SURFACE WAVE SIMULATION AND PROCESSING WITH MATSEIS

Beverly D. Thompson, Eric P. Chael, Chris J. Young, William R. Walter1, and Michael E. Pasyanos1

Sandia National Laboratories and 1Lawrence Livermore National Laboratory

Sponsored by U.S. Department of Energy

Contract No. DE-AC04-94AL85000

ABSTRACT

In order to exploit the information on surface wave propagation that is stored in large seismic event datasets, Sandia
and Lawrence Livermore National Laboratories have developed a MatSeis interface for performing phase-matched
filtering of Rayleigh wave arrivals. MatSeis is a MATLAB-based seismic processing toolkit which provides graphical
tools for analyzing seismic data from a network of stations. Tools are available for spectral and polarization
measurements, as well as beam forming and f-k analysis with array data, to name just a few. Additionally, one has full
access to the MATLAB environment and any functions available there. Previously we reported the development of
new MatSeis tools for calculating regional discrimination measurements. The first of these performs Lg coda analysis
as developed by Mayeda and coworkers at Lawrence Livermore National Laboratory. A second tool measures
regional phase amplitude ratios for an event and compares the results to ratios from known earthquakes and
explosions.

Release 1.5 of MatSeis includes the new interface for the analysis of surface wave arrivals. This effort involves the
use of regionalized dispersion models from a repository of surface wave data and the construction of phase-matched
filters to improve surface wave identification, detection, and magnitude calculation. The tool works as follows. First,
a ray is traced from source to receiver through a user-defined grid containing different group velocity versus period
values to determine the composite group velocity curve for the path. This curve is shown along with the upper and
lower group velocity bounds for reference. Next, the curve is used to create a phase-matched filter, apply the filter,
and show the resultant waveform. The application of the filter allows obscured Rayleigh arrivals to be more easily
identified. Finally, after screening information outside the range of the phase-matched filter, an inverse version of the
filter is applied to obtain a cleaned “raw” waveform which can be used for amplitude measurements.

Because all the MatSeis tools have been written as MATLAB functions, they can be easily modified to experiment
with different processing details. The performance of the propagation models can be evaluated using any event
available in the repository of surface wave events.

Key Words : data processing, data analysis, surface waves

Though improved regional discriminants are desirable for identifying small seismic events, Ms:mb remains as a
preferred method when Rayleigh arrivals are recognizable. Phase-matched filtering (Herrin and Goforth, 1977) is a
well-established method for enhancing and extracting Rayleigh waves from records of located events. This technique
requires a reasonably accurate estimate of the Rayleigh dispersion along the path from event to station. Better
models of surface-wave propagation at global and regional scales are now available (eg, Stevens and Adams, 1999;
Pasyanos et al., 1999). These models have become sufficiently mature to enable the routine use of phase-matched
filtering, which should permit reliable Ms measurements down to lower magnitudes.

To facilitate surface-wave analysis and Ms estimation, we have added an interactive phase-matched filtering
capability to MatSeis, a seismic toolkit based on MATLAB. Graphical interfaces make the surface wave analysis
routines easier to use and accessible to a wider audience. The user can select among different surface-wave
propagation models to evaluate their appropriateness for an observed Rayleigh arrival. In addition, the inherent
flexibility and openness of MATLAB simplifies the process of developing and modifying the algorithms. MatSeis
provides connections to a repository of surface wave data so that phase-matched filtering can be performed for any
events and waveforms stored there.

BACKGROUND

The MatSeis seismic processing toolkit was originally developed at Sandia to support Comprehensive Test Ban
Treaty (CTBT) R&D on improving event association and location (Harris and Young, 1997). Through menus in the
MatSeis user interface, a researcher can connect to a repository of surface wave data and select events, arrivals and
waveforms for analysis. Once the desired data have been obtained, the waveforms can be displayed as a record
section for any event, with signals from the various stations organized vertically based on their epicentral distance
(Figure 1).

Selected travel-time curves may be overlaid on the plot, to assist in identifying phases. The package provides a wide
assortment of functions to help the user interpret the signals and hence characterize the event. A variety of filters can
be applied to the signals. Arrivals can be picked or retimed, then their amplitude and period may be measured. The
user may relocate the event using an interface to a location routine descended from TTAZLOC (Bratt and Bache,
1988), and display station and event positions on a map through a connection to the M_Map mapping toolbox
(Pawlowicz, 1998).

Modules are included for spectrum estimation, waveform correlation, polarization analysis, beamforming and
frequency-wavenumber analysis. MatSeis serves as a key tool for developing and testing the DOE Knowledge Base,
a system for storing and accessing region-specific information. Thus the analysis functions in MatSeis can exploit
the contents of the Knowledge Base for optimal performance in a given geographic area.

