GENERALIZED LINEAR INVERSION OF 2.5 - DIMENSIONAL GRAVITY AND MAGNETIC ANOMALIES (WISCONSIN, NEBRASKA, MEXICO, NORTH CAROLINA)

An iterative generalized linear inversion (GLI) routine based on a 2.5-dimensional model has been developed for interpretation of potential field data. The inversion process is accomplished by minimizing an objective function that expresses the mean square error between observational data and theoretical values of the resultant model.; All problems treated are simultaneously underdetermined and overconstrained. Thus unacceptably high variance of model parameters may occur, if one intends to fit the observation data as precisely as possible. Statistical analysis emphasizing on influence of data errors, magnitude of eigenvalue, and accuracy of eigenvectors has been made in order that an optimum inverse can be constructed.; The inversion routine is designed to solve the geometrical shape of the subsurface structures only, so the density/susceptibility contrast is assumed to be known. To understand the significant features of the solutions solved by this technique a series of tests have been performed.; Also developed is the nonlinear inversion technique in which the quadratic terms of the Taylor series expansion of forward formulae are involved in the inversion procedure. The problem is dealt with in wavenumber domain for easier evaluation of the second-derivative terms.; To illustrate the capabilities of the GLI method, we solved several real data problems of various geologic situations. In northern Mexico gravity profiles were used to study the deep crustal structures of the Rio Grande rift and Sierra Madre Occidental, as well as an igneous body and a Cenozoic basin. Three dimensional models of two igneous bodies, one in Wisconsin, the other in Elk Creek of Nebraska, were constructed based on the GLI solutions of the profiles traversing the bodies. Gravity inversion was also used to study the data from a buried feature in the Broken Bow uplift area of the Ouachita foldbelt trend. In the last example three gravity and magnetic profiles were analyzed to delineate the Sanford basin in North Carolina.