Amplitude variation with offset (AVO) inversion has been widely used in reservoir characterization to predict lithology and fluids. However, some existing AVO inversion methods that use [Formula: see text] norm regularization may not obtain the block boundary of subsurface layers because the AVO inversion is a severely ill-posed problem. To obtain sparse and accurate solutions, we have introduced the [Formula: see text] minimization method as an alternative to [Formula: see text] norm regularization. We used [Formula: see text] minimization for simultaneous P- and S-impedance inversion from prestack seismic data. We first derived the forward problem with multiangles and set up the inversion objective function with constraints of a priori low-frequency information obtained from well-log data. Then, we introduced minimization of the difference of [Formula: see text] and [Formula: see text] norms, denoted as [Formula: see text] minimization, to solve this objective function. The nonconvex penalty function of the [Formula: see text] minimization method is decomposed into two convex subproblems via the difference of convex algorithm, and each subproblem is solved by the alternating direction method of multipliers. Compared to [Formula: see text] norm regularization, the results indicate that [Formula: see text] minimization has superior performance over [Formula: see text] norm regularization in promoting blocky/sparse solutions. Tests on synthetic and field data indicate that our method can provide sparser and more accurate P- and S-impedance inversion results. The overall results confirm that our method has great potential in the detection and identification of fluids.
Millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems can significantly reduce the number of radio frequency (RF) chains by using lens antenna arrays, because it is usually the case that the number of RF chains is often much smaller than the number of antennas, so channel estimation becomes very challenging in practical wireless communication. In this paper, we investigated channel estimation for mmWave massive MIMO system with lens antenna array, in which we use a mixed (low/high) resolution analog-to-digital converter (ADC) architecture to trade-off the power consumption and performance of the system. Specifically, most antennas are equipped with low-resolution ADC and the rest of the antennas use high-resolution ADC. By utilizing the sparsity of the mmWave channel, the beamspace channel estimation can be expressed as a sparse signal recovery problem, and the channel can be recovered by the algorithm based on compressed sensing. We compare the traditional channel estimation scheme with the deep learning channel-estimation scheme, which has a better advantage, such as that the estimation scheme based on deep neural network is significantly better than the traditional channel-estimation algorithm.
Using seismic data, logging information, geological interpretation data, and petrophysical data, it is possible to estimate the stratigraphic texture and elastic parameters of a study area via a seismic inversion. As such, a seismic inversion is an indispensable tool in the field of oil and gas exploration and development. However, due to unknown natural factors, seismic inversions are often ill-conditioned problems. One way to work around this unknowable information is to determine the solution to the seismic inversion using regularization methods after adding further a priori constraints. In this study, the nonconvex L1−2 regularization method is innovatively applied to the three-parameter prestack amplitude variation angle (AVA) inversion. A forward model is first derived based on the Fatti approximate formula and then low-frequency models for P impedance, S impedance, and density are established using logging and horizon data. In the Bayesian inversion framework, we derive the objective function of the prestack AVA inversion. To further improve the accuracy and stability of the inversion results, we remove the correlations between the elastic parameters that act as initial constraints in the inversion. Then, the objective function is solved by the nonconvex L1−2 regularization method. Finally, we validate our inversion method by applying it to synthetic and observational data sets. The results show that our nonconvex L1−2 regularization seismic inversion method yields results that are highly accurate, laterally continuous, and can be used to identify and locate reservoir formation boundaries. Overall, our method will be a useful tool in future work focused on predicting the location of reservoirs.
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