.pi/2.0) * 0.999 

 

if zturn[0] >= zin: 

x, t = s.xt(p, zpart=[zin, z]) 

else: 

x, t = s.xt(p, zpart=[z, zin]) 

zxt.append((z, sx + x, st + t)) 

back.append((z, x, t)) 

 

if type(s) is HeadwaveStraight: 

x = xstretch 

t = s.x2t_headwave(xstretch) 

else: 

x, t = s.xt(p) 

 

sx += x 

st += t 

if back: 

for z, x, t in reversed(back): 

zxt.append((z, sx - x, st - t)) 

 

# gather results as arrays with such that x[ip, ipoint] 

fanz, fanx, fant = [], [], [] 

for z, x, t in zxt: 

fanz.append(z) 

fanx.append(x) 

fant.append(t) 

 

z = num.array(fanz).T 

x = num.array(fanx).T 

t = num.array(fant).T 

 

# cut off the endgaps, add exact endpoints 

xmax = x[:, -1] - dxr 

tmax = t[:, -1] - dtr 

zstart, zstop = endgaps[:2] 

zs, xs, ts = [], [], [] 

for i in range(nout): 

t_ = t[i] 

indices = num.where(num.logical_and(0. <= t_, t_ <= tmax[i]))[0] 

n = indices.size + 2 

zs_, xs_, ts_ = [num.empty(n, dtype=num.float) for j in range(3)] 

zs_[1:-1] = z[i, indices] 

xs_[1:-1] = x[i, indices] 

ts_[1:-1] = t[i, indices] 

zs_[0], zs_[-1] = zstart, zstop 

xs_[0], xs_[-1] = 0., xmax[i] 

ts_[0], ts_[-1] = 0., tmax[i] 

zs.append(zs_) 

xs.append(xs_) 

ts.append(ts_) 

 

return zs, xs, ts 

 

def _analyse(self): 

if self._p is not None: 

return 

 

p = self.make_p(nmin=20) 

xmin, xmax, tmin, tmax = self.xt_limits(p) 

 

self._x, self._t, self._p = xmax, tmax, p 

self._xmin, self._xmax = xmin.min(), xmax.max() 

self._tmin, self._tmax = tmin.min(), tmax.max() 

 

def draft_pxt(self, endgaps): 

self._analyse() 

 

if not self._is_headwave: 

cp, cx, ct = self._p, self._x, self._t 

pcrit = min( 

self.critical_pstart(endgaps), 

self.critical_pstop(endgaps)) 

 

if pcrit < self._pmin: 

empty = num.array([], dtype=num.float) 

return empty, empty, empty 

 

elif pcrit >= self._pmax: 

dx, dt = self.xt_endgaps(cp, endgaps) 

return cp, cx-dx, ct-dt 

 

else: 

n = num.searchsorted(cp, pcrit) + 1 

rp, rx, rt = num.empty((3, n), dtype=num.float) 

rp[:-1] = cp[:n-1] 

rx[:-1] = cx[:n-1] 

rt[:-1] = ct[:n-1] 

rp[-1] = pcrit 

rx[-1], rt[-1] = self.xt(pcrit, endgaps) 

dx, dt = self.xt_endgaps(rp, endgaps) 

rx[:-1] -= dx[:-1] 

rt[:-1] -= dt[:-1] 

return rp, rx, rt 

 

else: 

dx, dt = self.xt_endgaps(self._p, endgaps) 

p, x, t = self._p, self._x - dx, self._t - dt 

p, x, t = p[0], x[0], t[0] 

xh = num.linspace(0., x*10-x, 10) 

th = self.headwave_straight().x2t_headwave(xh) 

return filled(p, xh.size), x+xh, t+th 

 

def interpolate_x2pt_linear(self, x, endgaps): 

'''Get approximate ray parameter and traveltime for distance.''' 

 

self._analyse() 

 

if self._is_headwave: 

dx, dt = self.xt_endgaps(self._p, endgaps) 

xmin = self._x[0] - dx[0] 

tmin = self._t[0] - dt[0] 

el = self.headwave_straight() 

xok = x[x >= xmin] 

th = el.x2t_headwave(xstretch=(xok-xmin)) + tmin 

return [ 

(x_, self._p[0], t, None) for (x_, t) in zip(xok, th)] 

 

else: 

if num.all(x < self._xmin) or num.all(self._xmax < x): 

return [] 

 

rp, rx, rt = self.draft_pxt(endgaps) 

 

xp = interp(x, rx, rp, 0) 

xt = interp(x, rx, rt, 0) 

 

if (rp.size and 

len(xp) == 0 and 

rx[0] == 0.0 and 

any(x == 0.0) and 

rp[0] == 0.0): 

 

xp = [(0.0, rp[0])] 

xt = [(0.0, rt[0])] 

 

return [ 

(x_, p, t, (rp, rx, rt)) for ((x_, p), (_, t)) in zip(xp, xt)] 

 

def __eq__(self, other): 

if len(self.elements) != len(other.elements): 

return False 

 

return all(a == b for a, b in zip(self.elements, other.elements)) 

 

def __hash__(self): 

return hash( 

tuple(hash(x) for x in self.elements) + 

(self.phase.definition(), )) 

 

def __str__(self, p=None, eps=1.): 

x = [] 

start_i = None 

end_i = None 

turn_i = None 

 

def append_layers(si, ei, ti): 

if si == ei and (ti is None or ti == si): 

x.append('%i' % si) 

else: 

if ti is not None: 

x.append('(%i-%i-%i)' % (si, ti, ei)) 

else: 

x.append('(%i-%i)' % (si, ei)) 

 

for el in self.elements: 

if type(el) is Straight: 

if start_i is None: 

start_i = el.layer.ilayer 

if el._direction_in != el._direction_out: 

turn_i = el.layer.ilayer 

end_i = el.layer.ilayer 

 

elif isinstance(el, Kink): 

if start_i is not None: 

append_layers(start_i, end_i, turn_i) 

start_i = None 

turn_i = None 

 

x.append(str(el)) 

 

if start_i is not None: 

append_layers(start_i, end_i, turn_i) 

 

su = '(%s)' % self.used_phase(p=p, eps=eps).used_repr() 

 

return '%-15s %-17s %s' % (self.phase.definition(), su, ''.join(x)) 

 

def critical_pstart(self, endgaps): 

'''Get critical ray parameter for source depth choice.''' 

