Surface potential and gravity changes due to internal dislocations in a spherical earth-I. Theory for a point dislocation

Abstract

S U M M A R YThis paper studies the potential and gravity changes caused by dislocations in spherically symmetric earth models. We define dislocation Love numbers to describe the elastic deformation of the earth raised by point sources. We discuss the shear and tensile dislocations, which can be expressed by four independent components: a vertical strike-slip, a vertical dip-slip, a tensile opening on a horizontal plane, and a tensile opening on a vertical plane.The results for a homogeneous earth model agree very well, at least within lo, with those predicted from flat-earth theory. The far-field results indicate no larger than 10per cent difference within 10". It makes little difference whether we use the theory on a sphere or that for a flat earth in the near field, while it is reasonable t o use the spherical theory for global calculation. We proceed to calculations with a radially heterogeneous earth model (Model 1066A). The results are as a whole similar to those for a homogeneous sphere. In some cases, however, the difference between the two becomes significant. For example, the locations of the nodal lines of the gravity change differ significantly between the two models. This indicates that the vertical layering can cause considerable effects on the deformation fields.

On the response of the Earth to a fault system: its evaluation beyond the epicentral reference frame

“…This result coincides with those obtained by previous works (Takeuchi and Saito, 1972;Sun and Okubo, 1993), taking care of the different definition of spherical harmonics (non-normalized complex spherical harmonics rather than real spherical harmonics normalized to 4 π here considered). Furthermore, it shows how the discontinuity of the spheroidal vector solution at the radius of the infinitesimal surface element can be decomposed into contributions from the isotropic and deviatoric parts of the surface moment-density tensor.…”

“…In this respect, our seismic Love numbers (or Green's functions) are organized in a different way compared to the treatment proposed by Sun and Okubo (1993) and their following works (Sun and Okubo, 1998;Tanaka et al, 2006;Sun et al, 2009). These previous treatments, indeed, introduce four Green's functions (for strike and dip slips on a vertical fault and tensile fracturing on horizontal and vertical faults), and the spheroidal perturbation due to general tensile and shear dislocations are obtained combining three and all four Green's functions, respectively (see eqs (115) and (117) of Sun and Okubo (1993)). The Green's function for tensile fracturing on a vertical plane is composed of both polar and quadrupolar perturbations (order m = 0 and ±2), while the Green's functions here presented do not mix the different types of perturbation, being organized just for separating them.…”

“…The first method is the simplest one but becomes numerically unstable at harmonic degrees greater than about 400 (Boerse et al, 2014). Differently, the other two methods perform well even at very high harmonic degrees (Sun and Okubo, 1993;Sun and Okubo, 1998;Attar and Woodhouse, 2008).…”

An analytical approach to estimate curvature effect of coseismic deformations

“…They considered the layered structures and the gravity effect (Wang 2005), but could not embody the curvature effect. Sun & Okubo (1993) proposed an approach to compute changes in potential and gravity for a spherical earth model based on 1066A (Gilbert & Dziewonski 1975) model and PREM (Dziewonski & Anderson 1981) model. Sun et al (2009) defined the dislocation Love numbers and Green's functions for four independent sources (strike-slip, dip-slip, horizontal tensile and vertical tensile) to calculate coseismic deformation based on the SNREI earth model.…”

Effects of Earth's layered structure, gravity and curvature on coseismic deformation

“…Okubo (1993) presented a reciprocity theorem between the dislocations and the conventional external forces in a SNREI (spherically symmetric, non-rotating, elastic and isotropic) earth model. Sun & Okubo (1993, 1998 and Sun et al (2009) introduced the dislocation Love numbers for calculating Green's functions for coseismic deformation, geoid and gravity changes based on the SNREI earth model. By comparing a layered spherical earth model (1066A) with a homogeneous half-space, Sun & Okubo (2002) found that the layering and curvature effects on the coseismic surface deformation (vertical displacement) can reach together the order of 20 per cent.…”