A data-driven amplitude variation with offset inversion method via learned dictionaries and sparse representation

Abstract

Amplitude variation with offset (AVO) inversion is a typical ill-posed inverse problem. To obtain a stable and unique solution, regularization techniques relying on mathematical models from prior information are commonly used in conventional AVO inversion methods (hence the name model-driven methods). Due to the difference between prior information and the actual geology, these methods often have difficulty achieving satisfactory accuracy and resolution. We have developed a novel data-driven inversion method for the AVO inversion problem. This method can effectively extract useful knowledge from well-log data, including sparse dictionaries of elastic parameters and sparse representation of subsurface model parameters. Lateral continuity of subsurface geology allows for the approximation of model parameters for a work area using the learned dictionaries. Instead of particular mathematical models, a sparse representation is used to constrain the inverse problem. Because no assumption is made about the model parameters, we consider this a data-driven method. The general process of the algorithm is as follows: (1) using well-log data as the training samples to learn the sparse dictionary of each elastic parameter, (2) imposing a sparse representation constraint on the objective function, making the elastic parameters be sparsely represented over the learned dictionary, and (3) solving the objective function by applying a coordinate-descent algorithm. Tests on several synthetic examples and field data demonstrate that our algorithm is effective in improving the resolution and accuracy of solutions and is adaptable to various geologies.

The high‐resolution seismic deconvolution method based on joint sparse representation using logging–seismic data

“…Within a work area, the physical properties of the subsurface often have a certain similarity and lateral continuity, and the elastic parameters located at different locations have some shared features. Based on this, we assume that each elastic parameter in the same area shares a common sparse representation basis (called sparse dictionary), which could be obtained from the well‐logging data (regarded as the training set) by sparse representation (She et al ., 2018). The learned dictionary d is a matrix of size $${{{\bf L}}_{\bm{a}}} \times {{{\bf N}}_{\bm{a}}}$$, in which each column vector of length L a is a prototype feature of the sample data (hence the name atom), N a represents the number of atoms of d .…”

“…This shows that with the increase of L a , the learned dictionary atoms contain more global information, and the dictionary is more conducive to storing the prior information derived from training samples. There is one more point to note, to keep the redundant nature of the dictionary, L a should be much smaller than N a (She et al ., 2018). At the same time, from Figure 4(b) we can see that the elapsed time increases with the increase of L a because the K‐SVD for dictionary learning takes more time for high‐dimensional samples.…”

“…Compared with conventional sparse‐spike deconvolution, our method has lower requirements on seismic wavelets. In field data processing, wavelet is mostly hard to obtain exactly (She et al ., 2018; Das et al ., 2019; Pan et al ., 2020; Wang et al ., 2021). The frequency of the wavelets is usually extracted from seismic data, and the phase of the wavelet is often difficult to determine.…”

A facies‐constrained geostatistical seismic inversion method based on multi‐scale sparse representation

“…SR of signals has always been a research hotspot in the field of signal processing. In the field of seismic signal processing, SR methods are commonly used for seismic data denoising, seismic data reconstruction and other problems (Beckouche & Ma, 2014;She et al, 2018;Shao et al, 2019). The set of atoms used in SR is called a dictionary.…”

Tensor Super-Resolution with Generative Adversarial Nets: A Large Image Generation Approach

“…Considering the advantages of small dictionary size and invariance of shifting [12], tensor sparse coding is the key point we want to apply in our model. We make the assumption [24] that the inner patterns of images can be at least approximately sparsely represented with a learned dictionary. For tensor dictionary representation, T = D * C, where T ∈ R d×N ×n , D ∈ R d×m×n , C ∈ R m×N ×n .…”