 

return self.first_straight().critical_p_in(endgaps) 

 

def critical_pstop(self, endgaps): 

'''Get critical ray parameter for receiver depth choice.''' 

 

return self.last_straight().critical_p_out(endgaps) 

 

def ranges(self, endgaps): 

'''Get valid ranges of ray parameter, distance, and traveltime.''' 

p, x, t = self.draft_pxt(endgaps) 

return p.min(), p.max(), x.min(), x.max(), t.min(), t.max() 

 

def describe(self, endgaps=None, as_degrees=False): 

'''Get textual representation.''' 

 

self._analyse() 

 

if as_degrees: 

xunit = 'deg' 

xfact = 1. 

else: 

xunit = 'km' 

xfact = d2m/km 

 

sg = ''' Ranges for all depths in source and receiver layers: 

- x [%g, %g] %s 

- t [%g, %g] s 

- p [%g, %g] s/deg 

''' % ( 

self._xmin*xfact, 

self._xmax*xfact, 

xunit, 

self._tmin, 

self._tmax, 

self._pmin/r2d, 

self._pmax/r2d) 

 

if endgaps is not None: 

pmin, pmax, xmin, xmax, tmin, tmax = self.ranges(endgaps) 

ss = ''' Ranges for given source and receiver depths: 

\n - x [%g, %g] %s 

\n - t [%g, %g] s 

\n - p [%g, %g] s/deg 

\n''' % (xmin*xfact, xmax*xfact, xunit, tmin, tmax, pmin/r2d, pmax/r2d) 

 

else: 

ss = '' 

 

return '%s\n' % self + ss + sg 

 

 

class RefineFailed(CakeError): 

pass 

 

 

class Ray(object): 

''' 

Representation of a ray with a specific (path, ray parameter, distance, 

arrival time) choice. 

 

**Attributes:** 

 

.. py:attribute:: path 

 

:py:class:`RayPath` object containing complete propagation history. 

 

.. py:attribute:: p 

 

Ray parameter (spherical) [s/rad] 

 

.. py:attribute:: x 

 

Radial distance [deg] 

 

.. py:attribute:: t 

 

Traveltime [s] 

 

.. py:attribute:: endgaps 

 

Needed for source/receiver depth adjustments in many 

:py:class:`RayPath` methods. 

''' 

 

def __init__(self, path, p, x, t, endgaps, draft_pxt): 

self.path = path 

self.p = p 

self.x = x 

self.t = t 

self.endgaps = endgaps 

self.draft_pxt = draft_pxt 

 

def given_phase(self): 

'''Get phase definition which was used to create the ray. 

 

:returns: :py:class:`PhaseDef` object 

''' 

 

return self.path.phase 

 

def used_phase(self): 

'''Compute phase definition from propagation path. 

 

:returns: :py:class:`PhaseDef` object 

''' 

 

return self.path.used_phase(self.p) 

 

def refine(self): 

if self.path._is_headwave: 

return 

 

if self.t == 0.0 and self.p == 0.0 and self.x == 0.0: 

return 

 

cp, cx, ct = self.draft_pxt 

ip = num.searchsorted(cp, self.p) 

if not (0 < ip < cp.size): 

raise RefineFailed() 

 

pl, ph = cp[ip-1], cp[ip] 

p_to_t = {} 

i = [0] 

 

def f(p): 

i[0] += 1 

x, t = self.path.xt(p, self.endgaps) 

p_to_t[p] = t 

return self.x - x 

 

try: 

self.p = brentq(f, pl, ph) 

self.t = p_to_t[self.p] 

 

except ValueError: 

raise RefineFailed() 

 

def takeoff_angle(self): 

'''Get takeoff angle of ray. 

 

The angle is returned in [degrees]. 

''' 

 

return self.path.first_straight().angle_in(self.p, self.endgaps) 

 

def incidence_angle(self): 

'''Get incidence angle of ray. 

 

The angle is returned in [degrees]. 

''' 

 

return self.path.last_straight().angle_out(self.p, self.endgaps) 

 

def efficiency(self): 

'''Get conversion/reflection efficiency of the ray. 

 

A value between 0 and 1 is returned, reflecting the relative amount of 

energy which is transmitted along the ray and not lost by reflections 

or conversions. 

''' 

 

return self.path.efficiency(self.p) 

 

def spreading(self): 

'''Get geometrical spreading factor.''' 

 

return self.path.spreading(self.p, self.endgaps) 

 

def surface_sphere(self): 

x1, y1 = 0., earthradius - self.endgaps[0] 

r2 = earthradius - self.endgaps[1] 

x2, y2 = r2*math.sin(self.x*d2r), r2*math.cos(self.x*d2r) 

return ((x2-x1)**2 + (y2-y1)**2)*4.0*math.pi 

 

def zxt_path_subdivided(self, points_per_straight=20): 

'''Get geometrical representation of ray path. 

 

Three arrays (depth, distance, time) with points on the ray's path of 

propagation are returned. The number of points which are used in each 

ray segment (passage through one layer) may be controlled by the 

``points_per_straight`` parameter. 

''' 

return self.path.zxt_path_subdivided( 

num.atleast_1d(self.p), self.endgaps, 

points_per_straight=points_per_straight, 

x_for_headwave=num.atleast_1d(self.x)) 

 

def __str__(self, as_degrees=False): 

if as_degrees: 

sd = '%6.3g deg' % self.x 

else: 

sd = '%7.5g km' % (self.x*(d2r*earthradius/km)) 

 

return '%7.5g s/deg %s %6.4g s %5.1f %5.1f %3.0f%% %3.0f%% %s' % ( 

self.p/r2d, 

sd, 

self.t, 

self.takeoff_angle(), 

self.incidence_angle(), 

100*self.efficiency(), 

100*self.spreading()*self.surface_sphere(), 

self.path.__str__(p=self.p)) 

 

 

def anything_to_crust2_profile(crust2_profile): 

from pyrocko.dataset import crust2x2 

if isinstance(crust2_profile, tuple): 

lat, lon = [float(x) for x in crust2_profile] 

return crust2x2.get_profile(lat, lon) 

elif isinstance(crust2_profile, (str, newstr)): 

return crust2x2.get_profile(crust2_profile) 

elif isinstance(crust2_profile, crust2x2.Crust2Profile): 

return crust2_profile 

else: 

assert False, 'crust2_profile must be (lat, lon) a profile ' \ 

'key or a crust2x2 Profile object)' 

 

 

class DiscontinuityNotFound(CakeError): 

def __init__(self, depth_or_name): 

CakeError.__init__(self) 

self.depth_or_name = depth_or_name 

 

def __str__(self): 

return 'Cannot find discontinuity from given depth or name: %s' % \ 

self.depth_or_name 

 

 

class LayeredModelError(CakeError): 

pass 

 

 

class LayeredModel(object): 

'''Representation of a layer cake model. 

