A method for inversion of 1D vertical soundings of gravity anomalies

We have developed a method to interpret potential fields, which obtains 1D models by inverting vertical soundings of potential field data. The vertical soundings are built through upward continuation of potential field data, measured on either a profile or a surface. The method assumes a forward problem consisting of a volume partitioned in layers, each of them homogeneous and horizontally finite, but with the density changing versus depth. The continuation errors, increasing with the altitude, are automatically handled by determining the coefficients of a third-order polynomial function of the altitude. Due to the finite size of the source volume, we need a priori information about the total horizontal extent of the volume, which is estimated by boundary analysis and optimized by a Markov chain process. For each sounding, a 1D inverse problem is independently solved by a nonnegative least-squares algorithm. Merging of the several inverted models finally yields approximate 2D or 3D models that are, however, shown to generate a good fit to the measured data. The method is applied to synthetic models, producing good results for either perfect or continued data. Even for real data, i.e., the gravity data of a sedimentary basin in Nevada, the results are interesting, and they are consistent with previous interpretation, based on 3D gravity inversion constrained by two gamma-gamma density logs.