Earth's Free Surface Complicates Inference of Absolute Stress From Earthquake-Induced Stress Rotations

The stress redistribution from an earthquake can produce localized measurable rotations of the principal stress axes if the absolute level of differential stress in the crust is on the order of the earthquake stress drop. Two simple analytic solutions have been developed to estimate the differential stress from an observed stress rotation. However, each has assumptions that may not be accurate near Earth's free surface. I model synthetic earthquakes in an elastic half-space, and show that the assumptions of the methods are accurate for strike-slip earthquakes, and for deep dip-slip earthquakes. However, they are incorrect for shallow dip-slip earthquakes. I introduce a free surface correction for one of the methods for dip-slip earthquakes. I revise an analysis of stress rotations due to great subduction zone earthquakes, including this correction. The results support the original conclusion of near complete stress drop for many shallow subduction zone earthquakes. Plain Language Summary Changes in stress due to an earthquake can be used to infer the absolute level of stress. Simple methods are commonly used to infer stress, but they neglect the effects of Earth's surface. I show that Earth's surface doesn't affect results for strike-slip earthquakes (two sides of the fault move horizontally relative to each other), or deep dip-slip earthquakes (two sides move both vertically and horizontally). However, Earth's surface affects results for shallow dip-slip earthquakes. I reanalyze a compilation of stress changes from large dip-slip earthquakes in subduction zones, including the effects of Earth's surface. While the results are somewhat changed, they support the original conclusion that absolute stress is low in the shallow part of subduction zones.