Poststack Seismic Inversion Using A Patch-based Gaussian Mixture Model

Seismic inversion is a severely ill-posed problem, because of noise in the observed record, band-limited seismic wavelets, and the discretization of a continuous medium. Regularization techniques can impose certain characteristics on inversion results based on prior information in order to obtain a stable and unique solution. However, it is difficult to find an appropriate regularization to describe the actual subsurface geology. We propose a new acoustic impedance inversion method via a patch-based Gaussian mixture model (GMM), which is designed using available well logs. In this method, firstly, the non-local means (NLM) method estimates acoustic impedance around wells in terms of the similarity of local seismic records. The extrapolated multichannel impedance are then decomposed into impedance patches. Using patched data rather than a window or single trace for training samples to obtain the GMM parameters, which contain local lateral structural information, can provide more impedance structure details and enhance the stability of the inversion result. Next, the expectation maximization (EM) algorithm is used to obtain the GMM parameters from the patched data. Finally, we apply the alternating direction method of multipliers (ADMM) to solve the conventional Bayesian inference illustrating the role of regularization, and construct the objective function using the GMM parameters. Therefore, the inversion results are compliant with the local structural features extracted from the borehole data. Both synthetic and field data tests validate the performance of our proposed method. Compared with other conventional inversion methods, our method shows promise in providing a more accurate and stable inversion result.

An Analytical Solution for Pressure-Induced Deformation of Anisotropic Multilayered Subsurface

We present a generalized Geertsma solution that can consider any number of finite-thickness layers in the subsurface whose mechanical properties are different from layer to layer. In addition, each layer can be assumed either isotropic or anisotropic. The accuracy of the generalized solution is validated against a numerical reference solution. The generalized Geertsma solution is further extended by a linear superposition framework that enables a response simulation due to an arbitrarily-distributed non-uniform pressure anomaly. The linear superposition approach is tested and validated by solving a realistic synthetic model based on the In Salah CO2 storage model and compared with a full 3D finite element solution. Finally, by means of a simple inversion exercise (based on the linear superposition approach), we learn that the stiffnesses of cap rock and reservoir are the most influencing parameter on the inversion result for a given layering geometry, suggesting that it is very important to estimate high-confidence mechanical properties of both cap rock and reservoir.

High-Resolution Seismic Acoustic Impedance Inversion with Sparsity-based Statistical Model

Seismic acoustic impedance inversion plays an important role in subsurface quantitative interpretation. Due to the band-limited property of the seismic record and the discretization of the continuous elastic parameters with a limited sampling interval, the inverse problem suffers from serious ill-posedness. Various regularization methods are introduced into the seismic inversion to make the inversion results comply with the pre-specified characteristics. However, conventional seismic inversion methods can only reflect fixed distribution characteristics and do not take into account discretization challenges. We propose a new post-stack seismic impedance inversion method with upsampling and adaptive regularization. The adaptive regularization is constructed with two trained dictionaries from the true model and upsampled model-based inversion result to capture the features of high- and low-resolution details, and a sparsity-based statistical model is proposed to build the relationship between their sparse representations. The high-resolution components can be recovered based on the prediction model and low-resolution sparse representations, and the parameters of the statistical prediction model can be obtained effectively with conventional optimization algorithms. The synthetic and field data tests show that the model-based inversion is dependent on the sample interval, and the proposed method can reveal more thin layers and enhance the extension of the strata compared with conventional inversion methods. Moreover, the inverted impedance variance of the proposed method well matches borehole observations. The tests demonstrate the interpolated model-based inversion result combined with the sparsity-based prediction model can effectively improve the resolution and accuracy of the inversion results.

Model parameterization and amplitude variation with angle and azimuthal inversion in orthotropic media

Horizontal layered formations with a suite of vertical or near-vertical fractures are usually assumed to be an approximate orthotropic medium and are more suitable for estimating fracture properties with wide-azimuth prestack seismic data in shale reservoirs. However, the small contribution of anisotropic parameters to the reflection coefficients highly reduces the stability of anisotropic parameter estimation by using seismic inversion approaches. Therefore, a novel model parameterization approach for the reflectivity and a pragmatic inversion method are proposed to enhance the stability of the inversion for orthotropic media. Previous attempts to characterize orthotropic media properties required using four or five independent parameters. However, we have derived a novel formulation that reduces the number of parameters to three. The inversion process is better conditioned with fewer degrees of freedom. An accuracy comparison of our formula with the previous ones indicates that our approach is sufficiently precise for reasonable parameter estimation. Furthermore, a Bayesian inversion method is developed that uses the amplitude variation with angle and azimuth (AVAZ) of the seismic data. Smooth background constraints reduce the similarity between the inversion result and the initial model, thereby reducing the sensitivity of the initial model to the inversion result. Cauchy and Gaussian probability distributions are used as prior constraints on the model parameters and the likelihood function, respectively. These ensure that the results are within the range of plausibility. Synthetic examples demonstrate that the adopted orthotropic AVAZ inversion method is feasible for estimating the anisotropic parameters even with moderate noise. The field data example illustrates the inversion robustness and stability of the adopted method in a fractured reservoir with a single well control.

Numerical Simulation of Gravity Anomaly Based on the Unstructured Element Grid and Finite Element Method

Finite element method is an important method to solve mathematical problems in engineering. Many mathematical equations are difficult to solve, but it becomes very simple after using the finite element method. In this paper, the finite element method is applied to the calculation of gravity anomaly. First, the variational equation of gravity anomaly calculation is established, and then the gravity anomaly value ten times the distance away from the anomaly body is used as the boundary condition. By comparing the gravity anomaly obtained by solving the stiffness matrix with the analytical solution, it can be found that the method in this paper has high accuracy. Finally, the model of Jinchuan copper nickel deposit is used for calculation, and the calculated gravity anomaly field is inverted with Growth3D. It can be found that the inversion result is very close to the model, which verifies the effectiveness of the algorithm in this paper.