 

There are several ways to initialize an instance of this class. 

 

1. Use the module function :py:func:`load_model` to read a model from a 

file. 

2. Create an empty model with the default constructor and append layers and 

discontinuities with the :py:meth:`append` method (from top to bottom). 

3. Use the constructor :py:meth:`LayeredModel.from_scanlines`, to 

automatically create the :py:class:`Layer` and :py:class:`Discontinuity` 

objects from a given velocity profile. 

 

An earth model is represented by as stack of :py:class:`Layer` and 

:py:class:`Discontinuity` objects. The method :py:meth:`arrivals` returns 

:py:class:`Ray` objects which may be e.g. queried for arrival times of 

specific phases. Each ray is associated with a :py:class:`RayPath` object. 

Ray objects share common ray paths if they have the same 

conversion/reflection/propagation history. Creating the ray path objects is 

relatively expensive (this is done in :py:meth:`gather_paths`), but they 

are cached for reuse in successive invocations. 

''' 

 

def __init__(self): 

self._surface_material = None 

self._elements = [] 

self.nlayers = 0 

self._np = 10000 

self._pdepth = 5 

self._pathcache = {} 

 

def copy_with_elevation(self, elevation): 

'''Get a copy of the model with surface layer stretched to given elevation. 

 

:param elevation: new surface elevation in [m] 

 

Elevation is positiv upward, contrary to the layered models downward 

`z` axis. 

''' 

 

c = copy.deepcopy(self) 

c._pathcache = {} 

surface = c._elements[0] 

toplayer = c._elements[1] 

 

assert toplayer.zbot > -elevation 

 

surface.z = -elevation 

c._elements[1] = toplayer.copy(ztop=-elevation) 

c._elements[1].ilayer = 0 

return c 

 

def zeq(self, z1, z2): 

return abs(z1-z2) < ZEPS 

 

def append(self, element): 

'''Add a layer or discontinuity at bottom of model. 

 

:param element: object of subclass of :py:class:`Layer` or 

:py:class:`Discontinuity`. 

''' 

 

if isinstance(element, Layer): 

if element.zbot >= earthradius: 

element.zbot = earthradius - 1. 

 

if element.ztop >= earthradius: 

raise CakeError('Layer deeper than earthradius') 

 

element.ilayer = self.nlayers 

self.nlayers += 1 

 

self._elements.append(element) 

 

def elements(self, direction=DOWN): 

'''Iterate over all elements of the model. 

 

:param direction: direction of traversal :py:const:`DOWN` or 

:py:const:`UP`. 

 

Objects derived from the :py:class:`Discontinuity` and 

:py:class:`Layer` classes are yielded. 

''' 

 

if direction == DOWN: 

return iter(self._elements) 

else: 

return reversed(self._elements) 

 

def layers(self, direction=DOWN): 

'''Iterate over all layers of model. 

 

:param direction: direction of traversal :py:const:`DOWN` or 

:py:const:`UP`. 

 

Objects derived from the :py:class:`Layer` class are yielded. 

''' 

 

if direction == DOWN: 

return (el for el in self._elements if isinstance(el, Layer)) 

else: 

return ( 

el for el in reversed(self._elements) if isinstance(el, Layer)) 

 

def layer(self, z, direction=DOWN): 

'''Get layer for given depth. 

 

:param z: depth [m] 

:param direction: direction of traversal :py:const:`DOWN` or 

:py:const:`UP`. 

 

Returns first layer which touches depth ``z`` (tolerant at boundaries). 

''' 

 

for l in self.layers(direction): 

if l.contains(z): 

return l 

else: 

raise CakeError('Failed extracting layer at depth z=%s' % z) 

 

def walker(self): 

return Walker(self._elements) 

 

def material(self, z, direction=DOWN): 

'''Get material at given depth. 

 

:param z: depth [m] 

:param direction: direction of traversal :py:const:`DOWN` or 

:py:const:`UP` 

:returns: object of type :py:class:`Material` 

 

If given depth ``z`` happens to be at an interface, the material of the 

first layer with respect to the the traversal ordering is returned. 

''' 

 

lyr = self.layer(z, direction) 

return lyr.material(z) 

 

def discontinuities(self): 

'''Iterate over all discontinuities of the model.''' 

 

return (el for el in self._elements if isinstance(el, Discontinuity)) 

 

def discontinuity(self, name_or_z): 

'''Get discontinuity by name or depth. 

 

:param name_or_z: name of discontinuity or depth [m] as float value 

''' 

 

if isinstance(name_or_z, float): 

candi = sorted( 

self.discontinuities(), key=lambda i: abs(i.z-name_or_z)) 

else: 

candi = [i for i in self.discontinuities() if i.name == name_or_z] 

 

if not candi: 

raise DiscontinuityNotFound(name_or_z) 

 

return candi[0] 

 

def adapt_phase(self, phase): 

'''Adapt a phase definition for use with this model. 

 

This returns a copy of the phase definition, where named 

discontinuities are replaced with the actual depth of these, as defined 

in the model. 

''' 

 

phase = phase.copy() 

for knee in phase.knees(): 

if knee.depth != 'surface': 

knee.depth = self.discontinuity(knee.depth).z 

for leg in phase.legs(): 

if leg.depthmax is not None and isinstance(leg.depthmax, str): 

leg.depthmax = self.discontinuity(leg.depthmax).z 

 

return phase 

 

def path(self, p, phase, layer_start, layer_stop): 

''' 

Get ray path for given combination of ray parameter, phase definition, 

source and receiver layers. 

 

:param p: ray parameter (spherical) [s/rad] 

:param phase: phase definition (:py:class:`PhaseDef` object) 

:param layer_start: layer with source 

:param layer_stop: layer with receiver 

:returns: :py:class:`RayPath` object 

 

If it is not possible to find a solution, an exception of type 

:py:exc:`NotPhaseConform`, :py:exc:`MinDepthReached`, 

:py:exc:`MaxDepthReached`, :py:exc:`CannotPropagate`, 

:py:exc:`BottomReached` or :py:exc:`SurfaceReached` is raised. 

