Input Waveform Data

Waveform data are provided to the moment tensor modules for inversion in time windows which depend on considered phase type and epicentral distance. The data source is configured through the RecordStream interface. It typically considers local or remote waveform archives or servers or miniSEED files. When fetching the data stations with epicentral distance up to automt.maximumDistance are considered. The data processing is described in section Algorithms.

Green’s functions

The waveforms are compared with synthetic seismograms, the Green’s functions. The sampling rate of the Green’s functions is used to resample the observed waveform data.

The computation of the Green’s functions follows notations in the publication by Minson and Dreger [10]. The Green’s functions can be calculated using available programs for calculating full waveforms in 1D heterogeneous media. Alternatively, gempa GmbH may be contacted for providing the Green’s functions.

Green’s functions are a set of pre computed waveforms for three fundamental sources representing a deviatoric point source: vertical strike-slip (SS), vertical dip-slip (DS) and a dip-slip with 45° of dip (DD) or an isotropic source (EP).

A set of Green’s functions is computed for a particular distance and depth. Each set pf Green’s function consists of at least 8 components: ZSS, ZDS, ZDD, RSS, RDS, RDD, TSS and TDS where Z, R and T refer to the vertical, radial and tangential components. For computing the full moment tensor, 2 additional components are required: REP, ZEP.

SeisComP supports by default two Green’s function formats:

  • sc3gf1d: SeisComP-native format for Green’s functions for 1D media, recommended format

  • Helmberger: An alternative format for 1D media.

sc3gf1d

File Format

This is the recommend format and structure for providing the Green’s functions following the notations in Minson and Dreger [10]. The sc3gf1d format stores the displacement in SAC files.

File and Directory Structure

The general file and directory structure contains

  • a description file ending on .desc and

  • actual Green’s functions as component files (all other files)

as follows:

[name].desc
[name]/[depth]/[dist]/[depth].[dist].ZSS
[name]/[depth]/[dist]/[depth].[dist].ZDD
[name]/[depth]/[dist]/[depth].[dist].ZDS
[name]/[depth]/[dist]/[depth].[dist].RSS
[name]/[depth]/[dist]/[depth].[dist].RDD
[name]/[depth]/[dist]/[depth].[dist].RDS
[name]/[depth]/[dist]/[depth].[dist].TSS
[name]/[depth]/[dist]/[depth].[dist].TDS
[name]/[depth]/[dist]/[depth].[dist].REP
[name]/[depth]/[dist]/[depth].[dist].ZEP

  • [name]: name of the set of Green’s functions which is provided. The set is located in the directory defined by

    Hint

    Multiple sets of Green’s functions can be provided and considered in scmtv but only one in scautomt.

  • [depth]: depths in units of 100m, format: (%4.4i)

  • [dist]: epicentral distance in units of kilometers, format: (%5.5i)

Each component file is a SAC record and the unit of the samples is expected to be in cm. The suffices indicate the components. Different sets are required for the inversion:

  • Inversion for deviatoric moment tensors (5 elements, tr(M)=0) requires 8 components:

    ZSS, ZDD, ZDS, RSS, RDD, RDS, TSS, TDS

  • Inversion for full moment tensors (6 elements) requires 10 components:

    ZSS, ZDD, ZDS, RSS, RDD, RDS, TSS, TDS, REP, ZEP

The description file name.desc contains a general description of the archive and an optional definition of the travel-time interface. In particular the available depths and distances. Units are kilometer.

# depth [from] [to] [step]
depth 10 30 2
depth 30 700 10
# distance [from] [to] [step]
distance 10 10000 10
# travel times
times LOCSAT iasp91_scanloc

In the example above the archive contains depth from 10km to 30 km in steps of 2 km and from 30 km to 700 km in steps of 10 km. Distances are stored from 10 km to 10000 km in steps of 10 km. The line starting with times specifies the travel-time interface and the profile considered for predicting arrival times. Both must exist. The predicted times are shown in the waveform window of scmtv and used for aligning measured waveforms with Green’s functions.

Note

The specification of the travel-time interface by the line starting with times is optional. If missing, libtau with iasp91 is considered.