Two-dimensional Time-domain Full Waveform Inversion of On-ground Common-offset GPR Data Based on Integral Preprocessing

Full waveform inversion (FWI) is an advanced inversion technique for ground penetrating radar (GPR), which could provide quantitative, high-resolution subsurface imaging. FWI has been used widely to process crosshole and on-ground multi-offset GPR data, but its application to on-ground common-offset GPR data is more difficult and being developed. This is mainly because that on-ground common-offset GPR has much less coverage of the subsurface and mainly includes reflective information. The application of conventional FWI to pure reflection data in the absence of a highly accurate starting velocity model is difficult. Here, we demonstrate a means of achieving this successfully by preprocessing the observed data and the residual fields with an integral algorithm, which could produce a more reasonable gradient and therefore lead to better inversion results. Several cases verify the effectiveness of this method. We achieve the simultaneous inversion of relative permittivity and conductivity for on-ground common-offset GPR, and discuss the trade-off between permittivity and conductivity in details. According to the inversion results of test models, it seems that the inversion result of relative permittivity is more credible in most cases.

Bayesian Inversion for Geoacoustic Parameters in Shallow Sea

Geoacoustic parameter inversion is a crucial issue in underwater acoustic research for shallow sea environments and has increasingly become popular in the recent past. This paper investigates the geoacoustic parameters in a shallow sea environment using a single-receiver geoacoustic inversion method based on Bayesian theory. In this context, the seabed is regarded as an elastic medium, the acoustic pressure at different positions under low-frequency is chosen as the study object, and the theoretical prediction value of the acoustic pressure is described by the Fast Field Method (FFM). The cost function between the measured and modeled acoustic fields is established under the assumption of Gaussian data errors using Bayesian methodology. The Bayesian inversion method enables the inference of the seabed geoacoustic parameters from the experimental data, including the optimal estimates of these parameters, such as density, sound speed and sound speed attenuation, and quantitative uncertainty estimates. The optimization is carried out by simulated annealing (SA), and the Posterior Probability Density (PPD) is given as the inversion result based on the Gibbs Sampler (GS) algorithm. Inversion results of the experimental data are in good agreement with both measured values and estimates from Genetic Algorithm (GA) inversion result in the same environment. Furthermore, the results also indicate that the sound speed and density in the seabed have fewer uncertainties and are more sensitive to acoustic pressure than the sound speed attenuation. The sea noise could increase the variance of PPD, which has less influence on the sensitive parameters. The mean value of PPD could still reflect the true values of geoacoustic parameters in simulation.

ANALISIS AMPLITUDE VERSUS OFFSET (AVO) MENGGUNAKAN PARAMETER PETROFISIKA LAMBDA MU RHO (LMR) DAN EXTENDED ELASTIC IMPEDANCE (EEI) UNTUK KARAKTERISASI RESERVOAR KARBONAT

The research that refers to the characterization of carbonate reservoir to identify lithology and fluid had been done to the Baturaja Formation in South Sumatera Basin. The method used is analyzed of Amplitude Versus Offset (AVO) by utilizing the petrophysics parameter of Lambda Mu Rho (LMR) and Extended Elastic Impedance (EEI). The goal of the research is to find out the comparison of the application of petrophysics parameter LMR and EEI to characterization carbonate reservoir, besides finding a prospect location or proposed well. The result of data analysis of Al-Fatah well shows that the carbonate reservoir position with liquefied gas is located deeper around 350 meters with a thickness of around 7.62 meters. Interpretation of seismic from inversion result by using the petrophysics parameter of LMR and EEI shows the presence of a prospect location to the CDP 4253 up to 4301, which is carbonate reservoir with fluid accumulation (gas).

A comparison of regularized, sharp boundary and tear zone inversions along an MT profile in Sabalan geothermal field, Iran

This paper investigates magnetotelluric (MT) data recorded along a profile in the Sabalan geothermal region, NW of Iran. To find the range of relevant models consistent with the data, this study employed the so-called regularized, tear zone, and sharp boundary inversions. This study could effectively derive three alternative classes of models. Although the models show stable common resistive and conductive features there are some inconsistent details. Unaltered surface rocks and porous Basalt exhibit a high resistive overburden underlain by relatively more conductive Paleozoic sediments. A common signature of hydrothermal systems appears, and resistivities increase beneath a highly conductive clay cap in deeper parts. An intriguing feature resolved in the smoothest inversion model is a second deep conductor of 30 Ωm resistivities at a depth of 3 km, extending close to the surface. It can be related to the hot, solidified volcanic intrusions, resemblingthe heat source in a geothermal system. This study applied the two other inversion approaches for further hypothesis tests. Although the tear zone inversion re-establish the deep conductor (with 38 Ωm resistivities at 3 km depth), it is absent in the sharp boundary inversion result. This study concludes that the second deep conductor has a limited structure resolution.

Retraction Note to: Estimation of the source process and forward simulation of long-period ground motion of the 2018 Hokkaido Eastern Iburi, Japan, earthquake

The authors have retracted this article [1] because after its publication, they noticed that the source inversion was not done with the intended setting. Although it was mentioned in this article [1] that the rupture starting point of the fault model was set at the hypocenter determined by JMA as shown in Fig. 1, the rupture starting point in the real analysis was accidentally set at an incorrect location, the center point of the subfault southern neighbor of the hypocenter subfault. Thus, the source-inversion result (Figs. 2, 3, S1, and S2) and the forward ground-motion simulation result for the mainshock (Figs. 4 and 5), which used the source-inversion result as a source input, need to be corrected.