Centroid moment tensor from W-phase observations

This step-by-step guide explains how to obtain a probabilistic W-phase centroid moment tensor (CMT) solution for the Mw 8.2 2015 Illapel (Chile) earthquake using Grond.

Setup

To repeat this exercise on your machine, you should first install Pyrocko and Grond (see Installation), if you have not already done so. Then create the example project with:

grond init example_wphase grond-playground-wphase/

The project folder

The project folder now contains a configuration file for Grond, some utility scripts to download pre-calculated Green’s functions and to download seismic waveforms from public data centres.

grond-playground-wphase        # project folder
├── bin                        # directory with scripts
│   ├── download_gf_stores.sh  # download pre-calculated Green's functions
│   ├── grondown               # a simple event-based waveform downloader
│   └── grondown_wphase.sh     # downloader configured for this exercise
└── config                     # directory for configuration files
    └── wphase_cmt.gronf       # Grond configuration file for this exercise

Green’s function download

To download the pre-calculated Green’s functions needed in this exercise, run

bin/download_gf_stores.sh

When the command succeeds, you should have a new subdirectory gf_stores in your project folder:

gf_stores
└── global_20s_shallow/... # Green's function store

It contains a Pyrocko Green’s function store, named global_20s_shallow, which has been created using the Fomosto tool of Pyrocko and the modelling code QSSP. The Green’s functions in this store have been calculated for the global ak135-f-continental earth model for a source depths between 0 and 100 km in 4 km steps. It is sampled at 0.05 Hz, which is sufficient for our target frequency range of 0.001 - 0.005 Hz.

Seismic waveform data download

A preconfigured script is provided to download seismic waveform recordings via FDSN web services from the IRIS, GEOFON, and ORFEUS datacenters. Just run it with the GEOFON event ID of the study earthquake. The GEOFON event ID of the great Illapel (Chile) earthquake is gfz2015sfdd (you can find the ID in the GEOFON catalog event links).

To download the seismic waveform data, now run:

bin/grondown_wphase.sh gfz2015sfdd

This shell script calls the data downloader bin/grondown with parameters appropriate to get a dataset of broadband seismometer recordings, sufficient for a W-phase CMT optimisation. It performs the following steps for us:

  • Query the GEOFON catalog for event information about gfz2015sfdd.

  • Select time windows based on event origin and time, considering that we want to analyse the signals at very low frequencies (0.001 - 0.005 Hz).

  • Query data centres for seismic stations with epicentral distance between 3000 and 11000 km.

  • Select a small set of stations (N=40) providing a good coverage in azimuth and distance.

  • From the available recorder channels select appropriate ones for a target sampling rate of 1 Hz.

  • Download raw waveform data for the selected stations and channels.

  • Download instrument transfer function meta-information for all successfully downloaded waveform data.

  • Calculate displacement seismograms for quality check (Grond will use the raw data). If all went well, the displacement seismograms should be valid in the frequency range 0.01 - 0.05 Hz, sampled at 1 Hz and rotated to radial, transverse, and vertical components. The rotation to radial and transverse components is with respect to the event coordinates from the GEOFON catalogue.

After running the download script, the playground directory should contain a new data directory with the following content:

data
└── events
    └── gfz2015sfdd
        ├── event.txt                 # catalogue information about the event
        └── waveforms
            ├── grondown.command
            ├── prepared/...          # rotated, displacement waveforms
            ├── raw/...               # raw Mini-SEED waveforms
            ├── rest/...
            ├── stations.geofon.xml   # instrument response information
            ├── stations.iris.xml
            ├── stations.orfeus.xml
            ├── stations.prepared.txt # stations files for Snuffler
            └── stations.raw.txt

Because of various data problems, like missing instrument response information, gappy traces, data inconsistencies and what not, only about half of the initially requested stations will be useful in the optimisation. Some problems are not detected by the downloader, so we will have to look at the seismograms.

Data screening

For a quick visual inspection of the dataset, we can use the Snuffler program contained in Pyrocko.

cd data/events/gfz2015sfdd/waveforms
snuffler --event=../event.txt --stations=stations.prepared.txt prepared
cd -  # change to previous folder

Figure 1 shows our view after some interactive adjustments in Snuffler. In particular, we may want to

  • sort the traces according to epicentral distance (Menu → check Sort by Distance).

  • configure display style (Menu → uncheck Show Boxes, check Common Scale per Station, uncheck Clip Traces).

  • filter between 0.001 and 0.01 Hz.

  • add markers for expected P and S phase arrivals, (Menu → Panels → Cake Phase (builtin)).

  • hide noisy stations: Command ‣ hide s h09n1 p061 aulhs pnps odz.

  • show only vertical components: Command ‣ c *z.

