Methods and programs for inverse modeling of underdetermined sets of gravity data
Vaughan, Raymond C.
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This work creates a comprehensive and systematic framework for inverse modeling of underdetermined sets of gravity data. Its conceptual basis, including geometric coefficients used in both Monte Carlo and vector methods, is implemented by a series of Fortran 95 programs. The double-precision programs incorporate linear algebra procedures and operate with low RMS error on a shared set of input-output files. The Monte Carlo algorithms, when combined with an appropriate loss function, produce a multitude of exact density solutions for the subsurface that converge toward a common solution in a given underdetermined problem. A subsurface grid of discrete subcells is assumed. Additional flexibility is obtained by recharacterizing modeling problems in an N -dimensional vector space, where N refers to the number of subcells in a given model. Solutions lie within a p -flat in this N -dimensional space, where p is the difference between N and the number of observations m . U - and Z -vectors that exist within the vector space are characterized, and other relationships and transformations are described, including the derivation of minimum-norm solutions. Attention is given to noise and data precision, yielding some useful results and identifying other problems that require further work. In models that use precise data, Monte Carlo methods are shown to achieve good resolution in all three dimensions , contrary to the prevailing geophysical opinion that gravity solutions are inherently unable to resolve the depth of modeled features. Effects of noisy data are evaluated and reviewed, and the work previews additional work needed to deal effectively with quantization noise , the well-known phenomenon in analog-to-digital signal processing that arises in gravity modeling when grids imposed by the model do not entirely match the subsurface geologic features being modeled.