''' 

 

phase = self.adapt_phase(phase) 

knees = phase.knees() 

legs = phase.legs() 

next_knee = next_or_none(knees) 

leg = next_or_none(legs) 

assert leg is not None 

 

direction = leg.departure 

direction_stop = phase.direction_stop() 

mode = leg.mode 

mode_stop = phase.last_leg().mode 

 

walker = self.walker() 

walker.goto_layer(layer_start) 

current = walker.current() 

 

ttop, tbot = current.tests(p, mode) 

if not ttop and not tbot: 

raise CannotPropagate(direction, current.ilayer) 

 

if (direction == DOWN and not ttop) or (direction == UP and not tbot): 

direction = -direction 

 

path = RayPath(phase) 

trapdetect = set() 

while True: 

at_layer = isinstance(current, Layer) 

at_discontinuity = isinstance(current, Discontinuity) 

 

# detect trapped wave 

k = (id(next_knee), id(current), direction, mode) 

if k in trapdetect: 

raise Trapped() 

 

trapdetect.add(k) 

 

if at_discontinuity: 

oldmode, olddirection = mode, direction 

headwave = False 

if next_knee is not None and next_knee.matches( 

current, mode, direction): 

 

headwave = next_knee.headwave 

direction = next_knee.out_direction() 

mode = next_knee.out_mode 

next_knee = next_or_none(knees) 

leg = next(legs) 

 

else: # implicit reflection/transmission 

direction = current.propagate(p, mode, direction) 

 

if headwave: 

path.set_is_headwave(True) 

 

path.append(Kink( 

olddirection, olddirection, oldmode, oldmode, current)) 

 

path.append(HeadwaveStraight( 

olddirection, direction, oldmode, current)) 

 

path.append(Kink( 

olddirection, direction, oldmode, mode, current)) 

 

else: 

path.append(Kink( 

olddirection, direction, oldmode, mode, current)) 

 

if at_layer: 

direction_in = direction 

direction = current.propagate(p, mode, direction_in) 

 

zturn = None 

if direction_in != direction: 

zturn = current.zturn(p, mode) 

 

zmin, zmax = leg.depthmin, leg.depthmax 

if zmin is not None or zmax is not None: 

if direction_in != direction: 

if zmin is not None and zturn <= zmin: 

raise MinDepthReached() 

if zmax is not None and zturn >= zmax: 

raise MaxDepthReached() 

else: 

if zmin is not None and current.ztop <= zmin: 

raise MinDepthReached() 

if zmax is not None and current.zbot >= zmax: 

raise MaxDepthReached() 

 

path.append(Straight(direction_in, direction, mode, current)) 

 

if next_knee is None and mode == mode_stop and \ 

current is layer_stop: 

 

if zturn is None: 

if direction == direction_stop: 

break 

else: 

break 

 

walker.go(direction) 

current = walker.current() 

 

return path 

 

def gather_paths(self, phases=PhaseDef('P'), zstart=0.0, zstop=0.0): 

''' 

Get all possible ray paths for given source and receiver depths for one 

or more phase definitions. 

 

:param phases: a :py:class:`PhaseDef` object or a list of such objects. 

Comma-separated strings and lists of such strings are also accepted 

and are converted to :py:class:`PhaseDef` objects for convenience. 

:param zstart: source depth [m] 

:param zstop: receiver depth [m] 

:returns: a list of :py:class:`RayPath` objects 

 

Results of this method are cached internally. Cached results are 

returned, when a given combination of source layer, receiver layer and 

phase definition has been used before. 

''' 

 

eps = 1e-7 # num.finfo(float).eps * 1000. 

 

phases = to_phase_defs(phases) 

 

paths = [] 

for phase in phases: 

 

layer_start = self.layer(zstart, -phase.direction_start()) 

layer_stop = self.layer(zstop, phase.direction_stop()) 

 

pathcachekey = (phase.definition(), layer_start, layer_stop) 

 

if pathcachekey in self._pathcache: 

phase_paths = self._pathcache[pathcachekey] 

else: 

hwknee = phase.headwave_knee() 

if hwknee: 

name_or_z = hwknee.depth 

interface = self.discontinuity(name_or_z) 

mode = hwknee.in_mode 

in_direction = hwknee.direction 

 

pabove, pbelow = interface.critical_ps(mode) 

 

p = min_not_none(pabove, pbelow) 

 

# diffracted wave: 

if in_direction == DOWN and ( 

pbelow is None or pbelow >= pabove): 

 

p *= (1.0 - eps) 

 

path = self.path(p, phase, layer_start, layer_stop) 

path.set_prange(p, p, 1.) 

 

phase_paths = [path] 

 

else: 

try: 

pmax_start = max([ 

radius(z)/layer_start.v(phase.first_leg().mode, z) 

for z in (layer_start.ztop, layer_start.zbot)]) 

 

pmax_stop = max([ 

radius(z)/layer_stop.v(phase.last_leg().mode, z) 

for z in (layer_stop.ztop, layer_stop.zbot)]) 

 

pmax = min(pmax_start, pmax_stop) 

 

pedges = [0.] 

for l in self.layers(): 

for z in (l.ztop, l.zbot): 

for mode in (P, S): 

for eps2 in [eps]: 

v = l.v(mode, z) 

if v != 0.0: 

p = radius(z)/v 

if p <= pmax: 

pedges.append(p*(1.0-eps2)) 

pedges.append(p) 

pedges.append(p*(1.0+eps2)) 

 

pedges = num.unique(sorted(pedges)) 

 

phase_paths = {} 

cached = {} 

counter = [0] 

 

def p_to_path(p): 

if p in cached: 

return cached[p] 

 

try: 

counter[0] += 1 

path = self.path( 

p, phase, layer_start, layer_stop) 

 

if path not in phase_paths: 

phase_paths[path] = [] 

 

phase_paths[path].append(p) 

 

except PathFailed: 

path = None 

 

cached[p] = path 

return path 

 

def recurse(pmin, pmax, i=0): 

if i > self._pdepth: 

return 

path1 = p_to_path(pmin) 

path2 = p_to_path(pmax) 

if path1 is None and path2 is None and i > 0: 

return 

if path1 is None or path2 is None or \ 

hash(path1) != hash(path2): 

 

recurse(pmin, (pmin+pmax)/2., i+1) 

recurse((pmin+pmax)/2., pmax, i+1) 

 

for (pl, ph) in zip(pedges[:-1], pedges[1:]): 

recurse(pl, ph) 

 

for path, ps in phase_paths.items(): 

path.set_prange( 

min(ps), max(ps), pmax/(self._np-1)) 

 

phase_paths = list(phase_paths.keys()) 

 

except ZeroDivisionError: 

phase_paths = [] 

 

self._pathcache[pathcachekey] = phase_paths 

 

paths.extend(phase_paths) 

 

paths.sort(key=lambda x: x.pmin()) 

return paths 

 

def arrivals( 

self, 

distances=[], 

phases=PhaseDef('P'), 

zstart=0.0, 

zstop=0.0, 

refine=True): 

 

'''Compute rays and traveltimes for given distances. 

