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.