Quantification of geodetic strain rate uncertainties and implications for seismic hazard estimates

Abstract

Summary Geodetic velocity data provide first-order constraints on crustal surface strain rates, which in turn are linked to seismic hazard. Estimating the 2D surface strain tensor everywhere requires knowledge of the surface velocity field everywhere, while geodetic data such as Global Navigation Satellite System (GNSS) only have spatially scattered measurements on the surface of the Earth. To use these data to estimate strain rates, some type of interpolation is required. In this study, we review methodologies for strain rate estimation and compare a suite of methods, including a new implementation based on the geostatistical method of kriging, to compare variation between methods with uncertainty based on one method. We estimate the velocity field and calculate strain rates in southern California using a GNSS velocity field and five different interpolation methods to understand the sources of variability in inferred strain rates. Uncertainty related to data noise and station spacing (aleatoric uncertainty) is minimal where station spacing is dense and maximum far from observations. Differences between methods, related to epistemic uncertainty, are usually highest in areas of high strain rate due to differences in how gradients in the velocity field are handled by different interpolation methods. Parameter choices, unsurprisingly, have a strong influence on strain rate field, and we propose the traditional L-curve approach as one method for quantifying the inherent trade-off between fit to the data and models that are reflective of tectonic strain rates. Doing so, we find total variability between five representative strain rate models to be roughly 40 per cent, a much lower value than roughly 100 per cent that was found in previous studies (Hearn et al., 2010). Using multiple methods to tune parameters and calculate strain rates provides a better understanding of the range of acceptable models for a given velocity field. Finally, we present an open-source Python package (Materna et al., 2021) for calculating strain rates, Strain_2D, which allows for the same data and model grid to be used in multiple strain rate methods, can be extended with other methods from the community, and provides an interface for comparing strain rate models, calculating statistics, and estimating strain rate uncertainty for a given GNSS dataset.

Seismic Moment Accumulation Rate From Geodesy: Constraining Kostrov Thickness in Southern California

“…Moreover, it does not distinguish between on‐ or off‐fault moment accumulation. The main disadvantages are: (a) the calculation of strain rate from geodetic velocities (GNSS and/or InSAR) is highly non‐unique because one must grid the components of velocity and then take the spatial gradient, which amplifies both the signal and noise (Maurer & Materna, 2023) and (b) the Kostrov thickness ( H ) is an unknown parameter.…”

“…One of the largest uncertainties in calculating the off‐fault moment rate is the method and parameters used to compute the strain rate from the residual GNSS velocities (e.g., Maurer & Materna, 2023). Our analysis uses the gpsgridder algorithm (Haines & Holt, 1993; Sandwell & Wessel, 2016) keeping 45% of the eigenvalues to provide some smoothing.…”

The Upper Crustal Deformation Field of Greece Inferred From GPS Data and Its Correlation With Earthquake Occurrence

“…To further examine the impact of the different weighting threshold values in the strain rate results and determine the optimal model compensating the inherent trade‐off between solution stability and resolution that characterizes every strain rate estimation (Maurer & Materna, 2023), we follow Shen et al. (2015) and inspect the differential strain rate fields of the second invariant which are produced as W t decreases from 24 to 3 (Figure S3 in Supporting Information S1).…”

“…To further examine the impact of the different weighting threshold values in the strain rate results and determine the optimal model compensating the inherent trade-off between solution stability and resolution that characterizes every strain rate estimation (Maurer & Materna, 2023), we follow Shen et al (2015) and inspect the differential strain rate fields of the second invariant which are produced as W t decreases from 24 to 3 (Figure S3 in Supporting Information S1). It can be observed that the strain rate pattern in Figure S3a in Supporting Information S1, which corresponds to the decrease of W t from 24 to 18, is smooth and the majority of the differential strain rates occurs across well-know fast deforming regions (e.g., western Greece, Gulf of Corinth, NAF and north Aegean Sea).…”

Comparative Analysis of Methods to Estimate Geodetic Strain Rates from GNSS Data in Italy

“…The method executes a local linear regression without applying any additional weights to the data [Maurer and Materna, 2023] and the computations are bypassed if there are not 𝑁 stations within the window. As the window's radius acts as a threshold distance, subsequent analyses will vary only the number of stations, maintaining an arbitrarily large radius to enable strain rate estimation throughout the entire region.…”