Seismic Absorption Qualitative Indicator via Sparse Group-Lasso-Based Time–Frequency Representation

Abstract

Time-frequency (TF) analysis is an available tool to estimate seismic absorption qualitatively. The high TF concentration is a key factor for the seismic attenuation qualitative estimation. To obtain a more concentrated TF representation, we propose a sparse TF method based on sparse representation (SR) and sparse Group-Lasso (GL) penalty function. Based on the SR theory, TF representation can be regarded as an inverse problem, and thus, sparse GL penalty function can be added in this inverse problem to enhance the TF concentration. Sparse GL penalty function, including <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> penalty and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</sub> penalty, can provide group-wise and within-group sparsity for TF coefficients. Using the proposed sparse GL-based TF (GLTF) method, we develop a workflow to characterize seismic attenuation qualitatively. Finally, a synthetic data of viscoacoustic model and a 2-D field data are applied to test the validity and effectiveness of the proposed workflow for indicating the gas and oil reservoirs.