Multipole expansions of extended sources of elastic deformation

Abstract

Seismic-moment tensors for composite point sources which consist of coherent and incoherent assemblages of elementary sources are examined. We estimate the sizes of the higher-order source components for several simple deterministic and stochastic models of the source region geometry, as well as for a model of stochastic fault geometry developed earlier by us, to simulate both the tensor and scalar geometrical properties and the temporal properties of complex faults and sources. We study the complexity of earthquake focal zones using expansions of seismic radiation of a finite source in vector spherical harmonics and/or in seismic-moment tensors of a rank higher than two. Five point elementary sources (one second-rank and four fourth-rank) are non-zero for planar earthquake faults; four possible other sources and zero for planar faults. Thus, the presence of seismic radiation from the latter sources can be used as an indicator of the complexity (non-planarity) of the source. If the source zone is almost planar, the number of free parameters contained in these sources can be greatly reduced, and their inversion from earthquake records becomes possible. Three classes of geometrical barriers (disclinations) corresponding to rotations around three nodal axes are identified for this condition. The strength of multipoles can be connected to particular geometric features of heterogeneous faults, i.e. the presence and strength of asperities, segmentation of a fault zone, like en échelon faulting, hence important tectonic results may be obtained from the inversions. Such a model, which involves barriers, requires a maximum of 20 degrees of freedom for its characterization.