The SCEC Community Geodetic Model V1: Horizontal Velocity Grid

(1) Abstract

The SCEC community is constructing and updating a suite of models for the Southern California region to facilitate cross-disciplinary research (CFM, CVM, CGM, CSM, and CRM). Here we are concerned with the development of the Community Geodetic Model (CGM). Eventually the CGM will consist of vector deformation time series at ~1 km resolution, and better than seasonal sampling. As a first step we are constructing a 0.01˚ resolution grid of horizontal vector velocities and 2-D tensor strain rate covering the areas of interest to SCEC scientists. Our approach is to first assemble 15 available velocity and strain rate models for the SCEC region. There were 4 main approaches to model construction: isotropic interpolation, interpolation guided by known faults, interpolation of a rheologically-layered lithosphere, and model fitting using deep dislocations in an elastic layer or a half space. We then evaluate the 15 strain rate models in terms of roughness, cross correlation, seismicity rate, and SHmax to select a subset of 10 usable models. Since all the models are based on slightly different geodetic data and use a variety of reference frames, we re-gridded velocities from the 10 models at a 0.01˚ grid spacing. This is accomplished by forcing each velocity model to match the best available GPS velocity data for the region. The 10 velocity models were averaged and their standard deviation was also computed. Standard deviations are generally small (< 0.5 mm/yr) in areas of good GPS coverage; areas of large standard deviation illustrate where InSAR velocities will contribute most. This uniform velocity is a first step in the development of the full 3-D time dependent CGM. This result is important for seismic hazard evaluation as well as InSAR time series analysis. As new GPS and InSAR data become available this SCEC community model will continue to evolve. The full compilation of the GPS velocity data, the contributed models, and the consensus products will be available on the SCEC web site.

(2) Uses of Horizontal Velocity Grid

Why construct a uniform velocity grid since crustal deformation is a complex time series related to all types of transient processes such as co- and post-seismic deformation as well as seasonal hydrological signals?

Velocity uncertainties expose areas of weak GPS coverage and jigh temporal variability.

The uniform velocity model is useful for constraining long-wavelength errors in InSAR analyses.

Strain rate maps and their uncertainties are useful for off-fault hazard assessment.

This is the first step to a full vector time-dependent model.

(3) GPS data

Figure 1 shows the 1339 GPS velocity vectors and uncertainties in the Stable North America Reference Frame (SNARF).

Zeng and Shen [2016b]

McCaffrey et al., [2013]

Crowell et al., [2013]

(4) Contributed velocity and strain rate models

Figure 2. Second invariant of strain rate ordered from smoothest model (mccaffrey) to roughest model (bird). The background seismicity rate M 5.0 to 7.0 [Petersen et al., 2008] was scaled into the log of the second invariant to enable cross correlation. Profiles A - A’ and B - B’ have high density GPS arrays so the actual strain rate can be measured.

(5) Ranking and Winnowing of 15 Models

Eliminate Smooth Models

Figure 3. Profiles of second invariant of strain rate for each of the 15 models across the Carrizo and Imperial Faults (profiles A - A’ and B - B’ in Figure 2). These locations have enough GPS coverage to accurately model the strain rate using a vertical dislocation (thick grey curves) [Carrizo, D=17 km, V=35 mm/yr, Hearn et al., 2010; Imperial, D=6 km, V=40 mm/yr, Lyons et al., 2002]. The smooth models (dashed curves) all underestimate the strain rate close to the fault but overestimate strain rate away from the fault.

Table 1. Velocity and strain rate models contributed to the CGM

NAME	MODEL VEL	MODEL STRAIN_RATE	STRAIN RATE EVAL.	PUBLICATION
rms	SHmax	corr
becker	O	X	81	14.5	.76	Platt and Becker, 2010
bird	X	X	183	19.2	.58	Petersen et al., 2014; Field et al., 2014
bormann_hammond	X	X	99	19.2	.64	Johnson et al., 2013
gpsgridder	X	X	109	17.1	.77	Sandwell and Wessel, 2016
hackl	X	X	134	26.1	.70	Hackl, 2009
holt	X	X	124	18.3	.73	Flesch et al., 2000
kreemer	X	X	152	20.4	.71	Kreemer et al., 2014
loveless_meade	X	X	147	19.1	.64	Loveless and Meade, 2011
mccaffrey	X	X	93	17.6	.60	McCaffrey et al., 2013
parsons	O	X	92	24.4	.42	Parsons et al., 2006
shen	X	X	91	12.7	.74	Shen et al., 2015
smith_konter	X	X	171	14.0	.63	Smith-Konter and Sandwell, 2009
tape	O	X	73	26.1	.66	Tape et al., 2009
tong	X	X	173	15.4	.60	Tong et al., 2013
zeng	X	X	139	14.0	.72	Zeng and Shen, 2016a

The rms column is the rms of the second invariant of the strain shown in Figure 2. The SHmax is the standard deviation in degrees of the difference between the orientation of the direction of maximum compression and SHmax from seismic moment tensors [Yang and Haukkson, 2013]. The corr column is the average of the cross correlation of each model with all the other models in the set. Boxes shaded in grey were not used in the consensus CGM model because of the following reasons. The bormann_hammond model did not completely cover the region of interest. The becker, parsons, and tape models have no velocity grid. The hackl, parsons, and tape models had very poor fit to SHmax.

(6) Cross Correlation Among Models

Figure 4. Cross correlation between 10 models selected for the use in the CGM. The values in red indicate the average correlation between each model and all the other models.

Compare with SHmax

Figure 5. Comparison between significant SHmax [blue Yang and Haukkson, 2013] and direction of maximum compression where the second invariant exceeds 10 nanostrain/yr. (left) smooth shen model and (right) rough smith_konter model.

(7) Polishing and Averaging of 10 Models

To facilitate a comparison among the models, we used a remove/interpolate/restore method [Sandwell and Wessel, 2016] to adjust each model to fit the common 1339 GPS velocity vectors in the region. The interpolation method does not fit the GPS vectors exactly and the typical rms difference is 1 mm/yr. and slightly smaller when the points in the creeping section are excluded (Table 2). The mean velocity is shown in Figure 6 along with the GPS vectors and uncertainties. The rms difference between the mean model and the individual models was also computed with and without the masked areas shown in Figure 7. The rougher models fit the mean model better than the smoother models. The average strain tensor is shown in in Figure 8 along with the second invariant of the mean strain tensor (Figure 9) and its uncertainty (Figure 10.).

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