Estimation of the orientation of stress in the Earth\u2019s crust without earthquake or borehole data

Andrew A Delorey,Paul A Johnson,Götz H R Bokelmann,Christopher W Johnson

doi:10.1038/s43247-021-00244-1

Abstract

Mechanical stress acting in the Earth’s crust is a fundamental property that is important for a wide range of scientific and engineering applications. The orientation of maximum horizontal compressive stress can be estimated by inverting earthquake source mechanisms and measured directly from borehole-based measurements, but large regions of the continents have few or no observations. Here we present an approach to determine the orientation of maximum horizontal compressive stress by measuring stress-induced anisotropy of nonlinear susceptibility, which is the derivative of elastic modulus with respect to strain. Laboratory and Earth experiments show that nonlinear susceptibility is azimuthally dependent in an anisotropic stress field and is maximum in the orientation of maximum horizontal compressive stress. We observe this behavior in the Earth—in Oklahoma and New Mexico, U.S.A, where maximum nonlinear susceptibility coincides with the orientation of maximum horizontal compressive stress measured using traditional methods. Our measurements use empirical Green’s functions and solid-earth tides and can be applied at different temporal and spatial scales.

Highlights

Mechanical stress acting in the Earth’s crust is a fundamental property that is important for a wide range of scientific and engineering applications
Our results show that the Earth exhibits stress-induced anisotropy of NS that is aligned with SHmax in these two different geologic settings, suggesting that the creep rate is fastest in the orientation of SHmax
In Oklahoma, a sine function fitted to the results shows that the maximum NS occurs between 69 and 91°, depending upon the selection of stations (Figs. 2 and 4)

Summary

Introduction

Mechanical stress acting in the Earth’s crust is a fundamental property that is important for a wide range of scientific and engineering applications. We present an approach to determine the orientation of maximum horizontal compressive stress by measuring stress-induced anisotropy of nonlinear susceptibility, which is the derivative of elastic modulus with respect to strain. Laboratory and Earth experiments show that nonlinear susceptibility is azimuthally dependent in an anisotropic stress field and is maximum in the orientation of maximum horizontal compressive stress. Rock samples in laboratory experiments exhibit anisotropic linear and nonlinear elastic properties when differential stress is applied[41,42]. Differential stress is the difference between the two principal stresses To demonstrate this nonlinear effect, Nur and Simmons (1969) applied uniaxial stress to a cylinder of granite, normal to the cylinder axis, and measured the travel time of an elastic wave as a function of angle with respect to the uniaxial stress[42]. Stress-induced anisotropy in nonlinear elasticity is exhibited by the stress derivative of

Methods

Results

Conclusion