An incompressible finite element model has been used to study the plane strain deformation of two‐phase aggregates deformed by dislocation creep. Input for the model includes the power law flow laws of the two end‐member phases and their volume fractions and configuration. The model calculates the overall flow law of the aggregate as well as the stress and strain rate variations within it. The input flow laws were experimentally determined for monomineralic aggregates of clinopyroxene and plagioclase. Results were calculated for a temperature of 1000°C, strain rates from 10−4 to 10−12S−1, and stresses of 1–1000 MPa. For these conditions, the end‐member flow laws intersect on a log stress versus log strain rate plot at 10−8S−1. Some runs were made on finite element grids fit to an actual diabase texture (∼64% pyroxene, ∼ 36% plagioclase.) Other runs were made on idealized geometries to test the effects of varying the volume fraction of two phases, shape of inclusions, and relative strengths of inclusion and matrix. Important results include the following: (1) The model results satisfy the requirement that the aggregate strength must lie between the bounds set by the end‐member flow laws and those set by assumptions of uniform stress and uniform strain rate. (2) The calculated diabase flow law matches well with that experimentally determined. (3) The aggregate strength within the uniform stress and uniform strain rate bounds is primarily affected by volume fraction, although certain phase geometries can also affect the strength. (4) Although the flow law for an aggregate of power law phases need not be a simple power law, we find it to be a good approximation. We have developed two simple methods of estimating the strength of an aggregate, given the end‐member flow law parameters and volume fractions; both give results that agree with the finite element model calculations. (1) One method takes into account the phase geometry and gives a strength for the aggregate at any strain rate. (2) The other method can be used even if the phase geometry is unknown and gives expressions for the aggregate flow law parameters.

Various Green’s functions occurring in Poisson potential field theory can be used to construct non‐orthogonal, non‐compact, continuous wavelets. Such a construction leads to relations between the horizontal derivatives of geophysical field measurements at all heights, and the wavelet transform of the zero height field. The resulting theory lends itself to a number of applications in the processing of potential field data. Some simple, synthetic examples in two dimensions illustrate one inversion approach based upon the maxima of the wavelet transform (multiscale edges). These examples are presented to illustrate, by way of explicit demonstration, the information content of the multiscale edges. We do not suggest that the methods used in these examples be taken literally as a practical algorithm or inversion technique. Rather, we feel that the real thrust of the method is towards physically based, spatially local filtering of geophysical data images using Green’s function wavelets, or compact approximations thereto. To illustrate our first steps in this direction, we present some preliminary results of a 3‐D analysis of an aeromagnetic survey.

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We present a model which predicts seismological complexity even with no complexity in geometry or heterogeneity in material properties. Fault slip is numerically modeled using a Dieterich‐type rate and state variable friction law at the planar interface of two infinitely long massless elastic slabs. A constant velocity boundary condition is imposed a distance H from each interface. No geometrical, frictional, elastic, or remote loading variations are allowed in the direction parallel to the plane of the fault. In the numerical solution a periodic boundary condition is imposed, and the fault surface is divided into N subregions each of which is represented by a mathematical point. At these N points, all of which are mutually coupled by discretized two‐dimensional elasticity solutions, the friction law differential equations are numerically solved. The character of the solutions depends on model parameter values and initial conditions. Solutions are found that are periodic, quasi‐periodic, or aperiodic in time; and that are spatially homogeneous for all time, nearly homogeneous except during fast slip events, or essentially inhomogeneous for all time. For given parameter values the solutions have a qualitative character which is nearly independent of initial conditions. At any instant in time these solutions ultimately appear roughly as some superposition of those spatial sine waves which are unstable in a linearized calculation. When spatially complex, the solutions can simultaneously exhibit regions that have steady sliding, large slip rates, and local propagating creep events. Special initial conditions can generate other solutions such as steady propagating creep waves that span the whole fault. The variety of simulated slip motions and long‐term patterns of slip predicted by this spatially homogeneous nonlinear dynamical model suggests a possible role for dynamics, and not just complex geological structure, as a generator of temporal and spatial complexity in seismic phenomena.