Quantitative Characterization of Crustal Heterogeneity: Implications for Seismic
Wave Propagation
Principal Investigator: John A. Goff
Funded by: Rice University
Projected plans are: 1) to stochastically analyze fine-scale geologic maps in order to
build a statistical database of structural and seismic properties (seismic velocity and
density) of the crust and upper mantle in different tectonic environments, 2) to develop
models which contain lithospheric seismic velocity heterogeneity which is both
deterministic (long wavelength) and stochastic (short wavelength), 3) to relate the
statistics of the stochastic models to the statistics of synthetic seismic wavefields in
the 0.5-40Hz seismic band using full waveform methods for computing synthetic seismograms
and using theoretical methods for analyzing wave scattering, and 4) to conduct parallel
research on seismic field data from different tectonic environments. The crustal scale
models will be useful for predicting long range propagation of crustal and upper mantle
phases associated with earthquakes or large explosive sources, as well as for estimating
the complexity in teleseismic signals introduced by heterogeneities in the lithosphere.
Latest Published Results:
Goff, J. A., and A. Levander, Incorporating "sinuous connectivity" into
stochastic models of crustal heterogeneity: Examples from the Lewisian gneiss complex,
Scotland, the Franciscan formation, California, and the Hafafit gneiss complex, Egypt,
Journal of Geophysical Research, Vol. 101, pp. 8489-8501, 1996. (Copyright: American
Geophysical Union)
Abstract Stochastic models are valuable and sometimes essential tools for
investigating the behavior of complex phenomena. In seismology, stochastic models can be
used to describe velocity heterogeneities that are too small or too numerous to be
described deterministically. Where analytic approaches are often infeasible, synthetic
realizations of such models can be used in conjunction with finite difference algorithms
to systematically investigate the response of the seismic wavefield to complex
heterogeneity. This paper represents a continuing effort at formulating a complete and
robust stochastic model of lithologic heterogeneity within the crust, and the means of
generating synthetic realizations; "complete" implies that the model is flexible
enough to describe all types of random heterogeneity within the crust, while
"robust" implies sufficiently constrained parameterization that an inversion
problem may be well-posed. We use as a basis for investigation geologic maps of crustal
exposures and petrophysically inferred velocities. Earlier efforts at stochastic modeling
have focused on characterization of the univariate probability density function, which is
typically modal (i.e., binary, ternary, etc.), and the covariance function, which is
typically fit with a von Karman function. Here we provide a means of characterizing the
property of "sinuous connectivity" and for generating realizations that possess
this property. Sinuous connectivity is the tendency for individual lithologic units to be
continuous over long and highly contorted paths; there is no means in the earlier modeling
of either characterizing or synthesizing this property. We generate sinuously connective
realizations by mapping regions encompassed by two contours in a Gaussian-distributed
surface into the two values of the binary field. This operation is non-unique, as one can
choose in many ways values for the contours.
Comparison of digitized Franciscan formation (red: melange; white: sandstone) to a
synthetic, sinuously connective binary field with identical second-order statistics.
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