Mathematical Methods Of Geophysical Exploration

Geophysical methods is a rapidly developing world technology methods, but also a highly technical subjects observed. At present seismic exploration, radioactive exploration, gravity prospecting, electrical prospecting, magnetic prospecting are the main methods of geophysical exploration . Geophysical exploration methods in the analytical continuation method, Fourier series and transform, time-frequency analysis, differential settlement spectral difference method is frequently used mathematical methods.This is the application of mathematical methods in geophysical exploration that are reviewed. Analytical continuation in magnetic exploration is the main method of information processing, analytical continuation into analytic continuation of upward and downward analytical continuation. Upward continuation can be eliminated by surface or shallow sources of magnetic interference.The magnetic anomalies become smoother, and magnetic anomalies shows a regional anomaly. You can get up the value of analytical continuation (?)It can be obtained by analytical continuation of space in the magnetic anomaly contour, whereby you can analyze the source of magnetic body shape and occurrence and distribution in space and thus can obtain the desired results. Zhu Lin, Liu Huai-shan analytical continuation applications such as Peach Village magnetic exploration of information processing, through the upward and downward continuation Continuation method determines the location of the fault zone. Wen Yi-bo, Shi Xiao-ping exploration through the magnetic detection of underground caves, the application Analytical continuation method of processing information, to receive the basic structure of the cave.Modern developments in seismic exploration is one of the fastest growing geophysical. Oil and gas structures for exploration of oil and even directly to the main geophysical methods. digitizing of seismic data processing, it will involve many fundamental issues, for example, the problem of wavelet, Z transform problem, Fourier transform problems, issues related to computing. In this article we only describes the problem sub-wave, seismic exploration in the main wave equation, wave equation in the Fourier series and the main application Fourier transform, resulting in (?)These formulas take q different values, the waveform of the information obtained through the computer to obtain geological information. Zhang Tai-zhou, bears strong chapter on the use of seismic stratigraphy, using Fourier transform method in the isolation of the different seismic records of Swiss modes Ray surface wave, and further to ground information.Time-frequency analysis is an emerging geophysical exploration of signal processing methods. Hilbert-Huang Transform is a time-frequency analysis of the main tools. Hilbert-Huang transform of the amplitude and frequency are a function of time, and in the Fourier transform ,the amplitude and frequency values are fixed, Hilbert transform for the Fourier transform to break the limitations, which Hilbert transform for the extraction of non-stationary signal characteristics have a distinct advantage. in the time-frequency analysis is often used in time-frequency distribution of Cohen class, Cohen class time-frequency distribution can be applied to the array of acoustic Acoustic logging data measured by time-frequency analysis, the distribution of oil and water layers were analyzed. Cohen class time-frequency distribution of the expression is(?)dudτdθTake (? )Time-frequency distribution is obtained by Cohen-Williams distribution, the Cohen-Williams distribution of the corresponding expression for (?)By Cohen-Williams distribution of the nature of the array wave train acoustic logging data, the actual calculations, to verify the Cohen-Williams distribution approach for multi component of the acoustic logging signal time-frequency distribution and characteristics of performance effectiveness. Zhu-wen Wang, Jing-hua Liu, Chun-yan Nie application of Hilbert-Huang transform array acoustic logging signal time-frequency analysis of the characteristics of non-stationary signal a good show. Zhu-Wen Wang, Jing-Hua Liu, Chun-yan Nie application of Choi-Williams time-frequency distribution of the array acoustic logging signal for time-frequency analysis of dense rock and broken rock detection, fully reflects this time-frequency analysis of the structure for different types of lithology Response has a good ability to distinguish and identify.Acoustic logging is one of the basic means of geophysical exploration, acoustic logging is widely applied to petroleum exploration and development and engineering. sonic logging is a two-dimensional spectrum of sound waves through the calculation of two-dimensional spectrum by acoustic sound pressure waveform , The analysis can reflect changes in borehole acoustic wave propagation, but also directly reflects the hard formation and soft formation acoustic propagation characteristics. in the calculation of two-dimensional spectrum in the process of (?)This can be two-dimensional spectrum ( )Αω, kz. NMR logging is the main method of geophysical exploration, solution NMR spectral logging data processing method is the main tool, the application can deal with the well solution spectral signals recorded information, you can obtain the matrix equationY = PX Solutions (?)Given differentαvalues, you can know the level of the standard deviation of fit. Yuechong Yang, Zhu-Wen Wang, etc., the use of two-dimensional spectral analysis of borehole acoustic logging changes in response to the impact study finds a different hole diameter on the acoustic wave propagation, which has a great influence, Through the research of information, formation characteristics can be drawn. Liu Hongjiang, Zhu-Wen Wang, through the use of nuclear magnetic resonance well logging method, based on singular value decomposition of the NMR spectrum of logging solution algorithm, Processing the data, making the exploration formation skeleton to avoid the impact on low porosity, low resistance and low permeability such as the evaluation of complex formation better and better distinguish the oil, gas and water layer.Finite difference method for solving differential equations is an important method. the investigation of radon concentration, the use of a mathematical model, we obtain differential equations, then apply the finite difference method. Through the measurement of radon concentrations of elements to predict th existence of underground geological structures, potential areas of geothermal resources and the enrichment of uranium ore district and other geological information, this information can be judged according to a variety of geological formations, geological resources and hazards. Jing-Hua Liu, Zhu-Wen Wang, through the active fault distribution of radon concentration in the soil to establish a numerical simulation of radon transport equation, finite difference numerical solution method for solving equations, clear analysis of radon concentration anomalies and the geological formation of the relationship.