A Study On Characteristics Of Nonlinear Wave Propagation In Solid Medium And The Lithologic Analysis

Along with the rapid growth of economy, the energy issue has become the focus of increasing concern at home and abroad. New methods and techniques are being developed to support the detection of energy.Seismic method, as a detection way, is important to understand the information of earth's interior resources, especially the detection of deep crustal structure. In recent years, seismic method develops rapidly, but more precise information and data are needed to ensure the economy and effectiveness of detection.Therefore a great number of works are done in two aspects. On one hand, around previous theories, more research is made on methods of improving resolution and signal-to-noise ratio(SNR), and these new results are applied into practice; on the other hand, based on the advanced theories of other disciplinaries, new theoretical research are made and applies into practice. For example, the wavelet theory is used to improve the resolution, fractal theory is to prospect the mines and nondestructive examination (NDE) of nonlinear wave. And good results are achieved.The research on nonlinear wave can be dated from middle of 19th century, and it has been realized that the nonlinear effect in solid medium is greater than that in fluid medium. The nonlinear effect in rocks relates not only the nonlinear effect itself, but also the character and crystal lattice of the rocks. And it is an effective way to solve the problem of exploration accuracy and to improve the resolution. This linearness of solid medium is the focus of linear theory and also focus of the exploration practice. Therefore it is necessary to research the relationship between nonlinear wave propagation and lithologic characters.The paper outlines the current status of nonlinear wave and raises the main contents of researches, and its discussion is concerned with the relationship between propagation features of nonlinear wave and rock characters.First, it is the identified signals that are regarded as the last processing data. So the preliminary work is around energy, and it undergoes from four aspects: the relationships between energy of nonlinear wave and formation of shock wave, the interface, the attenuation of medium and the interacting of waves. Based on the study of current status of nonlinear wave research, the three main influential factors and four directions of further study are proposed. The three factors are the influence of hypocenter, complexity of medium, the character of nonlinear wave; and the further studies are on the testing methods of coefficient of elasticity, propagation features of nonlinear wave in solid medium, solving of nonlinear wave equation and the application of nonlinear wave theory, among which the core issue is the study on the propagation features of nonlinear wave. Based on this core issue and the requirement of improving resolution, the paper discusses the relationship between nonlinear wave and rock characters. To solve this problem, we must rely on the nonlinear wave equation, which may be deduced from the basic equation of nonlinear wave propagation in solid medium. To supply scientific theory for research, the paper discusses the existence of solution of equation and the reductive perturbation in one-dimensional propagation.Next, we choose the numerical solution of high-order finite difference equation to replace the genuine solution of wave equation to study the features of wave propagation. The algorithm used is the dominant high-order finite difference equation. That is because the sampling rate in high-order finite difference way is less than in low-order way, and the frequency dispersion can be repressed. To ensure the efficiency of numerical solution of high-order finite difference, two basic problems on array of difference are discussed, that is, its convergence and its stability.At last, with the support of above theories, we program the high-order difference to study the relationship between features of nonlinear wave propagation and rock characters. It can be found that the difference method is feasible to simulate the propagation of nonlinear wave, and the rock character influences directly the propagation of nonlinear wave. This study supplies strong basis for the further research.Based on above analysis, the paper concludes the discussion and outlooks the further study on nonlinear wave.