An Adaptive Noise-Free Method of Seismic Resolution Enhancement Based on Extrapolated Multiresolution Singular Value Decomposition

Abstract

The maximum vertical seismic resolution is a critical parameter in seismic data processing and interpretation. In general, conventional methods such as spectral whitening and zero-phase deconvolution assume randomness in the reflectivity spectrum that may not always be valid. The method proposed herein, extrapolated multiresolution singular value decomposition (EMRSVD), avoids some of these assumptions. We reasonably assume that original seismic data constitute a low-frequency component of high-resolution data, of which high-frequency component is attenuated. To recover this high-resolution component, EMRSVD adaptively extrapolates attenuated high-frequency information based on multiresolution singular value decomposition (MRSVD) and polynomial fitting to broaden the valid frequency bandwidth and improve the resolution of original seismic data. In our work, we first decompose a signal into a series of approximate and detailed subsignals exhibiting different resolutions using MRSVD. Then, we apply a polynomial fitting algorithm to the singular values corresponding to the detailed subsignals and obtain an expression of the singular values. Next, based on this expression, we extrapolate new singular values to construct new detailed subsignals. We repeat this process iteratively, where the number of iterations is determined by a modified variance model with an exponential transformation. Finally, we add these extrapolated detailed subsignals back into the original signal to obtain a high-resolution result. Examples with two synthetic signals and one field seismic data demonstrate that the proposed method significantly improves the resolution of seismic data without introducing noise and efficiently broadens the frequency bandwidth of reflection signals without sacrificing low-frequency information, which facilitates the resolution of thin layers.