UTIG RESEARCH PROJECTS ARCHIVE

Principal Investigator: Mrinal K. Sen and Jay Pulliam

Funded by: National Science Foundation, Earth Sciences

Project Summary

Most crustal rocks of interest to exploration geophysics are either inherently anisotropic or behave as anisotropic materials when sampled by seismic waves. Thin layering in sedimentary rocks, preferred orientation of crystals or the presence of fractures in subsurface rocks cause anisotropic wave propagation in rock layers. Anisotropic propagation is manifested in seismic data as anomalies in travel time, amplitude and waveforms. Observations of such anomalies at all scales of resolution (exploration to whole earth) have been reported in the literature.

Here we propose a rigorous investigation of anisotropic parameter estimation from such observations using recently developed methods of geophysical inversion. We will use a forward modeling technique based on the reflectivity method and global optimization methods such as simulated annealing and genetic algorithms for the parameter estimation problem. Prior analytic and numerical investigations reveal that the dependence of model parameters on seismic data for anisotropic media is highly nonlinear and, therefore, a nonlinear, global optimization method is appropriate for this purpose. Crucial questions we would like to address include

• How uniquely can we determine anisotropy parameters with a given data set?
• What sort of data is needed to best determine anisotropy parameters?
• How important is it to include anisotropy in modeling a given data set?

We will address these questions by casting the inverse problem in a Bayesian framework and estimating the marginal posterior probability density (PPD) function, the posterior covariance and correlation matrices by the Gibbs' sampling technique.

Ultimately we intend to investigate the range of models that fit the data acceptably rather than find a single, best-fitting model. By conducting a global search and estimating the PPD we can not only catalog characteristics of models that are consistent with the data, but proscribe characteristics that are required by the data. This offers a means by which, first, physical implications of acceptable models may be ranked as to their priority for explanation and, second, the usefulness of a given data set in answering geophysically interesting questions. For example, in the first case, if modeling results for a given data set include anisotropic and isotropic models with roughly equal preferences, the more complicated case of anisotropy would not immediately require an explanation from mineral physicists or geodynamicists. Instead, one would conclude that the data used do not discriminate adequately between isotropic and anisotropic models and seek either additional or different data that do discriminate adequately. Even if no additional data are available, knowing the sorts of features acceptable models must have represents the best contribution seismologists can make to explaining Earth phenomena. Practitioners of other disciplines, such as geodynamic modeling, experimental mineral physics, gravity or geomagnetic field modeling or, in the case of exploration- and regional-scale problems, geologists and decision makers, will then know where to concentrate their efforts to narrow the field further.