A least-squares minimization approach to depth determination from numerical horizontal gravity gradients

摘要

The sphere and the horizontal cylinder models can be very useful in quantitative interpretation of gravity data measured in a small area over buried structures. Several graphical and numerical methods have been developed by many workers for interpreting the residual gravity anomalies caused by these models to find the depth of most geologic structures. Excellent reviews are given in Saxov and Nygaard (1953) and Bowin et al. (1986). The numerical approaches (Odegard and Berg, 1965; Gupta, 1983; Sharma and Geldart, 1968; Lines and Treitel, 1984; and Shaw and Agarwal, 1990) may have advantages in theory and practice over graphical depth estimation techniques (Pick et al., 1973: Nettleton, 1976; Telford et al., 1976). However, effective quantitative interpretation procedures using the least-squares method based on the analytical expression of simple numerical horizontal gravity gradient anomalies are yet to be developed. The aim of the present study is to develop an interpretive technique based on fitting a simple model convolved with the same horizontal gradient filter as applied to the observed Bouguer gravity data. The depth determination problem from observed horizontal gravity gradient anomaly is transformed into the problem of finding a solution of a nonlinear equation of the form f(z) = 0. Formulas are derived for the sphere and horizontal cylinder. Procedures are also formulated to estimate the radius of the buried structure.