Inversion of low to medium frequency velocities and densities from AVO data using invertible neural networks

AVO (amplitude variation with offset) inversion and neural networks are widely used to invert elastic parameters. With more constraints from well log data, neural network-based inversion may estimate elastic parameters with greater precision and resolution than traditional AVO inversion, however, neural network approaches necessitate a massive number of reliable training samples. Furthermore, because the lack of low-frequency information in seismic gathers leads to multiple solutions of the inverse problem, both inversions rely heavily on proper low-frequency initial models. To mitigate the dependence of inversions on accurate training samples and initial models, we propose solving inverse problems with the recently developed invertible neural networks (INNs). Unlike conventional neural networks, which address the ambiguous inverse issues directly, INNs learn definite forward modeling and use additional latent variables to increase the uniqueness of solutions. Motivated by the newly developed neural networks, we propose an INN-based AVO inversion method, which can reliably invert low to medium frequency velocities and densities with randomly generated easy-to-access datasets rather than trustworthy training samples or well-prepared initial models. Tests on synthetic and field data show that our method is feasible, anti-noise capable, and practicable.

Research on Seepage Control of Jurong Pumped Storage Hydroelectric Power Station

Based on the geological and hydrogeological conditions of the Jurong Pumped Storage Hydroelectric Power Station (JPSHP), a 3D groundwater flow model was developed in the power station area, which took into account the heterogeneity and anisotropy of fractured rocks. A control inversion method for fractured rock structural planes was proposed, where larger-scale fractures were used as water-conducting media and the relatively intact rock matrix was used as water-storage media. A statistical method was used to obtain the geometric parameter values of the structural planes, so as to obtain the hydraulic conductivity tensor of the fractured rocks. Combining the impermeable drainage systems of the upper storage reservoir, underground powerhouse and lower storage reservoir, the 3D groundwater seepage field in the study area was predicted using the calibrated model. The leakage amounts of the upper storage reservoir, powerhouse and lower storage reservoir were 710.48 m3/d, 969.95 m3/d and 1657.55 m3/d, respectively. The leakage changes of the upper storage reservoir, powerhouse and lower storage reservoir were discussed under the partial and full failure of the anti-seepage system. The research results provide a scientific basis for the seepage control of the power station, and it is recommended to strengthen the seepage control of the upper and lower storage reservoirs and the underground powerhouse to avoid excessive leakage and affect the efficiency of the reservoir operation.

Estimating adsorption isotherm parameters in chromatography via a virtual injection promoting double feed-forward neural network

The means to obtain the adsorption isotherms is a fundamental open problem in competitive chromatography. A modern technique of estimating adsorption isotherms is to solve a nonlinear inverse problem in a partial differential equation so that the simulated batch separation coincides with actual experimental results. However, this identification process is usually ill-posed in the sense that the uniqueness of adsorption isotherms cannot be guaranteed, and moreover, the small noise in the measured response can lead to a large fluctuation in the traditional estimation of adsorption isotherms. The conventional mathematical method of solving this problem is the variational regularization, which is formulated as a non-convex minimization problem with a regularized objective functional. However, in this method, the choice of regularization parameter and the design of a convergent solution algorithm are quite difficult in practice. Moreover, due to the restricted number of injection profiles in experiments, the types of measured data are extremely limited, which may lead to a biased estimation. In order to overcome these difficulties, in this paper, we develop a new inversion method – the virtual injection promoting double feed-forward neural network (VIP-DFNN). In this approach, the training data contain various types of artificial injections and synthetic noisy measurement at outlet, generated by a conventional physics model – a time-dependent convection-diffusion system. Numerical experiments with both artificial and real data from laboratory experiments show that the proposed VIP-DFNN is an efficient and robust algorithm.

SH-SH wave inversion for S-wave velocity and density

SS-waves (SV-SV waves and SH-SH waves) are capable of inverting S-wave velocity ( VS) and density ( ρ) because they are sensitive to both parameters. SH-SH waves can be separated from multicomponent data sets more effectively than the SV-SV wave because the former is decoupled from the PP-wave in isotropic media. In addition, the SH-SH wave can be better modeled than the SV-SV wave in the case of strong velocity/impedance contrast because the SV-SV wave has multicritical angles, some of which can be quite small when velocity/ impedance contrast is strong. We derived an approximate equation of the SH-SH wave reflection coefficient as a function of VS and ρ in natural logarithm variables. The approximation has high accuracy, and it enables the inversion of VS and ρ in a direct manner. Both coefficients corresponding to VS and ρ are “model-parameter independent” and thus there is no need for prior estimate of any model parameter in inversion. Then, we developed an SH-SH wave inversion method, and demonstrated it by using synthetic data sets and a real SH-SH wave prestack data set from the west of China. We found that VS and ρ can be reliably estimated from the SH-SH wave of small angles.

A Multi-Point Geostatistical Seismic Inversion Method Based on Local Probability Updating of Lithofacies

In order to solve the problem that elastic parameter constraints are not taken into account in local lithofacies updating in multi-point geostatistical inversion, a new multi-point geostatistical inversion method with local facies updating under seismic elastic constraints is proposed. The main improvement of the method is that the probability of multi-point facies modeling is combined with the facies probability reflected by the optimal elastic parameters retained from the previous inversion to predict and update the current lithofacies model. Constrained by the current lithofacies model, the elastic parameters were obtained via direct sampling based on the statistical relationship between the lithofacies and the elastic parameters. Forward simulation records were generated via convolution and were compared with the actual seismic records to obtain the optimal lithofacies and elastic parameters. The inversion method adopts the internal and external double cycle iteration mechanism, and the internal cycle updates and inverts the local lithofacies. The outer cycle determines whether the correlation between the entire seismic record and the actual seismic record meets the given conditions, and the cycle iterates until the given conditions are met in order to achieve seismic inversion prediction. The theoretical model of the Stanford Center for Reservoir Forecasting and the practical model of the Xinchang gas field in western China were used to test the new method. The results show that the correlation between the synthetic seismic records and the actual seismic records is the best, and the lithofacies matching degree of the inversion is the highest. The results of the conventional multi-point geostatistical inversion are the next best, and the results of the two-point geostatistical inversion are the worst. The results show that the reservoir parameters obtained using the local probability updating of lithofacies method are closer to the actual reservoir parameters. This method is worth popularizing in practical exploration and development.

Joint Inversion of Rayleigh and Love Dispersion Curves Extracted from Ambient Seismic Noise Based on Secular Function

Traditional multi-mode dispersion curve inversion requires correct mode discrimination. However, when the stratum contains complex structures such as low-speed soft interlayer or high-speed hard interlayer, the dispersion curve may show phenomena such as “mode kissing” and “mode jumping”, which can easily cause mode misjudgment and lead to erroneous inversion results. Based on the “secular function”, this paper constructs a new type of objective function applied to the inversion of dispersion curve. This objective function does not require prior mode discrimination, which effectively solves the “mode misjudgment” problem of multi-mode dispersion curve inversion. The joint inversion of Rayleigh and Love dispersion curves extracted from ambient seismic noise is used to improve the constraint of the inversion and avoid the inversion falling into a local minimum in the case of a large-scale search of parameters. Finally, a numerical simulation was performed to verify the feasibility of the new inversion method.