Damped regional‐scale stress inversions: Methodology and examples for southern California and the Coalinga aftershock sequence

Abstract

[1] We present a new focal mechanism stress inversion technique to produce regionalscale models of stress orientation containing the minimum complexity necessary to fit the data. Current practice is to divide a region into small subareas and to independently fit a stress tensor to the focal mechanisms of each subarea. This procedure may lead to apparent spatial variability that is actually an artifact of overfitting noisy data or nonuniquely fitting data that does not completely constrain the stress tensor. To remove these artifacts while retaining any stress variations that are strongly required by the data, we devise a damped inversion method to simultaneously invert for stress in all subareas while minimizing the difference in stress between adjacent subareas. This method is conceptually similar to other geophysical inverse techniques that incorporate damping, such as seismic tomography. In checkerboard tests, the damped inversion removes the stress rotation artifacts exhibited by an undamped inversion, while resolving sharper true stress rotations than a simple smoothed model or a moving-window inversion. We show an example of a spatially damped stress field for southern California. The methodology can also be used to study temporal stress changes, and an example for the Coalinga, California, aftershock sequence is shown. We recommend use of the damped inversion technique for any study examining spatial or temporal variations in the stress field.

Focal mechanisms and stress field in the Atotsugawa fault area, central Honshu, Japan

“…The method used in this study is SATSI (Spatial And Temporal Stress Inversion) developed by Hardebeck and Michael (2006), which is a modified version of Michael's code (Michael, 1987). In the SATSI a study area is divided into small subareas, and a damped inversion method is applied to simultaneously invert for stress in all subareas while minimizing the difference in stress between adjacent subareas.…”

“…In the SATSI a study area is divided into small subareas, and a damped inversion method is applied to simultaneously invert for stress in all subareas while minimizing the difference in stress between adjacent subareas. Stress orientation uncertainty was estimated using 2000 bootstrap resampling of the entire data (Hardebeck and Michael, 2006). The 1-sigma confidence region of the stress model is defined by the 68% of bootstrap solutions closest to the preferred solution.…”

“…The nodes with less than 8 events were used just to smooth gaps in the seismicity and the results were not adopted. We chose the damping parameter e (equation (14) in Hardebeck and Michael (2006)) on the basis of the trade-off curve between model length and data variance (Fig. 11).…”

“…To determine focal mechanism solutions we used a program HASH produced by Hardebeck and Shearer (2002). To conduct a stress tensor inversion we used a program SATSI developed by Hardebeck and Michael (2006). GMT (Wessel and Smith, 1991) was used to make figures.…”

Focal mechanisms and size distribution of earthquakes beneath the Krafla central volcano, NE Iceland

“…Furthermore, the focal solutions need to show enough orientation diversity with the fault slip parallel to the maximum resolved shear stess, and that the movement of one fault does not influence the slip direction of others. We invert for a uniform stress field using the SATSI algorithm [Hardebeck and Michael , 2006] by exploiting the fact that such a stress field applied to randomly oriented faults leads to a range of DC solutions [McKenzie, 1969]. Strike, dip direction and dip angles of randomly picked DC nodal planes are provided as input.…”