Wavelet Based Simulation of Elastic Wave Propagation

One of the multiresolution-based schemes reinforced with mathematical background is the wavelet theory. Development of this theory is simultaneously done by scientists, mathematicians and engineers [1]. Wavelets can detect different local features of data; the properties that locally separated in different resolutions. Wavelets can efficiently distinguish overall smooth variation of a solution from locally high transient ones separated in different resolutions. This multiresolution feature has been interested many researchers, especially ones in the numerical simulation of PDEs [1]. Wavelet based methods are efficient in problems containing very fine and sharp transitions in limited zones of a computation domain having an overall smooth structure. In brief, the most performance of such multiresolution-based methods is obtained in systems containg several length scales.

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