Dispersion Comparison

Introduction

As part of the systematic determination of earthquake moment tensors for North American earthquakes, multiple filter analysis is used to obtain the fundmantal mode Love and Rayleigh wave spectral amplitudes and group velocities to provide the data set for one type of source inversion. As of May 05, 2015, there are over 2033872 dispersion measurements available for other use.

We applied a tomography technique developed by Ammon (personal communication) and outlined in Cho et al (2006) to obtain tomographic images of group velocity disperion for North America with emphasis on the contiguous 48 states of the United States. The objective of this exercise was to compare actual dispersion to that predicted from the two velocity models used for source inversion - the CUS model for the for east of the Rocky Mountains and the WUS model for the region west of the Rocky Mountain front. An advantage of using dispersion measurements from regional earthquakes is the ability to obtain the dispersion at periods less than 15 seconds which is difficult to obtain from teleseismic data.

Tomography Results and Comparison

The following images compare the tomography results from the current data set (left and center column) to recent determinations by Benson (U. Colorado) (right column) based on a priority models, earthquake dispersion measurements (?) and the cross correlation of ground noise. Our results were computed on a 100 km grid, while the U. Colorado results are given on a 0.5 x 0.5 degree grid. To provide some semblance for a visual comparison, the U. Colorado results are plotted on a 1x1 degree grid.

The figure on the left is the "checkerboard" test applied ot the ray paths used in the SLU/PSU tomography. The "pseudo" data set was based on the paths used for the tomography (center column). The "checkerboard" test used patches corresponding to a plus-minus 10 percent variation about the mean value of 3.0 km/sec, e.g., 2.7 km/s for the low values and 3.3 km/sec for the high values. The tomography annotation provides the mean velocity of all paths. The observation that the mean is very close to 3.0 km/sec indicates the relatively uniform ray coverage of the data set.

The SLU/PSU computations were performed for periods of 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, 9.5, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0, 17.0, 18.0, 19.0, 20.0, 21.0, 22.0, 23.0, 24.0, 25.0, 26.0, 27.0, 28.0, 29.0, 30.0, 32.0, 34.0, 36.0, 38.0, 40.0, 42.0, 44.0, 46.0, 48.0, 50.0, 55.0, 60.0, 65.0, 70.0, 75.0, 80.0, 85.0, 90.0, 95.0, and 100.0 seconds. The U. Colorado results are presented at periods of 8, 10, 12, 14,16, 81,20, 25, 30, 35,40, 45,50, 55, 60, 65, 70, 75 and 80 seconds.

Note In order to make the comparison, the SLU/PSU tomography results wereused to define the mean velocity for each period. These values were then used to define the percent variation of the tomography values across the grid (-10 to +20 percent). The same mean value was used for the U. Colorado values in order to present a very similar picture. The mean value differs slight for the SLU/PSU results since the code calculated yet another mean value.

Note Since the SLU/PSU results used continental earthquakes dispersion values in the oceans, Gulf of Mexico and Hudson Bay are the mean background value since few if any rays cross these regions. On the other hand the U. Colorado work provides dispersion values for these regions, although few of these can be base on the cross-correlation of ground noise. So do not focus on differences in the oceans.

Love Wave Images

SLU/PSU Checkerboard	SLU/PSU	U. Colorado

Dispersion Comparison

Rayleigh Wave Images

SLU/PSU Checkerboard	SLU/PSU	U. Colorado

Dispersion Comparison

The following figures compare the model predicted disperison to the dispersion curve imaged for specific coordinates. The predicted curve is given in red,a and the tomographically estimated dispersion is shown as the solid black dots.

The U Colorado dispersion is given as red dots.

NY (43, -75)

Comparison of observed and predicted dispersion. The predicted values are for the CUS model. The black symbols are the dispersion from the tomography of the group velocity observations derived from the study of local and regional earthquakes in north America. The red symbols are from G. Benson at U. Colorado and is base on ground noise. The green symbols are from the Harvard global group velocity tomography.

GEORGIA (33, -85)

OHIO (40, -83)

MISSOURI (39, -90)

MINNESOTA (45, -95)

NEBRASKA (40, -100)

E COLORADO (38, -104)

UTAH (40, -110)

Comparison of observed and predicted dispersion. The predicted values are for the WUS model. The black symbols are the dispersion from the tomography of the group velocity observations derived from the study of local and regional earthquakes in north America. The red symbols are from G. Benson at U. Colorado and is base on ground noise. The green symbols are from the Harvard global group velocity tomography.

MONTANA (47, -110)

ARIZONA (33, -110)

WASHINGTON (48, -120)

S. CALIFORNIA (35, -120)

Discussion

Noting that the tomographic dispersion estimates are imperfect because of path coverage, and also noting that few California events are in the data set, the results support he use of just two basic velocity models for the source analysis, especially for waveform inversion which is restricted to using waveforms at stations within 500 km of the earthquake.

In the dispersion comparisons, focus on the periods less than 30 seconds, since these are the periods that usually have adequate signal-to-noise ratios for the M = 4 earthquakes that are really of interest in this study, The figures are presents in a roughly East to West profile across the US. Each figure title gives the latitude and longitude of the target tomography cell.

The CUS model is used for the in the plots west to Eastern Colorado, which the WUS model is used west of there. The CUS model starts to breakdown at the periods in Nebraska and is too fast for Eastern Colorado. The Eastern Colorado model would be fit better in the Rayleigh waves either by using the WUS model or by increasing the crustal thickness of the model.

The WUS model is adequate for most of the western US. The lack of agreement in southern California may be real or just an artifact of inadequate data.

What Next?

For our paper on source mechanisms, I need to clean up the WUS model. The model does not look realistic because I just put together a model that fit observed dispersion - the inadequacy is due ot the smoothing constraint used in the inversion of the surface-wave dispersion. Specifically,

I need a simpler model for the paper - DONE - now WUS model
I believe the tomographic model may be useful for constructing a phase match filter for isolating the surface wave for a given source-receiver path as a step toward automation and, more importantly, driving the magnitude threshold lower for completeness in the moment tensor catalog.
The U Colorado results and ours agree very well. Note however that we have shorter periods. This is because the process with LH data instead of BH