High-Order Finite-Difference Numerical Analyses Of 2.5-D Acoustic Wave Equation

In order to carry out numerical simulation of complex reservoir and resolve its exploration and development, modeling for 3-D seismic wavefield is still computationally intensive. With the rapid advancement of computer hardware, researches on forward seismic modeling algorithm for 3-D seismic wavefield and its application has recently become one of the hot topics in such field. Undoubtedly, 3-D seismic data processing and interpretation through large -scale seismic exploration will be a arduous progress,even for parallel computers. Therefore, as far as general seismic data processing is concerned, imposing 3-D modeling technology to seismic wavefield modeling with exploration scale is unprepared. On the contrary, 3-D modeling of theoretical modeling is easy to implement based on the current computer hardware configuration. Accordingly, the original intention put forward 2.5-D seismic wave simulation consist in settling inconsistency between the scale of actual seismic exploration, the urgent demand of energy sources and the development rate of the hardware. the 2.5-D approximation is a reasonable compromise in terms of the practical situation. The most attractive advantage of 2.5-D case is that it has capable of numerical computation of the 3-D wavefield exactly without parallel computer or computer groups. In addition, so-called 2.5-D situation is very suitable for PC due to the computer memory requirement much smaller than that of 3-D case In a word, nowadays it is a significative subject to do extensive and detailed research work for 2.5-D wave propagation. Based on the summarizations of advance of researches on 2.5-D situation, this thesis focused on the inherent features of 2.5-D approximate equation method, 2.5-D quasi-cylindrical method and 2.5-D Fourier method. The involved research contents in this thesis include three aspects, as follows:1) Adoption three simulation techniques of 2.5-D case to design the corresponding 2.5-D acoustic wave equation respectively;2) Numerical simulation with each 2.5-D wave equation using regular-grid and staggered-grid finite difference method, the stability condition and restricted condition of numerical dispersion are provided. Much attention is paid to the analysis on the key points about modeling;3) Through single shot seismogram, zero offsets section, VSP profile, snapshot by modeling of geological structural model, interpretation and analysis various fluctuations concerning structural model and causes so as to better comprehend the theory of seismic wave propagation;4) Accuracy analysis for 2.5-D modeling methods, involving amplitude and waveform;5) Comparison of computation cost, such as the CPU time needed by lower and higher finite-difference operator and that of three methods of 2.5-D modeling; Although basic principles of three technologies of 2.5-D modeling aredifferent one another, the common purpose is to calculate 3-D wavefield precisely and greatly reduced computation cost. Here, after 2.5-D modeling for given geology model, some conclusion can be provided, as follows:1) 2.5-D approximate acoustic wave equation shows a spatially and temporally damped nature of design.2) 2.5-D quasi-cylindrical method is available not only for wavefield numerical simulation of axisymmetric models, but also for non-rotationally symmetric situations. In other words, the method can model the wave propagation on both sides of the source location on the measurement line.3) 2.5-D Fourier method apply the spatial Fourier transform to the out of plane direction and impose finite difference method to the other two spatial coordinate and time partial derivative, also use the medium symmetry. Actually, this method is part of hybrid numerical methods, and in nature it is as good as 3-D numerical method.4) The rank of numerical solution accuracy in sequence is as follows from high to low: 2.5-D Fourier method, 2.5-D quasi-cylindrical method, 2.5-D approximate equation method. Except 2.5-D Fourier method, the others exists waveform alteration. The effect on waveform of 2.5-D quasi-cylindrical method is much stronger than the rests.5) Computation cost of 2.5-D Fourier method mainly depends on the number of wavenumbers. In general, it requires long computation times comparable to that of other 2.5-D modeling methods. To overcome this problem, we propose two approaches—2.5-D pseudo spectral methods or by parallel hardware for large-sized problems. The most economical approach for modeling of 3-D field amid those mentioned above is 2.5-D quasi-cylindrical method.6) After tradeoff for integration of above factors, an important conclusion has been performed that the best scheme for 2.5-D situation is 2.5-D Fourier method. It is necessary to select an optimal method for actual surveys according to the complexion of geology and geophysics.The potential application for results of the research in this thesis has three main effects. Firstly, carrying out integrated comparison with the advantages and disadvantages of various 2.5-D methods; Secondly, resulting maps of forward modeling provides adequate academic research datum for new development and future direction of 2.5-D wave modeling and new method and thought on simple and efficient implement for 3-D wavefield simulation; Thirdly, convenience for researchers to choose suitable 2.5-D method in the light of seismic survey with data acquisition, the precision of numerical solution and computation time as well as other limited conditions.