Parallel Algorithms for Solving Inverse Gravimetry Problems: Application for Earth’s Crust Density Models Creation

The paper describes a method of gravity data inversion, which is based on parallel algorithms. The choice of the density model of the initial approximation and the set on which the solution is sought guarantees the stability of the algorithms. We offer a new upward and downward continuation algorithm for separating the effects of shallow and deep sources. Using separated field of layers, the density distribution is restored in a form of 3D grid. We use the iterative parallel algorithms for the downward continuation and restoration of the density values (by solving the inverse linear gravity problem). The algorithms are based on the ideas of local minimization; they do not require a nonlinear minimization; they are easier to implement and have better stability. We also suggest an optimization of the gravity field calculation, which speeds up the inversion. A practical example of interpretation is presented for the gravity data of the Urals region, Russia.

A Stable and High-Precision Downward Continuation Method of Magnetic Data

Downward continuation is an effective technique that can be used to transform the magnetic data measured on one surface to the data that would be measured on another arbitrary lower surface. However, it suffers from amplitude attenuation and is susceptible to noise, especially when the continuation distance is large. To solve these problems, we present a stable and high-precision downward continuation method combining the ideas of equivalent source technique, Tikhonov regularization, radial logarithmic power spectrum analysis, and constrained strategy. To implement this method, the observed data is used to construct the equivalent source in the study area, and the small amount of measured magnetic data at the lower surface (relative to the original observation surface) is employed to constrain the calculation procedure simultaneously. Then the magnetic data at the target surface can be obtained by using a forward calculation procedure instead of the risky downward continuation procedure. The proposed method is tested on both synthetic model data and real magnetic data collected in the South China sea. Various obtained results demonstrate that the method reported in this study has higher accuracy and better noise resistance than the traditional downward continuation methods.

Interpretation Method of GATEM Data based on PID Controller Iteration Downward Continuation Method

The Ground-source Airborne Time-domain Electromagnetic (GATEM) system has advantages for high efficiency and complex areas such as mountainous zone. Because of ignoring the impact of flight height, the section interpretation method seriously affects the interpretation and imaging accuracy of shallow anomalies. The PID controller iteration downward continuation method is proposed. Based on the original iteration continuation method, the differential coefficient and integral coefficient are added. The result shows that the new method remarkably decreases the iteration number, and the accuracy are verified by comparison with the numerical integration solution. The PID controller iteration downward continuation method is applied to the interpretation of GATEM data. For synthetic data, the interpretation results of continued electromagnetic response are closer to the true model than the z = 30 m interpretation results. The method is also applied to GATEM field data in Yangquan City, Shanxi Province, China. The interpretation results perform reliability using PID controller iteration downward continuation method in a GATEM field.

Functional approach to the search for quasi-optimal value of regularization parameter in downward continuation of potential field

The Tikhonov regularized approach to the downward continuation of potential fields is a partial but strong answer to the instability and ambiguity of the inverse problem solution in studies of applied gravimetry and magnetometry. The task is described with two functionals, which incorporate the properties of the desired solution, and it is solved as a minimization problem in the Fourier domain. The result is a filter in which the high-pass component is damped by a stabilizing condition, which is controlled by a regularization parameter (RP) — this parameter setting is the crucial step in the regularization approach. The ability of using the values of the functionals themselves as the tool for RP setting in the comparison with commonly used tools such as various types of LP norms is demonstrated, as well as their possible role in the source’s upper boundary estimation. The presented method is tested in a complex synthetic data test and is then applied to real detailed magnetic data from an unexploded ordnance survey and regional gravity data as well to verify its usability.