Timing

Times of the Green’s functions are relative to source time. The source time is 01-JAN-1970 00:00:00. It must be considered for setting the start times in the SAC files when computing Green’s functions with leading samples or when considering reduced times. The start time t of the Green’s functions is then

\text{t} = \text{t}_0 - \text{t}_{lead} + \frac{\text{d}}{\text{v}},

where \text{t}_0: source time, \text{t}_{lead}: lead time, d: distance, v: reduction velocity.

While lead times may be useful to optimize later data processing, time reduction helps to reduce the time length of the computed Green’s functions. Typically, lead times of 200 s and no time reduction are applied to compute Green’s functions at 1 Hz sampling.

Alignment with observed waveforms

Initially, Green’s functions and observed waveforms are aligned in time based on configured times windows. When time windows are set relative to phase arrivals, e.g. by automt.profiles.$name.signalBegin.body.P and automt.profiles.$name.signalEnd.body.P, then measured pick times and phase arrival times prediced by travel-time interfaces are considered:

  • For Green’s functions, the arrival times are provided by the travel-time interface.

  • For measured waveforms the measured pick time is used. If the pick time is unavailable, the time is predicted by the travel-time interface.

The travel-time interface is defined through the description file in the Green’s functions directory. When selecting Green’s functions interactively in scmtv the travel-time interface is reloaded accordingly.

Configuration

Provide the type and the location of the Green’s functions by configuration:

  • scmtv: gfaUrls for the type and the location:

    gfaUrls = [type]://[location]
gfaUrls = sc3gf1d:///home/data/greensfunctions

  • scautomt: gfaUrl for the type and the location and automt.gfModel for the model name:

    gfaUrl = [type]://[location]
gfaUrl = sc3gf1d:///home/data/greensfunctions
automt.gfModel = gemini-prem

Helmberger

File Format

This format is a simple ASCII format where each depth/distance pair is stored in one file.

File and Directory Structure

The general directory layout looks like this:

name.depths
name.dists
name.vel
name/name[dist]d[depth].disp

The file name.depths contains the information about the available depths in km as a simple list, e.g.:

0002
0004
0006
0008
0010
0020
0030
0040
0050

The file name.dists contains all available distances in km per depth.

0020
0025
0030
0035
0040
0045
0050
0055
0060
0065
0070
0075
0080
0085
0090
0095
0100

Timing

The optional file name.vel defines the reduction velocity. The reduction velocity is used to cut the displacement traces (*.disp). If the file is not given a reduction velocity of 9 km/s is assumed. The reduction velocity v defines the start time t of the Green’s functions at distance d with respect to source time. It is used to compute the time stamp of the first displacement sample by dividing the distance with the velocity:

\text{t} = \frac{\text{d}}{\text{v}}

The file name.vel just contains one number which is the used reduction velocity in units of km/s.

File Format Description

Each Green’s function is stored according to the above naming convention in a separate ASCII file. The format is quite simple and contains 8 blocks for each component in the order: TSS, TDS, RSS, RDS, RDD, ZSS, ZDS and ZDD. The file starts with a two line header:

       8
(6e12.5)

The first line contains the number of components stored which must be 8 otherwise the file is not used by scautomt. The second line defines the format for each displacement sample in format ([n]e[w].[d]) where n is the number of samples per line, w the total width of a sample and d the number of digits. The format specifier ‘e’ stored each number with exponent of base 10.

After the initial two lines the block header starts:

 0.0000e+00     0.0000e+00      0  0  0.00
1024   1.00000  0.0000e+00

The first line is ignored and from the second line only the first two values are used specifying the number of samples in this block and the sampling time in seconds.

Then a block starts:

-0.00000e+00-4.20540e-10-8.70203e-10-1.12867e-09-1.39191e-09-1.46233e-09
-1.54311e-09-1.43806e-09-1.36765e-09-1.10546e-09-9.15074e-10-5.57482e-10
-3.14872e-10 5.65648e-11 2.74140e-10 6.01314e-10 7.13883e-10 9.43205e-10
...

All subsequent blocks follow with no seems (no empty lines). The unit of the displacement samples is cm.

Configuration

Provide the location of the Green’s functions by configuration o f gfaUrl as for type sc3gf1d but use helmberger for the type.