Multiresolution Analysis Theory For Depth Imaging And Seismic Data Processing

Seismic data processing methods, especially the seismic migration imaging methods for wave equation, are the main research directions in late 20th century. The seismic migration imaging methods, based on the inverse wave field extrapolation for the wave equation, had made a great success. As the development of geophysics, these imaging methods were not satisfied the needs of seismic exploration. Many new methods are put forward and applied to seismic exploration. Another side, with the progress of seismic exploration technologies, a huge amount of data need to store and process. How to save the spaces (physical spaces and computing spaces) is becoming more and more concerned in seismic exploration works. To resolve those problems a lot of knowledge, such as geophysics, pure mathematics, computing mathematics, signal processing, computer technology, et. al, were embroiled. They will be significant topics for future researches. So the research has its values of theory and practice.The ridgelet transform which was developed from wavelet analysis, was defined as one dimensional wavelet transform on the Radon domain. Based on the theories and methods of recent harmonic analysis, combined with a serial of high dimension ridge functions iterative approach, it can represent the singularities (more than zero dimension singularities) of higher space. Because ridgelet transform has not only good local properties of wavelet, but also line (or plane) singularities analysis abilities of Radon transform, and the observing seismic data just has this properties along line (or plane) singularities. Therefore, ridgelet transform can be as a good representation tool of seismic data.The multi-scale seismic migration inverse extrapolation imaging method, applied ridgelet transform, was proposed in this thesis. Thismethod can describe the structure of the wave field more efficiently. The theoretical analysis and experimental results were showed that this method was more powerful to represent these complex local singularities and more accurate to describe the local characters of the physical geography structure. It is a development of using wavelet analysis in seismic imaging, which often failed when it is used to represent the higher singularities, such as linear (or curvilinear), plane (or curved surface) singularities.Using wavelet non-uniform sampling, a new high multiresolution imaging method, which based on the integral solution of wave equation, was introduced. Appling the multi-resolution analysis theory, the multi-resolution wavelet representation for the second partial differential operator was deduced, and was applied to wave equation imaging treatment. The 2D/3D wavelet domain - frequency domain - depth imaging method (WFD) has been established. By applying this method to synthetic models and practical seismic data imaging, good results were obtained.The Local Orthonormal Finite Ridgelet Transform (LFRIT) was studied. Applied LFRIT or combined wavelet with LFRIT, some new seismic data (or image) de-nosing and compression methods were proposed in this thesis. The approaches can not only deal with line (or plane) singularities, but also deal with curve (or curved surface) singularities. Experimental results showed that it could achieve a higher compression ratio and good reconstructed image than Wavelet.