 

:param distances: list or array of distances [deg] 

:param phases: a :py:class:`PhaseDef` object or a list of such objects. 

Comma-separated strings and lists of such strings are also accepted 

and are converted to :py:class:`PhaseDef` objects for convenience. 

:param zstart: source depth [m] 

:param zstop: receiver depth [m] 

:param refine: bool flag, whether to use bisectioning to improve 

(p, x, t) estimated from interpolation 

:returns: a list of :py:class:`Ray` objects, sorted by 

(distance, arrival time) 

''' 

 

distances = num.asarray(distances, dtype=num.float) 

 

arrivals = [] 

for path in self.gather_paths(phases, zstart=zstart, zstop=zstop): 

 

endgaps = path.endgaps(zstart, zstop) 

for x, p, t, draft_pxt in path.interpolate_x2pt_linear( 

distances, endgaps): 

 

arrivals.append(Ray(path, p, x, t, endgaps, draft_pxt)) 

 

if refine: 

refined = [] 

for ray in arrivals: 

 

if ray.path._is_headwave: 

refined.append(ray) 

 

try: 

ray.refine() 

refined.append(ray) 

 

except RefineFailed: 

pass 

 

arrivals = refined 

 

arrivals.sort(key=lambda x: (x.x, x.t)) 

return arrivals 

 

@classmethod 

def from_scanlines(cls, producer): 

'''Create layer cake model from sequence of materials at depths. 

 

:param producer: iterable yielding (depth, material, name) tuples 

 

Creates a new :py:class:`LayeredModel` object and uses its 

:py:meth:`append` method to add layers and discontinuities as needed. 

''' 

 

self = cls() 

for z, material, name in producer: 

 

if not self._elements: 

self.append(Surface(z, material)) 

else: 

element = self._elements[-1] 

if self.zeq(element.zbot, z): 

assert isinstance(element, Layer) 

self.append( 

Interface(z, element.mbot, material, name=name)) 

 

else: 

if isinstance(element, Discontinuity): 

ztop = element.z 

mtop = element.mbelow 

elif isinstance(element, Layer): 

ztop = element.zbot 

mtop = element.mbot 

 

if mtop == material: 

layer = HomogeneousLayer( 

ztop, z, material, name=name) 

else: 

layer = GradientLayer( 

ztop, z, mtop, material, name=name) 

 

self.append(layer) 

 

return self 

 

def to_scanlines(self, get_burgers=False): 

def fmt(z, m): 

if not m._has_default_burgers() or get_burgers: 

return (z, m.vp, m.vs, m.rho, m.qp, m.qs, 

m.burger_eta1, m.burger_eta2, m.burger_valpha) 

return (z, m.vp, m.vs, m.rho, m.qp, m.qs) 

 

last = None 

lines = [] 

for element in self.elements(): 

if isinstance(element, Layer): 

if not isinstance(last, Layer): 

lines.append(fmt(element.ztop, element.mtop)) 

 

lines.append(fmt(element.zbot, element.mbot)) 

 

last = element 

 

if not isinstance(last, Layer): 

lines.append(fmt(last.z, last.mbelow)) 

 

return lines 

 

def iter_material_parameter(self, get): 

assert get in ('vp', 'vs', 'rho', 'qp', 'qs', 'z') 

if get == 'z': 

for layer in self.layers(): 

yield layer.ztop 

yield layer.zbot 

else: 

getter = operator.attrgetter(get) 

for layer in self.layers(): 

yield getter(layer.mtop) 

yield getter(layer.mbot) 

 

def profile(self, get): 

''' 

Get parameter profile along depth of the earthmodel. 

 

:param get: property to be queried ( 

``'vp'``, ``'vs'``, ``'rho'``, ``'qp'``, or ``'qs'``, or ``'z'``) 

:type get: string 

''' 

 

return num.array(list(self.iter_material_parameter(get))) 

 

def min(self, get='vp'): 

''' 

Find minimum value of a material property or depth. 

 

:param get: property to be queried ( 

``'vp'``, ``'vs'``, ``'rho'``, ``'qp'``, or ``'qs'``, or ``'z'``) 

''' 

 

return min(self.iter_material_parameter(get)) 

 

def max(self, get='vp'): 

''' 

Find maximum value of a material property or depth. 

 

:param get: property to be queried ( 

``'vp'``, ``'vs'``, ``'rho'``, ``'qp'``, ``'qs'``, or ``'z'``) 

''' 

 

return max(self.iter_material_parameter(get)) 

 

def simplify_layers(self, layers, max_rel_error=0.001): 

if len(layers) <= 1: 

return layers 

 

ztop = layers[0].ztop 

zbot = layers[-1].zbot 

zorigs = [l.ztop for l in layers] 

zorigs.append(zbot) 

zs = num.linspace(ztop, zbot, 100) 

data = [] 

for z in zs: 

if z == ztop: 

direction = UP 

else: 

direction = DOWN 

 

mat = self.material(z, direction) 

data.append(mat.astuple()) 

 

data = num.array(data, dtype=num.float) 

data_means = num.mean(data, axis=0) 

nmax = len(layers) // 2 

accept = False 

 

zcut_best = [] 

for n in range(1, nmax+1): 

ncutintervals = 20 

zdelta = (zbot-ztop)/ncutintervals 

if n == 2: 

zcuts = [ 

[ztop, ztop + i*zdelta, zbot] 

for i in range(1, ncutintervals)] 

elif n == 3: 

zcuts = [] 

for j in range(1, ncutintervals): 

for i in range(j+1, ncutintervals): 

zcuts.append( 

[ztop, ztop + j*zdelta, ztop + i*zdelta, zbot]) 

else: 

zcuts = [] 

zcuts.append(num.linspace(ztop, zbot, n+1)) 

if zcut_best: 

zcuts.append(sorted(num.linspace( 

ztop, zbot, n).tolist() + zcut_best[1])) 

zcuts.append(sorted(num.linspace( 

ztop, zbot, n-1).tolist() + zcut_best[2])) 

