1. Introduction
An improved understanding of how energy and seismic moment accumulate in
the crust and upper mantle along major plate boundaries is essential for
forecasting the size and timing of major earthquakes
[Smith-Konter & Sandwell , 2009; Field et al., 2015;Weiss et al., 2020; Rollins et al., 2020]. Recent
studies have shown that most damaging earthquakes occur in areas where
the crustal strain rate exceeds 100 nanostrain/yr [e.g., Elliot
et al ., 2016.; Zeng et al. , 2018; Bayona et al., 2021].
Many of these areas are heavily populated and have had major destructive
earthquakes. Moreover, one of the largest uncertainties in California
earthquake hazard models (i.e., UCERF-3 [Field et al ., 2014;Field et al. , 2015]) is the amount of plate boundary
deformation that is accommodated by off-fault strain and whether this
strain is accumulating as elastic or as plastic deformation. Therefore,
accurate strain rate measurements are needed to improve earthquake
forecasts. Achieving an ideal 100-nanostrain/yr accuracy at a 10-km
resolution (i.e., a typical fault locking depth in California) requires
a horizontal velocity model that has an accuracy of 1 mm/yr. Moreover,
moderate earthquakes, fault creep, and other transient processes produce
temporal variations in strain rate that commonly exceed
100-nanostrain/yr [Holt and Shcherbenko , 2013; Klein et
al., 2019]. Currently continuous GNSS measurements can provide vector
deformation better than the required 1 mm/yr accuracy but not with 10 km
spatial resolution. InSAR provides very high spatial resolution but
cannot achieve the 1 mm/yr accuracy, mainly due to the perturbations
from atmospheric noise [Emardson et al. , 2003]. In addition,
current InSAR systems provide only two components of surface deformation
and thus cannot uniquely distinguish between horizontal and vertical
strain [Shen and Liu , 2020]. Here we develop a path to
achieving the time-dependent strain rate mapping objective by combining
4.5 years of measurements from InSAR and GNSS along the San Andreas
fault system (SAFS).
The accuracy and spatial resolution of the current strain rate models
derived from GNSS velocities can be assessed by comparing results from
various groups. An accuracy analysis was performed as part of the
developing SCEC Community Geodetic Model (CGM-V1) [Sandwell et
al., 2016a]. The 17 models were taken from previous publications
[Zeng & Shen, 2016; Shen et al., 2015;
Smith-Konter & Sandwell, 2009; Tong et al., 2014;Tape et al., 2009; Petersen et al., 2008; Petersen
et al., 2014; Platt & Becker, 2010; McCaffrey, 2005;Loveless & Meade, 2011; Hackl et al., 2009;Parsons, 2006; Parsons et al., 2013; Kreemer et
al., 2014; Flesch et al., 2000; Field et al. , 2014;Sandwell & Wessel , 2016]. The mean and standard deviation of
the 10 “best” well-correlated models is shown in Fig. 1a. Note the
standard deviation (Fig. 1b) commonly exceeds 50 nanostrain/yr
especially above the major faults where the uncertainties can exceed 100
nanostrain/yr. These significant deviations among the models are not due
to inaccuracies in the GNSS data but to the incomplete spatial sampling
of the GNSS stations, which is typically 10-20 km in California
[Wei et al., 2010].
To further characterize this lack of spatial resolution of the strain
rate field, we analyzed the strain rate models by computing cross
spectra in their overlapping region in Southern California.
Radially-averaged cross spectra were computed between every pair of
models using Generic Mapping Tools (GMT) [Wessel et al.,2019]. As illustrated in Fig. 1c, there is a large variation in the
coherence between these models. Most models agree well at long
wavelengths, but generally disagree at short wavelengths, except those
having very similar, or identical, fault models like Shen et al .
[2015] and Zeng & Shen [2016] or Tong et al.[2014] and Smith-Konter & Sandwell [2009]. The
disagreements are due to different physical modeling approaches, assumed
fault geometries, and slightly different GNSS velocity data sets. For
most pairs, the coherence is high at very long wavelength and decreases
to zero coherence at ~10 km. The 0.2 coherence threshold
of the median of all the cross spectra is located at 30-40 km
wavelengths.