  • increase the gain factor until the W-phase becomes visible between the P and the S phase arrivals.

../../_images/example_snuffler-gfz2015sfdd.svg

Figure 1: Displacement seismograms for W-phase CMT optimisation as viewed in the waveform browser Snuffler.

Grond configuration

The project folder already contains a configuration file for W-phase CMT optimisation with Grond, so let’s have a look at it. It is a YAML file. If you have never heard about this file format, read section Configuration file structure and format (YAML) for an overview.

config/wphase_cmt.gronf (in project folder)
%YAML 1.1
# Example: Inversion of W-Phase from teleseismic observations.
--- !grond.Config

# All file paths referenced below are treated relative to the location of this
# configuration file, here we may give a common prefix. E.g. setting it to '..'
# if the configuration file is in the sub-directory '${project_root}/config'
# allows us to give the paths below relative to '${project_root}'.
path_prefix: '..'

# Path, where to store output (run directories). The placeholder
# '${problem_name}' will be expanded to a name configured below in
# problem_config.name_template and will typically include a config identifier
# and the event name.
rundir_template: 'runs/${problem_name}.grun'

# If given, restrict to processing of listed events
#event_names:
#- 'gfz2015sfdd'


# -----------------------------------------------------------------------------
# Configuration section for dataset (input data)
#
# The placeholder '${event_name}' will be expanded to the current event. This
# enables us to use the same configuration for multiple events. The available 
# events are detected by looking into possible expansions of
# dataset_config.events_path
# -----------------------------------------------------------------------------

dataset_config: !grond.DatasetConfig

  # List of files with station coordinates.
  stations_stationxml_paths: 
  - 'data/events/${event_name}/waveforms/stations.geofon.xml'
  - 'data/events/${event_name}/waveforms/stations.iris.xml'
  - 'data/events/${event_name}/waveforms/stations.orfeus.xml'

  # File with hypocenter information and possibly reference solution
  events_path: 'data/events/${event_name}/event.txt'

  # List of directories with raw waveform data
  waveform_paths: ['data/events/${event_name}/waveforms/raw']

  # List of stations/components to be excluded according to their STA, NET.STA,
  # NET.STA.LOC, or NET.STA.LOC.CHA codes
  blacklist: []

  # List of files with additional exclusion lists (one entry per line, same 
  # format as above)
  blacklist_paths:
  - 'data/events/${event_name}/waveforms/blacklist.txt'

  # List of files with instrument response information (can be the same as in
  # stations_stationxml_paths above)
  responses_stationxml_paths:
  - 'data/events/${event_name}/waveforms/stations.geofon.xml'
  - 'data/events/${event_name}/waveforms/stations.iris.xml'
  - 'data/events/${event_name}/waveforms/stations.orfeus.xml'


# -----------------------------------------------------------------------------
# Configuration section for the observational data fitting
#
# This defines the objective function to be minimized in the optimisation. It
# can be composed of one or more contributions, each represented by a
# !grond.*TargetGroup section.
# -----------------------------------------------------------------------------

target_groups:

- !grond.WaveformTargetGroup

  # Normalisation family (see the Grond documentation for how it works).
  # Use distinct normalisation families when mixing misfit contributors with
  # different magnitude scaling, like e.g. cross-correlation based misfit and 
  # time-domain Lx norm.
  normalisation_family: 'td'

  # Just a name used to identfy targets from this group. Use dot-separated path
  # notation to group related contributors
  path: 'td.wphase'

  # Epicentral distance range of stations to be considered
  distance_min: 3000e3
  distance_max: 10000e3

  # Names of components to be included. Available: N=north, E=east, Z=vertical
  # (up), R=radial (away), T=transverse (right)
  channels: ['Z','R']

  # How to weight contributions from this group in the global misfit
  weight: 1.0

  # subsection on how to fit the traces
  misfit_config: !grond.WaveformMisfitConfig

    # Frequency band [Hz] of acausal filter (flat part of frequency taper)
    fmin: 0.001
    fmax: 0.005

    # Factor defining fall-off of frequency taper (zero at fmin/ffactor and
    # fmax*ffactor)
    ffactor: 1.5

    # Time window to include in the data fitting. Times can be defined offset
    # to given phase arrivals. E.g. '{stored:P}-600' would mean 600 s
    # before arrival of the phase named 'P'. The phase must be defined in the
    # travel time tables in the GF store.
    tmin: '{stored:P}-600'
    tmax: '{stored:S}-60'
    # tfade: 120.0

    # How to fit the data (available: 'time_domain', 'frequency_domain',
    # 'log_frequency_domain', 'absolute', 'envelope', 'cc_max_norm')
    domain: 'time_domain'
    
