Seismic sources with observable glut moments of spatial degree two

Abstract

Let ζΛ and rΛ. be the hypocentral position and time of an extended indigenous seismic source. Backus showed that the force moment tensors of the source, Γ(m+1,n)(ζΛ, rΛ), determine and are determined by the motion which the source produces. For small m + n, only the long‐period motion is relevant. The glut moment tensor Λ(m,n) (ζΛ, rΛ.) can be calculated uniquely from γ(m+1,n)(ζΛrΛ) only if m= 0 or m = 1. The tensor G =Λ2,0(ζΛ) gives the spatial variance tensor WΛ of the source, and WΛ. roughly describes the size, shape and orientation of the source region. Therefore the failure of the observed F=Γ3,0(ζΛ) to determine G uniquely is of seismological interest. In the present paper we show that F determines G uniquely if we assume the source to be a simple straight line source (SSLS) or an ideal fault in an isotropic medium with isotropic prestress (IFIMIP). We give tests on F which determine whether it can come from a SSLS, from an IFIMIP or from a simple plane surface source (SPSS). If we assume the source to be a SPSS then knowing F and the fault plane determines G to within an unknown scalar multiple of a certain tensor tangent to the fault plane. Moreover F determines the fault plane uniquely unless F can come from a SSLS. If it can, then F determines this virtual source line uniquely, and F permits the fault plane to be any plane containing the virtual source line. Copyright © 1977, Wiley Blackwell. All rights reserved