Written in the MATLAB language, MatSeis can be readily modified or extended to include new functionality, so it
serves as a convenient platform for prototyping new algorithms. Because of this inherent flexibility, and the access to
region-specific information in the DOE Knowledge Base, we believe that MatSeis provides a suitable environment for
analyzing long-period surface-wave arrivals as well. Previously we reported the development of MatSeis tools for
calculating regional discrimination measurements (Chael et al., 1999). The first of these performs Lg coda analysis as
developed by Mayeda and coworkers at Lawrence Livermore National Laboratory. The second measures amplitude
ratios among regional arrivals for an event and compares the results to those from known earthquakes and
explosions.
 Figure 1. MatSeis Main Window Display

RESEARCH ACCOMPLISHED

The current Release 1.5 of the MatSeis package includes new tools for the analysis of surface wave arrivals. These
routines can generate phase-matched filters for any desired path, given a 2D model of Rayleigh group velocity
distribution. So far we have incorporated a regionalized model of the whole earth (Stevens and Adams, 1999), a
tomographic model for the Middle East and North Africa (Pasyanos, 1999), as well as individual dispersion curves for
some specific paths from the Lop Nor (China) test site. For each frequency available in the chosen model, the travel
time over the great circle from source to receiver is determined by following the path through the model grid, and
looking up the tabulated group velocity for each cell traversed. The resulting path-average dispersion curve is
plotted along with the maximum and minimum group velocities in the grid at any frequency. Next, the path-average
curve is used to create a phase-matched filter, using Equation 4b of Herrin and Goforth (1977). We chose to calculate
the correlation form of this filter, so that its waveform is effectively a unit-amplitude synthetic, which can be directly
compared to the recorded signal. Correlating this filter with the seismogram should result in a peak near zero lag if the
synthetic and observed waveforms agree, assuming there is sufficient signal energy relative to the noise in the data.
Finally, a window around the peak in the cross-correlation function can be extracted, then convolved with the phase-
matched filter. This redisperses the energy, which should produce a restored version of the original signal with
reduced noise, and hence a cleaner Rayleigh arrival.
 Figure 2. Phase Match Tool with ray traced path using LLNL Model.

To begin surface wave analysis in MatSeis, the user first selects from the main display one event and one long-
period waveform, identified by its station and channel codes. Next a time window spanning the expected Rayleigh
arrival is marked (the vertical dashed lines in Figure 1). When the 'Phase Match Tool' is chosen under the 'LP' menu,
the user interface shown in Figure 2 appears. The topmost waveform displays the selected seismogram of the event
from the main MatSeis window. The phase-matched filter for this source-station path is shown below this, plotted on
the same time axis. The third waveform represents the cross-correlogram of the data and the filter, centered on a lag
time of zero. The blue box on this plot highlights the segment of the correlogram to be extracted and redispersed. By
clicking and dragging with the mouse, the user can move and resize the blue box to extract any desired portion of the
trace. The restored waveform, fourth from the top, shows the result of convolving the correlogram segment within the
blue selection box with the phase-matched filter.

Figure 3. Phase Match Tool with ray traced path using Stevens Model.
 Figure 4. Restored Waveform for 100 sec window

Figure 5. Restored Waveform for 300 sec window

The dispersion curve used to construct the phase-matched filter is shown in the bottom right corner of Figure 2. The
dashed lines in the dispersion curve window indicate the maximum and minimum values among all cells in the model
at each frequency. At this point, the dispersion curve and synthetic signal have been created. The phase-matched
filter's frequency response spectrum is shown in the lower left corner window of the figure. The filter has an
amplitude response of one across the frequencies tabulated in the model, and tapers to zero outside this band. The
menu at the bottom of the interface allows the user to choose any available gridded dispersion model to test the
effect of each on the performance of the matched filter. Figures 2 and 3 illustrate the results obtained using two
different models with the same seismogram.

Figure 4 and Figure 5 demonstrate the effect of selecting different length segments of the correlogram. To restore the
original Rayleigh arrival and eliminate extraneous noise, the highlighted segment is convolved with the phase-
matched filter waveform to produce the restored waveform, shown at the bottom. As the selection box gets wider, the
restored trace more closely resembles the original seismogram, but may reintroduce more noise or multipathed
energy.
CONCLUSIONS AND RECOMMENDATIONS

We have implemented phase-matched filtering as MATLAB functions, and developed an easy-to-use graphical
interface, which can be invoked from the MatSeis toolkit. As a result, a user can apply these techniques to any event
in the database, and can select an appropriate Rayleigh propagation model. We will soon add the capability to
measure amplitudes and periods from either the original or restored waveforms, then compute Ms magnitudes.
Additionally, we plan to update the interface to allow the user to control the frequency response of the phase-
matched filter.

REFERENCES

Chael, E., M. Harris, C. Young, K. Mayeda, W. Walter, S. Taylor, A. Velasco, Prototyping regional discrimination
tools with MatSeis, Proceedings of the 21st Annual Seismic Research Symposium, Sept. 1999, 294-299.

Harris, M. and C. Young, MatSeis: a seismic GUI and toolbox for MATLAB, Seism. Res. Lett., 68, 267-269, 1997.

Herrin, E. and T. Goforth, Phase-matched filters: application to the study of Rayleigh waves, Bull. Seism. Soc. Am.,
67, 1259-1275, 1977.

Pasyanos, M. E., W. R. Walter and S. Hazler, Improving mb:Ms discrimination using phase matched filters derived
from regional group velocity tomography, Proceedings of the 21st Annual Seismic Research Symposium, Sept. 1999,
565-571.

Pawlowicz, R., M_Map: a mapping package for MATLAB, http://www.ocgy.ubc.ca/~rich/map.html, 1998.

Rezapour, M. and R. G. Pearce, Bias in surface-wave magnitude Ms due to inadequate distance corrections, Bull.
Seism. Soc. Am., 88, 43-61, 1998.

Stevens, J. L. and D. A. Adams, Improved methods for regionalized surface wave analysis, Proceedings of the 21st
Annual Seismic Research Symposium, Sept. 1999, 274-282.