    # For L1 norm: 1, L2 norm: 2, etc.
    norm_exponent: 1

  # How to interpolate the Green's functions (available choices:
  # 'nearest_neighbor', 'multilinear'). Choices other than 'nearest_neighbor'
  # may require dense GF stores to avoid aliasing artifacts in the forward 
  # modelling.
  interpolation: 'nearest_neighbor'

  # Name of the GF Store to use
  store_id: 'global_20s_shallow'


# -----------------------------------------------------------------------------
# Definition of the problem to be solved
#
# In this section the source model to be fitted is chosen, the parameter space
# defined, and how to combine the misfit contributions defined in the
# target_groups section above.
# 
# The marker !grond.CMTProblemConfig selects a centroid moment tensor source
# model. 
# -----------------------------------------------------------------------------

problem_config: !grond.CMTProblemConfig

  # Name used to identify the output
  name_template: 'wphase_cmt_${event_name}'

  # Definition of model parameter space to be searched in the optimisation
  ranges:
    # Time relative to hypocenter origin time [s]
    time: '-100 .. 100 | add'

    # Centroid location with respect to hypocenter origin [m]
    north_shift: '-200e3 .. 200e3'
    east_shift: '-200e3 .. 200e3'
    depth: '5e3 .. 40e3'

    # Range of magnitudes to allow
    magnitude: '7.5 .. 8.5'

    # Relative moment tensor component ranges (don't touch)
    rmnn: '-1.41421 .. 1.41421'
    rmee: '-1.41421 .. 1.41421'
    rmdd: '-1.41421 .. 1.41421'
    rmne: '-1 .. 1'
    rmnd: '-1 .. 1'
    rmed: '-1 .. 1'

    # Source duration range [s]
    duration: '50. .. 200.'

  # Clearance distance around stations (no models with origin closer than this
  # distance to any station are produced by the sampler)
  distance_min: 0.

  # Type of moment tensor to restrict to (choices: 'full', 'deviatoric', 'dc')
  mt_type: 'deviatoric'

  # How to combine the target misfits. For L1 norm: 1, L2 norm: 2, etc.
  norm_exponent: 1


# -----------------------------------------------------------------------------
# Configuration of pre-optimisation analysis phases. 
# determined during this phase.
# -----------------------------------------------------------------------------
#
analyser_configs:

# Balancing weights are determined with this analyser
- !grond.TargetBalancingAnalyserConfig

  # Number of models to forward model in the analysis, larger number -> better
  # statistics)
  niterations: 1000

# -----------------------------------------------------------------------------
# Configuration of the optimisation procedure
# -----------------------------------------------------------------------------

optimiser_config: !grond.HighScoreOptimiserConfig

  # Number of bootstrap realisations to be tracked simultaneously in the
  # optimisation
  nbootstrap: 100

  # stages of the sampler. Start with uniform sampling of the model space
  # (!grond.UniformSamplerPhase), then narrow down to the interesting regions
  # (!grond.DirectedSamplerPhase).
  sampler_phases:

  - !grond.UniformSamplerPhase

      # Number of iterations
      niterations: 1000

  - !grond.DirectedSamplerPhase

      # Number of iterations
      niterations: 20000

      # Multiplicator for width of sampler distribution at start of this phase
      scatter_scale_begin: 2.0

      # Multiplicator for width of sampler distribution at end of this phase
      scatter_scale_end: 0.5


# -----------------------------------------------------------------------------
# Configuration section for synthetic seismogram engine
#
# Configures where to look for GF stores.
# -----------------------------------------------------------------------------

engine_config: !grond.EngineConfig

  # Whether to use GF store directories listed in ~/.pyrocko/config.pf
  gf_stores_from_pyrocko_config: false

  # List of directories with GF stores
  gf_store_superdirs: ['gf_stores']

Checking the optimisation setup

Before running the actual optimisation, we can now use the command

grond check config/wphase_cmt.gronf gfz2015sfdd

to run some sanity checks. In particular, Grond will try to run a few forward models to see if the modelling works and if it can read the input data. If only one event is available, we can also neglect the event name argument in this and other Grond commands.

To get some more insight into the setup, we can now run

grond report -so config/wphase_cmt.gronf gfz2015sfdd

This will plot some diagnostic figures, create web pages in a new directory report, and finally open these in a web browser.

Starting the optimisation

Let’s start the optimisation with:

grond go config/wphase_cmt.gronf

During the optimisation a status monitor will show the optimisation’s progress.

../../_images/example_grond-run-insar.png

Figure 2: Runtime information given by grond go.

Depending on the configured number of iterations and the computer’s hardware the optimisation will run several minutes to hours.

Optimisation report

Once the optimisation is finished we can generate and open the final report with:

grond report -so runs/wphase_cmt_gfz2015sfdd.grun

Example report

Explore the online example reports to see what information the inversion reveals.