【作者】 谷社峰；

【导师】 吴燕冈；

【作者基本信息】 吉林大学 ， 地球探测与信息技术， 2005， 硕士

【摘要】 地面实测位场异常对应着地下异常源的分布特征,确定异常源的边界、埋深及其它物性参数是反演的主要目的。本文做了大量的正演模型计算,研究并改进了一些国内外最新的位场反演方法,改进了一般教材上常用的模型坐标关系,借用当前几种先进的符号计算工具,推导出了一些重要的公式和结论,基本形成了一套基于欧拉方程和希尔伯特变换位场反演方法,论证了局部波数法在位场数据反演中的可行性、有效性和优越性,编制了相应的计算程序。将地震数据处理中的复数道处理技术通过类比引入到位场数据处理当中,提出了位场中“信号与系统”的概念,讨论了时间域与空间域的“相通性”。借助希尔伯特变换构造解析信号,通过解析信号的相位和波数来研究异常源的空间分布特征。从理论上证明了位场水平导数与垂向导数构成希尔伯特变换对,并将此结论推广到高阶导数。以位场满足的拉普拉斯方程及欧拉方程为基础,推导出了局部波数与位场对应地质体边界、埋深及构造指数之间的关系式,从理论上证明了局部波数独立于地磁倾角的变化,并且它的极大值在地质体边界正上方(在观测面上的投影处)取得,与其它方法相比,它具有更高分辨能力,能更清晰、准确地确定目标体边界在剖面或平面上的投影位置。讨论了局部波数极大值点的坐标与地质体的倾斜角无关,而极大值的大小与深度成倒数关系。因此在理论上局部波数还可以用来判断地质体的倾斜大小,这一点对于断裂构造的位置和倾向的确定有理论指导意义。将本论文所讨论的方法用于实际资料的处理,取得了良好效果。此方法还适用于重力场数据的处理。更多还原

【Abstract】 The distribution feature of the geophysical field is correspond in the synthetic respondence of underground various geological body.Make use of the large volumes of regional potential field data, ascertaining the relation of the geological body and potential field is one of the main contents of the geophysical potential field theoris.Usually the depth to top edge, the location of its edges and physical properties parameters of the source causing the anomaly are the problems that we concern most.In recent years, our country carried on the extensively regional gravity , ground-magnetic and aeromagnetic surveys, acquiring a great deal of gravity and magnetic data with high precision and high resolution, the data almost overlaid a majority of national territory.Therefore make use of these data well and availably, withdrawing the geology information morely, further improving the interpretation’s veracity and precisions, have important realistic meaning. The gravity and magnetic survey take the physical properties( density, magnetism) difference of the geological body as the foundation, reflecting the physical properties distribution feature of the geological body unusually, we can determinate or estimate various physical properties parameter of the geological body on these grounds.From the angle of the potential field information, revealing the regional geology body information by various means, is a potential data processing technology’s general guiding thought.In various processing technology, the derivative play an important role, it can help certain or estimate the shape, location of its edges, depth to top edge, susceptibility contrast of the source causing the anomaly etc.. The total magnetic intensity anomaly corresponds distribution feature of the underground magnetic source causing the anomaly, determinating the location of its edges, depth to top edge of the source causing the anomaly etc. is main purpose of the inversion.Because actually geological body causing the anomaly are what we can only study, in other words, only did the physical properties of the geological body vary in the spacial distribution, the anomaly of physical field can be caused. potential field’s anomaly of surface of earth reflects the spacial distribution feature of the anomaly body( location of its edges, depth to top edge...etc.).So this thesis take withdrawing and identifying the spacial distribution feature of the source causing the anomaly as the emphases, determinating the location of the source’s edges causing the anomaly especially. Since the potential field anomalies correspond to the superposetion of effcets from all causative sources. the stacking and interfering of the potential field are inevitable.while identifying and judging the location of its edges of the potential field source causing the anomaly, unusually according to the measured potential field of earth’s surface is very difficult.But according to the property and characteristicses of the field in mathematics, people usually adopt the mathematical processing methods( such as continuation, making derivative.etc.), separating the interference possibly, determinating the location of its edges of the source causing the anomaly. This thesis regards the derivative technique as principle, using the seismic complex trace processing technology, based on a great deal of job which the other people had done, represents " Local Wavenumber method", reconstructed a few conventional derivatives to some new derivative-tilt derivatives, local wavenumbers.Compare with conventional derivative, the tilt derivative and local wavenumbers have the special advantage.The tilt derivative can enhancement the subtle anomalies, the local wavenumber reserved these enhancemented informations well.It makes use of " automatic gain" function of the tilt derivative, can enhancement and withdraw the weak magnetic anomaly effectively. Appling the Hilbert Transform that usually used in the seismic signal processing to the potential field data processing, by analogy, elaborate the mathematics physics meaning of the signal envelope, local phase, local frequemcy, reveal the basis of the theory by which the local wavenumber can determinate the geolgic bodies’location of its edges, and expand the application of the derivative in the determinating location of its edges theoretically. This thesis did a great deal of computation of forward model, researchs and improves some domestic and international latest potential field inversion methods, improves the coordinate relation which the general teaching material used .According to the relation between potential and field, with current few advanced symbol computation tools, deduces some important formuals and conclusion, becames basically a set of potential field inversion method according to Euler equation and HilbertTransform , proves the Local Wavenumber method’s possibility, efficiency and superiorities in the potential field data inversion. Introducing the complex trace processing technology of seismic data processing into the potential field data processing by analogy, represents the concept--" signal and system" in the potential field, discuss the " homology" of the time domain and space domain.Considering the relation between signal and system, see the researched object( one part of the earth in fact) as a system, it reformed the input of the hypocenter the creation contained some particular information related closesy with that system, is the output of system.As for magnetic field, the intrinsic magnetic field is the input of that system, various geological body with different physical properties and space shapes is magnetizd and again would influence original geomagnetic field. it is also equal to that the system reconstruct the input, the final output is the measured magnetic field. With the concept of the system, we comprehend the concept of the local phase, local wavenumber of the potential field signal very easily, the spacial change of the phase or wavenumber is the result of the system reconstruction, corresponding internal feature of the system.In the system, obviously, various spacial distribution feature of physical properties body correlate closely the phases or wavenumber.Take this as the basis also, structure the analytical signal with the Hilbert Transform, the analytical signal’s phase and wavenumbers can be used to interprete the spacial distribution of the source causing the anomaly.It is proved that the potential field horizontal derivative and vetical derivatives form a pair of Hilber transforms in theory, and extend this conclusion to the higher order derivative. Considering that the observed surface is outside the sources,Laplace’s equation and Euler’s equation are satisfied for the potential field anomalies. A equation ,based on it, can be deduced that indicates the relation among the local wavenumber ,the geological body’s location of its edges, depth to top edge and the structural index.It is theoreticly proved that the location of the local wavenumber’s maximum locates in the projection of the geological body’s location of its edges on the observed surface, and reveal the quantity relation of the local wavenumber’s maximum , the geological body’s depth to top edges and the structural index, Which lay theoretic foundation for applying the local wavenumber further and much effectively in the potential field data processing and interpreting. It is theoreticly proved that the local wavenumber independs on the variety of the inclination of earth’s field,its value has completely nothing to do with the inclination of更多还原