Seismic deconvolution and inversion with erratic data

Abstract

If there are some erratic data (e.g. outliers), which may arise from measurement error, or other reasons, in seismic data, the seismic deconvolution and inversion need to be implemented in a way that minimizes their effects. However, the deconvolution and inversion methods based on L2‐norm misfit function are highly sensitive to these erratic seismic observations. As an alternative, L1‐norm misfit functions are more robust and erratic‐resistant. In order to find the solution of the inverse problem constrained by an L1‐norm misfit function, an iteratively re‐weighted least squares algorithm is used frequently. However, it is relatively time consuming. In this paper, we propose a new method based on the sparse signal representation theory. The overcomplete dictionary used for the sparse representation of seismic data with erratic data is composed of two bases: a wavelet basis used for representing the seismic data to implement deconvolution and a Dirac basis used for representing the erratic data. In addition, at the stage of seismic inversion after deconvolution, total variation and a priori model are used as the regularization constraint terms to estimate inversion results with a blocky and laterally continuous structure. The new method is successfully tested on the noisy synthetic seismic data with erratic data. Finally, the proposed method is performed on a real seismic data section, and the inversion results are reasonable, i.e. consistent with the geologic structure of the original seismic data. Compared to the conventional sparse deconvolution and inversion method, the proposed method not only eliminates the effect of outliers, but also has highly improved computational efficiency.

Seismic inversion with L2,0-norm joint-sparse constraint on multi-trace impedance model

“…Usually, the inversion can improve the overall stability through compensating the lacked low-frequency components in original seismic data 20 . To compensate the low frequency components which coincide with true geological background, a priori model can be used 17 .…”

“…For example, the total variation regularization in image processing is the L1-norm sparse constraint on the magnitudes of image’s gradient 16 . The total variation regularization has also been widely applied in geophysical inverse problems 17 – 20 . The minimum gradient support regularization in geophysical inversion is in fact the modified Cauchy prior sparse constraint on the magnitude of the model parameters’ gradient 12 .…”

Sparse seismic reflectivity inversion using an adaptive fast iterative shrinkage‐thresholding algorithm

“…Sparse regularization has been widely used in seismic reflectivity inversion to obtain sparse solutions (Santosa and Symes, 1986). For example, sparsely distributed reflection coefficients can be obtained through Bayesian inversion where appropriate long-tailed prior probability distributions are used (Tarantola, 1987;Sacchi, 1997;Downton and Lines, 2003; Misra and Sac- * Email: lichuanhui@cugb.edu.cn; liuxw@cugb.edu.cn chi, 2008;Alemie and Sacchi, 2011;Zong et al, 2012Zong et al, , 2015Dai et al, 2016Dai et al, , 2018Dai and Yang, 2021).…”