Block Modeling with Connected Fault-Network Geometries and a Linear Elastic Coupling Estimator in Spherical Coordinates

Abstract

Geodetic observations of interseismic deformation provide constraints on the partitioning of fault slip across plate boundary zones, the spatial distribution of both elastic and inelastic strain accumulation, and the nature of the fault system evolution. Here we describe linear block theory, which decomposes surface velocity fields into four components: (1) plate rotations, (2) elastic deformation from faults with kinematically consistent slip rates, (3) elastic deformation from faults with spatially variable coupling, and (4) homogeneous intrablock strain. Elastic deformation rates are computed for each fault segment in a homogeneous elastic half-space using multiple optimal planar Cartesian coordinate systems to minimize areal distortion and triangular dislocation elements to accurately represent complex fault system geometry. Block motions, fault-slip rates, elastic coupling, and internal block strain rates are determined simultaneously using a linear estimator with constraints from both geodetically determined velocity fields and geologic fault-slip rate estimates. We also introduce algorithms for efficiently implementing alternative fault-network geometries to quantify parameter sensitivity to nonlinear perturbations in model geometry.

Monitoring of the spatio-temporal change in the interplate coupling at northeastern Japan subduction zone based on the spatial gradients of surface velocity field

“…In such studies, the degree of coupling, which has generally been expressed in terms of the backslip (or slip deficit) rate at the plate interface, is estimated by applying linear inversion methods while imposing some constraint conditions, such as the smoothness of the spatial distribution of the backslip, the non-negativity of the backslip, Dirichlet boundary condition and the a priori distribution of the backslip (e.g. Yabuki & Matsu'ura 1992;Mosegaard & Tarantola 1995;Matsu'ura et al 2007;Meade & Loveless 2009). These constraint conditions prevent the solution from becoming unstable, because it is difficult to resolve the backslip distribution at the plate interface far off the coast based only on terrestrial observations.…”

Slip rates and off‐fault deformation in Southern California inferred from GPS data and models

“…In each of these block models, the present‐day deformation field is expressed as the sum of a long‐term component that is steady in time, and a transient, interseismic component that results from elastic distortion due to locking of faults. The first model is a traditional elastic block model [e.g., McCaffrey , ; Meade and Loveless , ] in which fault‐bounded blocks rotate undeformed over the long term about Euler poles, and interseismic elastic strain is introduced with backwards slip on dislocations in an elastic half‐space. We refer to this as the “rigid block model.” The second model is a “deforming block model” which is the same as the previous model except the long‐term velocity field includes a component due to steady internal straining of the blocks [also see McCaffrey , ; Meade and Loveless , ].…”

Stress modulation on the San Andreas fault by interseismic fault system interactions

“…2A) (McClusky et al, 2001;Shen et al, 2003;Hammond and Thatcher, 2005;Williams et al, 2006;McCaffrey et al, 2007; Plate Boundary Observatory network velocity fi eld, http://pboweb.unavco.org) and a three-dimensional spherical block model (see the GSA Data Repository 1 ) (Meade and Loveless, 2009) to constrain kinematically consistent slip rates (Weldon and Humphreys, 1986;Minster and Jordan, 1987) on ~60,000 km 2 of fault area throughout the Southern California fault system. Block models describe the interseismic GPS velocity fi eld as the combined effects of two processes, long-term microplate rotations and local elastic strain accumulation effects (Savage and Burford, 1973;Savage, 1983;Matsu'ura et al, 1986).…”