Optimization of Earth crust profiles by collocation

Abstract

All gravimetric problems dealing with the inner gravity field of the Earth are ill-posed, ambiguous. Thus, we must complement the gravity data with other information, particularly with the results of deep seismic soundings and with the notions of the g-'.ologists of the structure of the Earth's crust if we want to solve our problems. Our task, however, is not solved for the actual Earth, but for its model. The most important information for us is the distribution of densities within the Earth's body. Thz construction of an uniform normal vertical density profile is of no use, since at least in the upper layers of the Earth's body the density is not a function of the d¢-pth only, but depends on the geological structure of the crust and varies from point to point. According to our opinion it would be better to use a different procedure. We have at our disposal the characteristics of the outer Earth's gravity field, and we are able to estimate its accuracy. We know the depths of the interfaces discovered by deep seismic soundings and, finally, there are some geological hypotheses about the structure of the Earth's crust in the place under consideration. Our task is now to process these three quite different sets of information using a suitable mathematical apparatus. We consider the new methods of mathematical statistics to be the most expectant for this purpose. In preparing for the extensive task mentioned above, we started with a quite simple case. We tried to derive a mathematical aid for optimizing the Earth's crust profiles, designed by seismologists and geologists. The collocation [1] was used to solve the problem. This method includes adjustment, filtering and data prediction.