The Research On The Equivalent Source Method For The Curved Surface Processing And Transformation Of Potential Field In The Frequency-domain

At present, China has launched a nationwide 1:50,000 survey of mineral resources. In this survey, the 1:50,000 magnetic observations on the ground and through the sky need to be conducted. The 1:50,000 magnetic observations is medium, large scale based. Topography terrain and the aviation flight have great impact on it. In the geophysical gravity and magnetic measurements, the observation surface is always a curved surface. Sometimes it is a discontinuous curved surface(for example, at the stitching position of different aeromagnetic observation data). The gravity and magnetic data that on these measuring points are still on the original observation points(curved surface) after the correction. This situation causes two difficulties to the gravity and magnetic anomaly’s interpretation. The first one is the mapping difficulty, especially in the aeromagnetic explanation. Currently, the aeromagnetic observation flight follows the near-surface principle. Different flight heights are used for mountain area and the flatland area. It will cause “fault terrace” when using observation data with different height or different time. The aero gravity data has the same problem. In order to draw a unity map, “leveling” method is used to “unified” different data. This will cause the “false anomaly”. The second difficulty is that qualitative interpretation is based on the gravity and magnetic anomaly features on the flat surface, rather than a curved surface in reality. The anomaly features are much more complicated and different than the anomaly features on a flat surface. If we take the anomaly on the curved surface as the anomaly on the flat surface, the interpretation results will deviate from the truth. So setting up a processing and transformation system with strong adaptability, high precision and fast calculation speed on curved surface is necessary for the real data.This dissertation is supported by the study of “Curved Surface Processing Demonstration of the Aeromagnetic Data” under the grant of(No.1212010913037) “1:50,000 Aeromagnetic Survey in Xinjiang East Kunlun Qimantage region” of the Ministry of Land’s project “High precision Aero Geophysical Survey”, and is jointly funded by the central universities fundamental research funds(No.2014G3262010) and the Chang’an University basic research support program special fund. Taking the strong adaptability, high precision and fast calculation curved surface processing and transformation method as the research objectives, the “basic theory- technical measures- software design- model testing- actual data processing” as the mainline, the theoretical research and the practical application research of the equivalent source method for the curved surface processing and transformation of potential field in frequency-domain were carried out. This study proposes the frequency-domain particle layer method. By unifying it with the frequency-domain dipole layer method, the equivalent source method is formed Equivalent source parameter inversion methods and the processing and transformation methods in a variety of computing surface conditions are derived. Related technical measurement methods are also studied. Software is designed using the structured programming idea, and the high-level programming language Fortran90. Using the theoretical model, the adaptability, accuracy and calculation speed of the frequency-domain equivalent source method are tested from four aspects: the source distribution, the observation surface terrain, the equivalent source arrange and the amount of data. Using a small area measured gravity data of Shanxi province and a small area measured aeromagnetic data, we tested the stability of the frequency-domain equivalent source method. Main research results of this dissertation are:(1) The frequency-domain particle layer method is proposed. It is suitable for the processing and transformation of the gravity anomaly and it’s any order mixed directional derivative. The frequency-domain dipole layer method is suitable for the processing and transformation of the magnetic anomaly and it’s any order mixed directional derivative. The frequency-domain particle layer method and the frequency-domain dipole layer method are unified to form the frequency-domain equivalent source method. This dissertation did systematic research on the basic theory of the frequency-domain equivalent source method. Research results show that the frequency-domain equivalent source method has the advantages of strong adaptability, and fast calculation speed. The only shortcoming of this method is that it cannot be used for the “strong topography” situation.(2) Related techniques of frequency-domain equivalent source method are improved for the curved surface processing and transformation of the potential field data. These techniques include the series stable and fast convergence technologies for the forward, the series stable and fast convergence technologies for the inversion of equivalent source parameters, single point fast Fourier transformation. Focus on the research of the filter characteristic of the minimum curvature difference iteration scheme, the research results show that non in situ iteration is not convergent, the in situ iteration is convergent. The research improves the minimum curvature net data expending edge technology, interpolation technology and gridding technology. The frequency-domain equivalent source arranges measure and the block processing measure are carried out to improve the computational accuracy and calculation speed. These technical measures not only improved the stability, adaptability and the accuracy of the frequency-domain equivalent source method for the processing and transformation of potential field data on curved surface, but also improve the efficiency.(3) Software of the frequency-domain equivalent source method for the processing and transformation of potential field data on curved surface using the structured programming idea is designed. Fortran90 high-level programming language is used. This software can use the potential field data(the gravity anomaly, magnetic anomaly and their any order mixed directional derivative) directly for processing and transformation on curved surface. It can realize the continuation, constituent transformation, directional derivative transformation, magnetization direction transformation, and magnetic source gravity anomaly calculation. The method can also realize the continuation and other transformation at the same time. The processing and transformation results have high accuracy, fast calculation speed and good stability.(4) Theoretical model test results show that: the frequency-domain equivalent source method is greatly influenced by the vertical discontinuous observation surface terrain, the influence of the point distance and the line distance is much smaller, the influence of the field source distribution is the smallest, and influence of the random disturbance is very small too.(5)Experiments on the processing of the actual measured data shows that, the frequency-domain equivalent source method can be used for processing and transformation of the actual measured gravity anomaly and magnetic anomaly(aeromagnetic anomaly) on curved surface.The main innovations of this dissertation are:(1) Proposed the frequency-domain particle layer method, unified it to the frequency-domain dipole layer method and form the frequency-domain equivalent source method. This dissertation did systematic research on the basic theory, technical measures, software design, theoretical model test, as well as the processing and transformation of the actual measured data.(2) Studied the convergence of the minimum curvature difference iteration scheme using the Fourier spectrum analysis theory. The results show that non in situ iteration is not convergent, only the in situ iteration is convergent. The iteration direction don’t affect the convergence of the minimum curvature difference iteration scheme. This improved the minimum curvature net data expending edge technique, interpolation technique and gridding technique of the random data.(3) Techniques and measures for the frequency-domain equivalent source stratification arrange and the block for the solving of the frequency-domain equivalent surface density are proposed. Solved the problem for the processing and transformation of large amount of data on curved surface.