Computer Programs in Seismology

Introduction

The programs wvfgrd96, wvfmtd96 and wvfmt96 output the time shift used to better match the observed and predicted waveforms in the sac header value USER9 in the predicted waveform, eg., CCMZ.pre. Until now this has not been used quantitatively, but has served an an indication of several different effects.

The convention for the time shift is that a positive value indicates that the synthetic traces must be moved later in time for alignment.

There are different causes for this time shift:

The origin time and epicentral distance are incorrect
The velocity model used for the inversion is incorrect
The velocity model used to define the P-arrival time is not the same as the velocity model used for the waveform inversion (assuming that the initial trace alignment is based on the P arrival time)

The program wvfdly96 considers the azimuthal variation of the Z R and T components, which are contained in the files Z.dat, R.dat and T.dat The files consist of one line per station with an entry

   Azimuth Time_Shift

Assuming only a mislocation, the time shifts are fit to a functional form as a function of azimuth to the station:

    Time_shift = A + B cos Azimuth + C Sin Azimuth

For small changes in epicentral location,

         A is the change in origin time

The second two terms can be rewritten, for interpretation, as

         R/V cos ( Az - Theta)

where R is the shift of the epicenter in km and Theta + 180 is the direction of the epicenter shift

Consider the following example with time shifts indicated by -, 0 + where I is the initial epicenter and E is the true epicenter

               
                       0          delay           * *
                       |            |           *    *
                       |            |          *       *
               + ------I--E--- -    **---|----|----|----| Az
                       |            | * 90  *180  270  360
                       |            |  *   *
                       |            |    *
                       0            |

This pattern would indicate a functional fit of

         time_shift = A + C sin Az  with C positive

The remove the time shift the epicenter should be moved to the east, e.g., 270 + 180 degrees

For use with regional moment tensor, it is assumed that the time shift is related to the delay of the Rayleigh wave on the Z and R components and the Love wave on the T component. Further is it assumed that the ratio of Love-wave group velocity to Rayleigh-wave is 0.92 and that there is no other dispersion effect in the frequency band of the waveform match. Further the code assumes that the Rayleigh-wave group velocity is 3.1 km/s.
Thus the time shift for the T component is of the form

 Time_shift = A + 0.92 B cos Azimuth + 0.92 C Sin Azimuth

The A, B and C parameters are determined by least squares and no weighting (e.g., distance) is applied to the regression.

DODELAY and wvfgrd96

After the source inversion, the script DODELAY is run to extract the delays from the predicted waveforms, to estiamte the shift and to plot the results using the program genplt.

The following example provides the background for writing this program and the DODELAY script:

A recent earthquake in the Northwest Territories of Canada was located by the USGS NEIC as follows:

USGS Location

2010/09/04 00:23:13 62.943 -125.718 7.1 4.50 NT, Canada

The time shifts associated with the waveforms showed significant delays. Running DODELAY yielded the following image:

Subsequencly the Natural Resources Canada (NRCAN) solution was published.

NRCAN Location

2010/09/04 00:23:11.35 62.864 -125.821 1.0 4.8 ML 120 km of Wrigley, NT

Following the source inversion starting with these coordinates, the interpreted delays yield the following figure:

The NRCAN solution is 10.24 km away from the USGS solution in an azimuthal direction of 210 degrees. A comparison of the intitial time shifts showed that those for the NRCAN location were smaller than for the NEIC solution. This is also evident in the plots where the inferred Rayleigh wave distance offsets are smaller for the NRCAN solution than for the NEIC solution. There is some consistency in the orgin time shift, e.g., that the NEIC solution would want 00:23:13.6 and the NRCAN solution 00:23:13.0.

The output of wvfdly96 is only mean to interpret waveform matching time shifts in terms of a source offset. It does not provide a true relation because of the simple assumptions of the group velocities used. Other factors such as poor station distribution and incorrect model still affect the results.

Large inferred time shifts are an indication that an examination of the initial location is appropriate.

Discussion

This program may have value for testing epicentral locations base on body-wave arrival times. If a significant azimuthal change is seen in the independent surface-wave field, then a reexamination of the location may be in order.

Last changed September 20, 2010