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UTIG's very active sea-going program generates large volumes of two-dimensional (2-D) and three-dimensional (3-D) seismic reflection data and offset 3-D ocean-bottom seismograph (OBS) data, which together provide the best available information about significant structures beneath the seafloor. In addition, UTIG scientists collect high-resolution near-offset 3-D data for mapping very shallow subsurface structures. While conventional data processing is carried out using commercial software, UTIG's quantitative geophysics group develops unique algorithms and innovative processing techniques for use by UTIG researchers and other marine geologists and geophysicists in academia and industry. The group's 3-D prestack migration methods, used to yield more robust estimates of velocity, and post-stack processing procedures have been found particularly effective for subsurface imaging. UTIG researchers have also developed a special-purpose migration code, based on the Kirchoff integral formula and ray tracing, to handle large volumes of seismic data. This code is designed to run on parallel machines and a cluster of workstations using message-passing software. Seismic modeling has become an essential companion of data processing as it plays an important role in data analysis and survey design. UTIG researchers have developed several innovative seismic modeling tools that are applicable for assessing 1-D, 2-D, and 3-D Earth models. Each tool iteratively compares a trial Earth model's computations to recorded data and updates the model until an acceptable fit is obtained. This automated model-fitting procedure is based on a general mathematical technique, called inverse theory, which helps to determine model perturbations based on the mismatch between the theoretical and recorded data. Since about 1989, UTIG scientists have pioneered the development of inverse methods to tackle the special problems that accompany multichannel reflection and OBS refraction data. There are four basic types of difficulties encountered inverting these data:
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Of these four difficulties, the last two-the non-linearity and the non-uniqueness problems-are the most troublesome, especially since they complicate efforts to determine the uncertainties of important model parameters. One would like to sample all possible crustal models and choose the best, but this is computationally impossible.
An early approach to this dilemma was the so-called Monte Carlo method, according to which models were selected completely at random. Only by increasing the number of models tested could analysts improve the chance that any one model would correspond closely to the data. A difficulty with the Monte Carlo approach is that it wastes a lot of time testing bad models. UTIG scientists have led the development of two 'directed' random methods, the so-called genetic algorithm (GA) and simulated annealing (SA) methods. Both of these methods allow a considerable degree of randomness in the model selection process, particularly as the inversion begins. But as it proceeds, the allowable class of models becomes more and more restricted to favor those that most nearly match the data. Genetic algorithms are evolutionary: the vectors representing model parameters are combined over many iterations just as genes on biological chromosomes recombine over many generations. The algorithms favor vectors that best fit the data just as natural selection favors organisms that best fit their environments. Simulated annealing methods operate instead according to a thermodynamic metaphor: a so-called temperature parameter controls how large the random variation between subsequent models can be. The temperature is initially set high and many different model types are explored; as the calculation proceeds, the temperature is gradually lowered so that only models that fit the data closely are evaluated. Several other new methods have been developed to compute travel time and ray tracing in laterally inhomogeneous media.
Because geophysical measurements and their mathematical interpretation are crucial when exploring for petroleum and minerals, valuable partnerships have formed between UTIG and industry. One example is SLOSEIS (Slowness Analysis Waveform Inversion and Uncertainty Estimation in Vertical Transverse Isotropy Media), a project under the direction of Mrinal Sen and Paul Stoffa. Their practical objective is to develop velocity analysis, imaging, and seismic waveform inversion software for use by supporting industry partners. Their approach involves adapting some of the UTIG-developed modeling tools mentioned above to provide for anisotropy. 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, fractures in subsurface rocks, and orientation preferences in crystals all cause anisotropic propagation, which is manifested in seismic data as anomalies in travel times, amplitudes, and waveforms. Ultimately, Sen and Stoffa hope to learn what sort of data are needed to best determine anisotropy parameters, how uniquely such parameters can be determined, and, most generally, how important it is when modeling data to provide for anisotropy at all. Committed to investigating the range of models that fit a given data set acceptably rather than a single best-fitting model, they have applied a forward modeling technique based on the reflectivity method and global optimization methods like simulated annealing. They have also cast the inverse problem in a Bayesian framework and estimated the marginal posterior probability density function, the posterior covariance, and the correlation matrices using the Gibbs sampling technique.
