Study On The Implementation Techniques Of The Quasi-analytical Approximation Theory Of Acoustic Scattering

Regarding the exploration seismology, the seismic wave scattering theory is a kind of powerful tool for surveying underground three dimensional heterogeneous, regarding the oil gas and the mineral exploration, the heterogeneity often takes to us a bigger interest and the hope, therefore the research of seismic wave scattering is of the very important value. At present, the methods for studying the earthquake wave scattering bring about the problems of the computer memory space and the calculating time which limit the application of each kind of research techniques. The original intention putting forward quasi-analytical approximation lies in to solute the contradiction between the scale of actual seismic survey and the application of tradition research methods. The most attractive advantages of quasi-analytical approximation are that it avoids calculating ultra-large equation systems thus save the computing time and enhance calculating efficiency. What's more, the need of computer storage is less than the tradition simulating methods so that greatly reduced the computation cost. it builds the theory foundation for the seismic wave forward simulating research. Therefore, it is very significant to research the quasi-analytical approximation at present stage.Based on the summarizations of seismic scattering theory, the studying significance and the present development situation of quasi-analytical approximation, this thesis begins with scattering integral equations, mainly discusses the elastic scattering integral equations and acoustic integral equations. In the process of elastic integral equations discussion, it focuses on the summarization of the researches on the elastic scattering, including elastic equations of motion, Green's dyadic, scattering by a surface of discontinuity, integral formulas for anisotropic media, body scattering and surface scattering. For the acoustic scattering, the thesis lists the integral formulas in the conditions of plane and irregular surface. Based on these formulas, following, the thesis introduces the principle of quasi-analytical approximation. According to the implementation of algorithm, then mainly discusses the detail problems in the implementation, including Green's function, the processing method of the singularity, the generalized sources of isotopic media and anisotropic media, varied methods of multiple numerical integrals, the principle of FFT algorithm and the storage of wave field frequency-series. Finally, the paper gives the quasi-analytical approximation forward modeling examples about the cube in the condition of the half-space and whole-space background of homogeneous media. It offers a single shot wave field maps, contrasts these maps and then interprets and analysis of the wave field fluctuations in the various origins of the phenomenon. We hope to deeply understand the seismic wave theory. Based on the numerical simulations of the models, the following conclusions can be provided:1) It is feasible to study the acoustic scattering problems by the means of the quasi-analytical approximation. Its precondition is that the scattering field is a linear function of the background field in the non-uniformity. This assumption circumstances, the accuracy of the final results can be guaranteed, otherwise the results will have significant error and the method is not suitable to be used to study on acoustic scattering problems.2) Viewed from the principle of the method, the quasi-analytical approximation avoids solving algebraic equations and bases on multiple integrals, so that it is easy to implemented, and therefore from the geological model for the large-scale numerical simulation, computer storage space requirements and calculation time are relatively small, reflects the superiority of the method. Therefore, the required computer memory space and computation time are relatively small in the numerical simulation for the large-scale geological models which reflect the superiority of the method.3) In order to be easy to implement the algorithm, we should pay attention to choose the background medium and the treatment of Green's function in the process of simulation. 4) From the perspective of the amount of computation, the time spend on the calculation depends primarily on the modeling scale, the scale of non-uniform, non-uniform and the total number of observation points in the source-wave spectrum sequence length. If the simulating region is greater, the selected non-uniform is bigger, with more internal observation points and the longer wave spectrum sequence of the source, the more time is consumed undoubtedly. So in the simulation process, we should select narrow band spectrum of wave source and the subdivision of the non-uniformity is not suitable too small. At the same time, the selection of the numerical calculation method for the multiple integral is also an important factor which affects the efficiency.5) From the perspective of the calculation accuracy, the implementation process depends on the truncation error of the numerical calculation methods for the multiple integrals. At the same time, the stability of calculation methods should also be considered. From these two factors, ultimately selecting the appropriate multiple integral numerical methods is to guarantee the key of accuracy.6) From the simulation results, there clearly reflects the characteristics information about reflected waves on the up and down interfaces of the non-uniform. There still exists the scattering wave and diffraction wave from the edge and the angular point, as well the multiple scattering wave in the non-uniform, but contrasting to the reflected wave, the energy of these fluctuations is weak. By changing the location of the source, the wave field emerged the asymmetry, from the asymmetry, we can judge the the relative position of the source and non-uniformity. This will be a very important guiding significance for determining the non-uniform distribution.In this paper, the results of research on the value embodies in the following four points: First, it provides a new idea for the simple and efficient implementation of acoustic scattering on the large-scale numerical simulations Second, it provides adequate experimental data for the research of acoustic scattering problems Third, it lays the theoretical foundation for the high-dimensional speed and the density inversions Fourth, it provides a new approach for the elastic wave scattering studies.