 

best = None 

for icut, zcut in enumerate(zcuts): 

rel_par_errors = num.zeros(5) 

mpar_nodes = num.zeros((n+1, 5)) 

 

for ipar in range(5): 

znodes, vnodes, error_rms = util.polylinefit( 

zs, data[:, ipar], zcut) 

 

mpar_nodes[:, ipar] = vnodes 

if data_means[ipar] == 0.0: 

rel_par_errors[ipar] = -1 

else: 

rel_par_errors[ipar] = error_rms/data_means[ipar] 

 

rel_error = rel_par_errors.max() 

if best is None or rel_error < best[0]: 

best = (rel_error, zcut, mpar_nodes) 

 

rel_error, zcut, mpar_nodes = best 

 

zcut_best.append(list(zcut)) 

zcut_best[-1].pop(0) 

zcut_best[-1].pop() 

 

if rel_error <= max_rel_error: 

accept = True 

break 

 

if not accept: 

return layers 

 

rel_error, zcut, mpar_nodes = best 

 

material_nodes = [] 

for i in range(n+1): 

material_nodes.append(Material(*mpar_nodes[i, :])) 

 

out_layers = [] 

for i in range(n): 

mtop = material_nodes[i] 

mbot = material_nodes[i+1] 

ztop = zcut[i] 

zbot = zcut[i+1] 

if mtop == mbot: 

lyr = HomogeneousLayer(ztop, zbot, mtop) 

else: 

lyr = GradientLayer(ztop, zbot, mtop, mbot) 

 

out_layers.append(lyr) 

return out_layers 

 

def simplify(self, max_rel_error=0.001): 

'''Get representation of model with lower resolution. 

 

Returns an approximation of the model. All discontinuities are kept, 

but layer stacks with continuous model parameters are represented, if 

possible, by a lower number of layers. Piecewise linear functions are 

fitted against the original model parameter's piecewise linear 

functions. Successively larger numbers of layers are tried, until the 

difference to the original model is below ``max_rel_error``. The 

difference is measured as the RMS error of the fit normalized by the 

mean of the input (i.e. the fitted curves should deviate, on average, 

less than 0.1% from the input curves if ``max_rel_error`` = 0.001).''' 

 

mod_simple = LayeredModel() 

 

glayers = [] 

for element in self.elements(): 

 

if isinstance(element, Discontinuity): 

for l in self.simplify_layers( 

glayers, max_rel_error=max_rel_error): 

 

mod_simple.append(l) 

 

glayers = [] 

mod_simple.append(element) 

else: 

glayers.append(element) 

 

for l in self.simplify_layers(glayers, max_rel_error=max_rel_error): 

mod_simple.append(l) 

 

return mod_simple 

 

def extract(self, depth_min=None, depth_max=None): 

'''Extract :py:class:`LayeredModel` from :py:class:`LayeredModel`. 

 

:param depth_min: depth of upper cut or name of :py:class:`Interface` 

:param depth_max: depth of lower cut or name of :py:class:`Interface` 

 

Interpolates a :py:class:`GradientLayer` at ``depth_min`` and/or 

``depth_max``.''' 

 

if isinstance(depth_min, (str, newstr)): 

depth_min = self.discontinuity(depth_min).z 

 

if isinstance(depth_max, (str, newstr)): 

depth_max = self.discontinuity(depth_max).z 

 

mod_extracted = LayeredModel() 

 

for element in self.elements(): 

element = element.copy() 

do_append = False 

if (depth_min is None or depth_min <= element.ztop) \ 

and (depth_max is None or depth_max >= element.zbot): 

mod_extracted.append(element) 

continue 

 

if depth_min is not None: 

if element.ztop < depth_min and depth_min < element.zbot: 

_, element = element.split(depth_min) 

do_append = True 

 

if depth_max is not None: 

if element.zbot > depth_max and depth_max > element.ztop: 

element, _ = element.split(depth_max) 

do_append = True 

 

if do_append: 

mod_extracted.append(element) 

 

return mod_extracted 

 

def replaced_crust(self, crust2_profile=None, crustmod=None): 

if crust2_profile is not None: 

profile = anything_to_crust2_profile(crust2_profile) 

crustmod = LayeredModel.from_scanlines( 

from_crust2x2_profile(profile)) 

 

newmod = LayeredModel() 

for element in crustmod.extract(depth_max='moho').elements(): 

if element.name != 'moho': 

newmod.append(element) 

else: 

moho1 = element 

 

mod = self.extract(depth_min='moho') 

first = True 

for element in mod.elements(): 

if element.name == 'moho': 

if element.z <= moho1.z: 

mbelow = mod.material(moho1.z, direction=UP) 

else: 

mbelow = element.mbelow 

 

moho = Interface(moho1.z, moho1.mabove, mbelow, name='moho') 

newmod.append(moho) 

else: 

if first: 

if isinstance(element, Layer) and element.zbot > moho.z: 

newmod.append(GradientLayer( 

moho.z, 

element.zbot, 

moho.mbelow, 

element.mbot, 

name=element.name)) 

 

first = False 

else: 

newmod.append(element) 

return newmod 

 

def perturb(self, rstate=None, keep_vp_vs=False, **kwargs): 

''' 

Create a perturbed variant of the earth model. 

 

Randomly change the thickness and material parameters of the earth 

model from a uniform distribution. 

 

:param kwargs: Maximum change fraction (e.g. 0.1) of the parameters. 

Name the parameter, prefixed by ``p``. Supported parameters are 

``ph, pvp, pvs, prho, pqs, pqp``. 

:type kwargs: dict 

:param rstate: Random state to draw from, defaults to ``None`` 

:type rstate: :class:`numpy.random.RandomState`, optional 

:param keep_vp_vs: Keep the Vp/Vs ratio, defaults to False 

:type keep_vp_vs: bool, optional 

 

:returns: A new, perturbed earth model 

:rtype: :class:`~pyrocko.cake.LayeredModel` 

 

.. code-block :: python 

 

perturbed_model = model.perturb(ph=.1, pvp=.05, prho=.1) 

''' 

_pargs = set(['ph', 'pvp', 'pvs', 'prho', 'pqs', 'pqp']) 

earthmod = copy.deepcopy(self) 

 

if rstate is None: 

rstate = num.random.RandomState() 

 

layers = earthmod.layers() 

discont = earthmod.discontinuities() 

prev_layer = None 

 

def get_change_ratios(): 

values = dict.fromkeys([p[1:] for p in _pargs], 0.) 

