Sparsity-regularized linear inverse problem has served as the base in many disciplines, such as remote sensing imaging, image processing and analysis, seismic deconvolution, compressed sensing, medical imaging, and so forth. The iterative hard thresholding algorithm (IHTA) and iterative soft thresholding algorithm (ISTA) are two frequently used methods to solve sparsity-regularized linear inverse problems. They are also the basic unit of other more complex methods. IHTA and ISTA are derived under the steepest descent method, i.e., iteratively perform gradient descent and thresholding shrinkage. The steepest descent method is a first-order algorithm, which is a powerful way to solve optimization due to its relatively simple implementation. However, a known issue of the first-order method is the possible poor convergence rate. Fast iterative thresholding-like algorithms have been proposed to overcome this issue in the existing works of literature. In history, another alternative way is second-order algorithms or quasi-second-order algorithms. In this letter, we include a quasi-Newton’s method, i.e., Davidon–Fletcher–Powell (DFP) formulations in the framework of iterative thresholding-like algorithms to replace gradient descent to form a hybrid method to further increase convergence rate. The proposed method has been performed on two numerical examples and a real-life application in sparse-spike seismic deconvolution. The numerical examples and real-life application showed that it provides an effective alternative method to solve sparsity-regularized linear inverse problems.

In exploration geophysics, seismic impedance is a physical characteristic parameter of underground formations. It can mark rock characteristics and help stratigraphic analysis. Hence, seismic data inversion for impedance is a key technology in oil and gas reservoir prediction. To invert impedance from seismic data, one can perform reflectivity series inversion first. Then, under a simple exponential integration transformation, the inverted reflectivity series can give the final inverted impedance. The quality of the inverted reflectivity series directly affects the quality of impedance. Sparse-spike inversion is the most common method to obtain reflectivity series with high resolution. It adopts a sparse regularization to impose sparsity on the inverted reflectivity series. However, the high resolution of sparse-spike-like reflectivity series is obtained at the cost of sacrificing small reflectivity. This is the inherent problem of sparse regularization. In fact, the reflectivity series from the actual impedance well log is not strictly sparse. It contains not only the sparse major large reflectivity, but also small reflectivity between major reflectivity. That is to say, the large reflectivity is sparse, but the small reflectivity is dense. To combat this issue, we adopt elastic-net regularization to replace sparse regularization in seismic impedance inversion. The elastic net is a hybrid regularization that combines sparse regularization and dense regularization. The proposed inversion method was performed on a synthetic seismic trace, which is created from an actual well log. Then, a real seismic data profile was used to test the practice application. The inversion results showed that it provides an effective new alternative method to invert impedance.

利用常规的相干类属性与蚂蚁追踪组合技术所获取的不连续性信息,难以满足油田对于河流相和三角洲相薄砂岩储层精细剖析的需求.为了更好地检测薄砂岩储层内部不连续性,首先利用对薄砂岩储层变化更加敏感的均方根振幅属性计算灰度共生矩阵的均质性统计量,初步得到薄砂岩储层的不连续性特征数据;然后根据其不连续性结构的展布特点,运用路径弯曲度约束人工蚂蚁的移动方向,优化蚁群算法的平面增强效果,达到压制干扰信息、突出不连续性特征的目的;最终形成更适应薄砂岩储层不连续性检测的组合技术.模型和实际工区数据的应用结果表明,采用上述组合技术能较好地识别薄砂岩体的边缘以及其内部的小尺度不连续性结构,说明了该技术对薄砂岩储层内部不连续性检测的有效性,并且其检测结果能用于提升砂岩厚度预测精度,为后续的砂体内部结构精细刻画提供技术支持.

The ill-posed feature is one basic attribute of geophysical inversion methods. As an example of geophysical inverse problem, AVA (Amplitude variation with incident angle) inversion of pre-stack seismic data is susceptible to noise and uncertainty in the acquisition. To get stable and accurate inversion results, the regularization constraints on model parameter need to be added into the objective function of AVA inversion. In AVA inversion, the most commonly used regularization includes sparsity constraint (e.g. L1-norm regularization, Cauchy regularization) and a priori model parameters constraint, and so forth. However, the existing AVA inversion methods do not consider the structural similarity of different model parameters. All of the different model parameters represent the same underground geological structure, so they should have similar structure. This paper adopts the cross gradient to measure the structural similarity of different model parameters. Next, the cross gradients of different model parameters are added into the objective function of AVA inversion as a regularization term to implement structural similarity constraint. Results of the model numerical tests and real seismic data indicate that the AVA inversion with cross-gradient constraint has higher stability compared to the AVA inversion without structural similarity constraint, especially for the density inversion results.

Elastic impedance (EI) inversion for partial angle stack seismic data is a key technology in seismic reservoir prediction within the oil and gas industry. EI inversion provides a consistent framework to invert partial angle stack seismic data, just as the AI inversion does for post-stack data. The commonly used EI inversion process is angle by angle. Hence, the inverted EI for different angles may be nonconforming, especially for the seismic data with a low signal-to-noise ratio. This paper proposes to simultaneously invert multiple partial angle stack seismic data to obtain EI for different angles at once. To obtain conformable EI, we used the joint sparse constraint on the reflection coefficients for different angles. Then, the objective function for simultaneous EI inversion was constructed. Next, synthetic seismic data profiles with three different angles were used to show the superiority of the proposed EI inversion method compared to the conventional method. At last, a real seismic data line was used to test the feasibility of the proposed method in practice. The inversion results of synthetic data and real data showed that it provides an effective new alternative method to estimate EI from partial stack seismic data.