A Fast Density Inversion Method Based On Nonlinear Function

Density inversion is an important method of gravity data processing and interpretation.The gravitational field is the natural physical field of the earth,and the gravitational anomaly field is the disturbance of the gravitational field,which is produced by the universal gravitation of the underground density difference.Therefore,the underground density difference can be quantitatively calculated through gravity anomalies,and this calculation process is density inversion.Density inversion mainly includes two steps: 1.Discretize the study area,and obtain the sensitivity matrix of the unit density discrete cell response at the observation point;2.Use the sensitivity matrix to invert the observation data to obtain the density value of each discrete cell.Therefore,the distribution of underground density can be obtained by the density inversion method with less prior information,and the method is widely used in gravity data processing.Since the number of discrete units and the number of observation data points are usually large,a large sensitivity matrix will be obtained.The 100×100 observation data and 100×100×100 discrete cells need to build a sensitivity matrix of 37.25 GB.In the most of the inversion methods,the number of discrete cells is often less than the number of observation data points and the inversion calculation needs to be solved iteratively.This leads to the density inversion requiring a large number of matrix operations.Therefore,since this method was firstly proposed,solving the problem of its computational efficiency has been one of the keys to its research.With the development of multi-dimensional gravity measurement technologies such as satellites,aviation,ground,and wells,the data volume and data accuracy of gravity data are increasing rapidly,and the demand for precise inversion of large data volumes is also increasing.Therefore,improving the calculation speed of inversion is a very important research topic.Studies have shown that the density changes of underground materials are continuous rather than discretely distributed.Therefore,the density distribution can be expressed as a function that changes continuously with the spatial position.This method is widely used in interface inversion and forward modeling.In this paper,a nonlinear polynomial fitting density inversion method is proposed,which used a polynomial to represent the density variation of prismatic cells in a certain space.The computation of each cell is substituted by the computation of the coefficients of nonlinear polynomial,and the nature that the number of nonlinear polynomial coefficients is less than the number of cells is utilized to significantly improve inversion efficiency.The undulating terrain areas often have complex tectonic movements and are enriched in a large number of mineral resources.With the improvement of the detection level,the research on the undulating terrain areas is the focus of current geophysical research work.In order to better reflect the topographic undulations of the study area,the density inversion often uses the simplest three-dimensional body—tetrahedron to discrete the study area.However,this discrete method will obviously increase the number of discrete cells,thereby increasing the amount of calculation for density inversion.It is often difficult to achieve fine inversion calculations for large amounts of observation data.Therefore,this paper applies the space-density function to the density inversion of the undulating terrain area,which is of great significance for the fine density inversion of the undulating terrain area with a large amount of data.With the development of high-performance computers,parallel technology has been widely used in many computing fields.The main calculations in density inversion are operations such as matrix product,and have good parallelism.Therefore,at the end of this paper,parallel technology is used to optimize the algorithm,which further improves the computational efficiency of density inversion.