 

for param, pval in kwargs.items(): 

if param not in _pargs: 

continue 

values[param[1:]] = float(rstate.uniform(-pval, pval, size=1)) 

return values 

 

# skip Surface 

while True: 

disc = next(discont) 

if isinstance(disc, Surface): 

break 

 

while True: 

try: 

layer = next(layers) 

m = layer.material(None) 

h = layer.zbot - layer.ztop 

except StopIteration: 

break 

 

if not isinstance(layer, HomogeneousLayer): 

raise NotImplementedError( 

'Can only perturbate homogeneous layers!') 

 

changes = get_change_ratios() 

 

# Changing thickness 

dh = h * changes['h'] 

changes['h'] = dh 

 

layer.resize(depth_max=layer.zbot + dh, 

depth_min=prev_layer.zbot if prev_layer else None) 

 

try: 

disc = next(discont) 

disc.change_depth(disc.z + dh) 

except StopIteration: 

pass 

 

# Setting material parameters 

for param, change_ratio in changes.items(): 

if param == 'h': 

continue 

 

value = m.__getattribute__(param) 

changes[param] = value * change_ratio 

 

if keep_vp_vs and changes['vp'] != 0.: 

changes['vs'] = (m.vp + changes['vp']) / m.vp_vs_ratio() - m.vs 

 

for param, change in changes.items(): 

if param == 'h': 

continue 

value = m.__getattribute__(param) 

m.__setattr__(param, value + change) 

 

logger.info( 

'perturbating earthmodel: {}'.format( 

' '.join(['{param}: {change:{len}.2f}'.format( 

param=p, change=c, len=8) 

for p, c in changes.items()]))) 

 

prev_layer = layer 

 

return earthmod 

 

def require_homogeneous(self): 

elements = list(self.elements()) 

 

if len(elements) != 2: 

raise LayeredModelError('More than one layer in earthmodel') 

if not isinstance(elements[1], HomogeneousLayer): 

raise LayeredModelError('Layer has to be a HomogeneousLayer') 

 

return elements[1].m 

 

def __str__(self): 

return '\n'.join(str(element) for element in self._elements) 

 

 

def read_hyposat_model(fn): 

'''Reader for HYPOSAT earth model files. 

 

To be used as producer in :py:meth:`LayeredModel.from_scanlines`. 

 

Interface names are translated as follows: ``'MOHO'`` -> ``'moho'``, 

``'CONR'`` -> ``'conrad'`` 

''' 

 

with open(fn, 'r') as f: 

translate = {'MOHO': 'moho', 'CONR': 'conrad'} 

lname = None 

for iline, line in enumerate(f): 

if iline == 0: 

continue 

 

z, vp, vs, name = util.unpack_fixed('f10, f10, f10, a4', line) 

if not name: 

name = None 

material = Material(vp*1000., vs*1000.) 

 

tname = translate.get(lname, lname) 

yield z*1000., material, tname 

 

lname = name 

 

 

def read_nd_model(fn): 

'''Reader for TauP style '.nd' (named discontinuity) files. 

 

To be used as producer in :py:meth:`LayeredModel.from_scanlines`. 

 

Interface names are translated as follows: ``'mantle'`` -> ``'moho'``, 

``'outer-core'`` -> ``'cmb'``, ``'inner-core'`` -> ``'icb'``. 

 

The format has been modified to include Burgers materials parameters in 

columns 7 (burger_eta1), 8 (burger_eta2) and 9. eta(3). 

''' 

with open(fn, 'r') as f: 

for x in read_nd_model_fh(f): 

yield x 

 

 

def read_nd_model_str(s): 

f = StringIO(s) 

for x in read_nd_model_fh(f): 

yield x 

f.close() 

 

 

def read_nd_model_fh(f): 

translate = {'mantle': 'moho', 'outer-core': 'cmb', 'inner-core': 'icb'} 

name = None 

for line in f: 

toks = line.split() 

if len(toks) == 9 or len(toks) == 6 or len(toks) == 4: 

z, vp, vs, rho = [float(x) for x in toks[:4]] 

qp, qs = None, None 

burgers = None 

if len(toks) == 6 or len(toks) == 9: 

qp, qs = [float(x) for x in toks[4:6]] 

if len(toks) == 9: 

burgers = \ 

[float(x) for x in toks[6:]] 

 

material = Material( 

vp*1000., vs*1000., rho*1000., qp, qs, 

burgers=burgers) 

 

yield z*1000., material, name 

name = None 

elif len(toks) == 1: 

name = translate.get(toks[0], toks[0]) 

 

f.close() 

 

 

def from_crust2x2_profile(profile, depthmantle=50000): 

from pyrocko.dataset import crust2x2 

 

default_qp_qs = { 

'soft sed.': (50., 50.), 

'hard sed.': (200., 200.), 

'upper crust': (600., 400.), 

} 

 

z = 0. 

for i in range(8): 

dz, vp, vs, rho = profile.get_layer(i) 

name = crust2x2.Crust2Profile.layer_names[i] 

if name in default_qp_qs: 

qp, qs = default_qp_qs[name] 

else: 

qp, qs = None, None 

 

material = Material(vp, vs, rho, qp, qs) 

iname = None 

if i == 7: 

iname = 'moho' 

if dz != 0.0: 

yield z, material, iname 

if i != 7: 

yield z+dz, material, name 

else: 

yield z+depthmantle, material, name 

 

z += dz 

 

 

def write_nd_model_fh(mod, fh): 

def fmt(z, mat): 

rstr = ' '.join( 

util.gform(x, 4) 

for x in ( 

z/1000., 

mat.vp/1000., 

mat.vs/1000., 

mat.rho/1000., 

mat.qp, mat.qs)) 

if not mat._has_default_burgers(): 

rstr += ' '.join( 

util.gform(x, 4) 

for x in ( 

mat.burger_eta1, 

mat.burger_eta2, 

mat.burger_valpha)) 

return rstr.rstrip() + '\n' 

