The objective of this project is to develop the theory and algorithms of wave propagation and imaging in the wavelet domain for direct application to compressed seismic data. We will strive to find optimum algorithms for both compression and processing of which imaging is the heart.
Processing huge seismic data sets has become of critical importance to the oil and gas industry in order to obtain high-resolution images of target areas beneath increasingly complicated structures. For imaging problems, the high-frequency ray-Kirchhoff method and the finite-difference wave equation method are commonly used. The former has low resolution and may not work for highly complex media. The latter is prohibitively time-consuming and memory intensive for large-size 3D problems. Therefore, the computational efficiency of wave propagation is vital to 3D imaging problems such as 3D prestack depth migration and inversion, or velocity analysis.
The newly developed fast wavelet transform (WT) is considered to be a revolutionary breakthrough in signal analysis/processing. In the same time frame, there has been significant progress in one-way wave propagation theory and algorithms, including the recently developed fast acoustic and elastic generalized screen propagators from our group (See our Technical report "Modeling and Imaging Project", No. 1 [1]). We propose to apply the wavelet transform to the generalized screen or other one-way wave propagation methods to develop efficient 3D imaging methods. The cross-breeding of these two new developments has the potential of revolutionizing modeling and imaging techniques for complex Earth media.
The generalized screen method for one-way wave propagation that we developed adopts a perturbation theory and a dual-domain implementation technique for fast computation. It has been shown that the method is 2--3 orders of magnitude faster than traditional finite-difference wave equation methods for medium sized problems and can have huge computer memory saving which makes it capable of handling large volume problems prohibitive to other methods. The algorithm shuttles between the space domain and the wavenumber domain with a fast Fourier transform (FFT) algorithm. Since both the Fourier transform (FT) and the inverse FT involve global operations, the background media (reference velocities) must also be global. This global nature in space or wavenumber domain hampers the further development and optimization of the generalized screen method. The wavelet transform (WT) has some specific features which make it more suitable for wave propagation problems than the FT. One is the flexibility of time-frequency (or space-wavenumber) localizations; the other is the multiscale/multiresolution nature. Due to these features, wave propagation can be optimized by using some special bases so that the computation time can be minimized while the accuracy and stability can be increased.