 

translate = { 

'moho': 'mantle', 

'cmb': 'outer-core', 

'icb': 'inner-core'} 

 

last = None 

for element in mod.elements(): 

if isinstance(element, Interface): 

if element.name is not None: 

n = translate.get(element.name, element.name) 

fh.write('%s\n' % n) 

 

elif isinstance(element, Layer): 

if not isinstance(last, Layer): 

fh.write(fmt(element.ztop, element.mtop)) 

 

fh.write(fmt(element.zbot, element.mbot)) 

 

last = element 

 

if not isinstance(last, Layer): 

fh.write(fmt(last.z, last.mbelow)) 

 

 

def write_nd_model_str(mod): 

f = StringIO() 

write_nd_model_fh(mod, f) 

return f.getvalue() 

 

 

def write_nd_model(mod, fn): 

with open(fn, 'w') as f: 

write_nd_model_fh(mod, f) 

 

 

def builtin_models(): 

return sorted([ 

os.path.splitext(os.path.basename(x))[0] 

for x in glob.glob(builtin_model_filename('*'))]) 

 

 

def builtin_model_filename(modelname): 

return util.data_file(os.path.join('earthmodels', modelname+'.nd')) 

 

 

def load_model(fn='ak135-f-continental.m', format='nd', crust2_profile=None): 

'''Load layered earth model from file. 

 

:param fn: filename 

:param format: format 

:param crust2_profile: ``(lat, lon)`` or 

:py:class:`pyrocko.crust2x2.Crust2Profile` object, merge model with 

crustal profile. If ``fn`` is forced to be ``None`` only the converted 

CRUST2.0 profile is returned. 

:returns: object of type :py:class:`LayeredModel` 

 

The following formats are currently supported: 

 

============== =========================================================== 

format description 

============== =========================================================== 

``'nd'`` 'named discontinuity' format used by the TauP programs 

``'hyposat'`` format used by the HYPOSAT location program 

============== =========================================================== 

 

The naming of interfaces is translated from the file format's native naming 

to Cake's own convention (See :py:func:`read_nd_model` and 

:py:func:`read_hyposat_model` for details). Cake likes the following 

internal names: ``'conrad'``, ``'moho'``, ``'cmb'`` (core-mantle boundary), 

``'icb'`` (inner core boundary). 

''' 

 

if fn is not None: 

if format == 'nd': 

if not os.path.exists(fn) and fn in builtin_models(): 

fn = builtin_model_filename(fn) 

reader = read_nd_model(fn) 

elif format == 'hyposat': 

reader = read_hyposat_model(fn) 

else: 

assert False, 'unsupported model format' 

 

mod = LayeredModel.from_scanlines(reader) 

if crust2_profile is not None: 

return mod.replaced_crust(crust2_profile) 

 

return mod 

 

else: 

assert crust2_profile is not None 

profile = anything_to_crust2_profile(crust2_profile) 

return LayeredModel.from_scanlines( 

from_crust2x2_profile(profile)) 

 

 

def castagna_vs_to_vp(vs): 

'''Calculate vp from vs using castagna's relation. 

 

Castagna's relation (the mudrock line) is an empirical relation for vp/vs 

for siliciclastic rocks (i.e. sandstones and shales). [Castagna et al., 

1985] 

 

vp = 1.16 * vs + 1360 [m/s] 

 

:param vs: S-wave velocity [m/s] 

:returns: P-wave velocity [m/s] 

''' 

 

return vs*1.16 + 1360.0 

 

 

def castagna_vp_to_vs(vp): 

'''Calculate vp from vs using castagna's relation. 

 

Castagna's relation (the mudrock line) is an empirical relation for vp/vs 

for siliciclastic rocks (i.e. sandstones and shales). [Castagna et al., 

1985] 

 

vp = 1.16 * vs + 1360 [m/s] 

 

:param vp: P-wave velocity [m/s] 

:returns: S-wave velocity [m/s] 

''' 

 

return (vp - 1360.0) / 1.16 

 

 

def evenize(x, y, minsize=10): 

if x.size < minsize: 

return x 

ry = (y.max()-y.min()) 

if ry == 0: 

return x 

dx = (x[1:] - x[:-1])/(x.max()-x.min()) 

dy = (y[1:] + y[:-1])/ry 

 

s = num.zeros(x.size) 

s[1:] = num.cumsum(num.sqrt(dy**2 + dx**2)) 

s2 = num.linspace(0, s[-1], x.size) 

x2 = num.interp(s2, s, x) 

x2[0] = x[0] 

x2[-1] = x[-1] 

return x2 

 

 

def filled(v, *args, **kwargs): 

''' 

Create NumPy array filled with given value. 

 

This works like :py:func:`numpy.ones` but initializes the array with ``v`` 

instead of ones. 

''' 

x = num.empty(*args, **kwargs) 

x.fill(v) 

return x 

 

 

def next_or_none(i): 

try: 

return next(i) 

except StopIteration: 

return None 

 

 

def reci_or_none(x): 

try: 

return 1./x 

except ZeroDivisionError: 

return None 

 

 

def mult_or_none(a, b): 

if a is None or b is None: 

return None 

return a*b 

 

 

def min_not_none(a, b): 

if a is None: 

return b 

if b is None: 

return a 

return min(a, b) 

 

 

def xytups(xx, yy): 

d = [] 

for x, y in zip(xx, yy): 

if num.isfinite(y): 

d.append((x, y)) 

return d 

 

 

def interp(x, xp, fp, monoton): 

if monoton == 1: 

return xytups( 

x, num.interp(x, xp, fp, left=num.nan, right=num.nan)) 

elif monoton == -1: 

return xytups( 

x, num.interp(x, xp[::-1], fp[::-1], left=num.nan, right=num.nan)) 

else: 

fs = [] 

for xv in x: 

indices = num.where(num.logical_or( 

num.logical_and(xp[:-1] >= xv, xv > xp[1:]), 

num.logical_and(xp[:-1] <= xv, xv < xp[1:])))[0] 

 

for i in indices: 

xr = (xv - xp[i])/(xp[i+1]-xp[i]) 

fv = xr*fp[i] + (1.-xr)*fp[i+1] 

fs.append((xv, fv)) 

 

return fs 

 

 

def float_or_none(x): 

if x is not None: 

return float(x) 

 

 

def parstore_float(thelocals, obj, *args): 

for k, v in thelocals.items(): 

if k != 'self' and (not args or k in args): 

setattr(obj, k, float_or_none(v))