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.

Effective diffraction separation using the improved optimal rank-reduction method

Seismic diffractions encoding subsurface small-scale geologic structures have great potential for high-resolution imaging of subwavelength information. Diffraction separation from the dominant reflected wavefields still plays a vital role because of the weak energy characteristics of the diffractions. Traditional rank-reduction methods based on the low-rank assumption of reflection events have been commonly used for diffraction separation. However, these methods using truncated singular-value decomposition (TSVD) suffer from the problem of reflection-rank selection by singular-value spectrum analysis, especially for complicated seismic data. In addition, the separation problem for the tangent wavefields of reflections and diffractions is challenging. To alleviate these limitations, we propose an effective diffraction separation strategy using an improved optimal rank-reduction method to remove the dependence on the reflection rank and improve the quality of separation results. The improved rank-reduction method adaptively determines the optimal singular values from the input signals by directly solving an optimization problem that minimizes the Frobenius-norm difference between the estimated and exact reflections instead of the TSVD operation. This improved method can effectively overcome the problem of reflection-rank estimation in the global and local rank-reduction methods and adjusts to the diversity and complexity of seismic data. The adaptive data-driven algorithms show good performance in terms of the trade-off between high-quality diffraction separation and reflection suppression for the optimal rank-reduction operation. Applications of the proposed strategy to synthetic and field examples demonstrate the superiority of diffraction separation in detecting and revealing subsurface small-scale geologic discontinuities and inhomogeneities.

Anisotropic Modeling with Geometric Multigrid Preconditioned Finite Element Method

Formation anisotropy in complicated geophysical environments can have a significant impact on data interpretation of electromagnetic surveys. To facilitate full 3D modeling of arbitrary anisotropy, we have adopted an h-version geometric multigrid preconditioned finite-element method based on vector basis functions. By using a structured mesh, instead of an unstructured one, our method can conveniently construct the restriction and prolongation operators for multigrid implementation, and then recursively coarsen the grid with the F-cycle coarsening scheme. The geometric multigrid method is used as a preconditioner for the biconjugate-gradient stabilized method to efficiently solve the linear system resulting from the finite-element method. Our method avoids the need of interpolation for arbitrary anisotropy modeling as in Yee’s grid-based finite-difference method, and it is also more capable of large-scale modeling with respect to the p-version geometric multigrid preconditioned finite-element method. A numerical example in geophysical well logging is included to demonstrate its numerical performance. Our h-version geometric multigrid preconditioned finite-element method is expected to help formation anisotropy characterization with electromagnetic surveys in complicated geophysical environments.

Inferring Hydraulic Connectivity of Induced Fractures in the Near-wellbore Region Using DAS-recorded Tube Waves Excited by Perforation Shots

We present a novel use of tube waves exited by perforation (or “perf”) shots and recorded on distributed acoustic sensing (DAS) to infer and compare the hydraulic connectivity of induced fractures near the wellbore on a stage-by-stage basis. Evaluating the fracture connectivity near the wellbore is critical since it controls the flow of the hydrocarbons from the formation to the wellbore. Currently, there are no established methods used to assess this property. However, we discuss how tube wave decay rates can be used to infer relative differences in fracture connectivity between stages and, through field observations on DAS, demonstrate the correlation between decay rates and frac effectiveness. Additionally, we consider other potential uses of this data in unconventional wells such as assessing plug integrity and constraining fracture geometry with Krauklis waves. DAS data is commonly acquired during the perf shots but primarily for fiber depth calibration purposes and has not been well studied. Our work illustrates the untapped potential of this data and how it can be easily repurposed to bring new insights about fracture characteristics in the near-wellbore region.

Predicting variations of the least principal stress with depth: Application to unconventional oil and gas reservoirs using a log-based viscoelastic stress relaxation model

Knowledge of layer-to-layer variations of the least principal stress, S hmin, with depth is essential for optimization of multi-stage hydraulic fracturing in unconventional reservoirs. Utilizing a geomechanical model based on viscoelastic stress relaxation in relatively clay rich rocks, we present a new method for predicting continuous S hmin variations with depth. The method utilizes geophysical log data and S hmin measurements from routine diagnostic fracture injection tests (DFITs) at several depths for calibration. We consider a case study in the Wolfcamp formation in the Midland Basin, where both geophysical logs and values of S hmin from DFITs are available. We compute a continuous stress profile as a function of the well logs that fits all of the DFITs well. We utilized several machine learning technologies, such as bootstrap aggregation (or bagging), to improve the generalization of the model and demonstrate that the excellent fit between predicted and observed stress values is not the result of over-fitting the calibration points. The model is then validated by accurately predicting hold-out stress measurements from four wells within the study area and, without recalibration, accurately predicting stress as a function of depth in an offset pad about 6 miles away.

Seismic Wave Field Model Excited by a Finite Long Cylindrical Charge

The amplitude-frequency characteristic of a seismic wave excited by explosion sources directly affects the accuracy of seismic exploration. To reveal the effect law related to a cylindrical charge, the research proposes a seismic wavefield model excited by a long cylindrical charge. According to the characteristics of the blasting cavity generated by a finite length cylindrical charge, the seismic wavefield characteristics of a cylindrical charge excitation is obtained by superposing the seismic wavefield excited by a series of spherical charges. Numerical simulation results show that the calculation error of the blasting cavity characteristics of the theoretical model is within 10%. The comparison with field experimental results shows that the error of the model is within 9.4%. The velocity field of the excited seismic wave is almost the same as that of the spherical charge when the explosion distance to the cylindrical charge with finite length is 16-21 times longer than the charge length, but the frequency of the seismic wave is 30% higher than for a spherical charge. Moreover, the explosive velocity has a certain influence on the amplitude-frequency characteristic of the seismic wave excited by the cylindrical charge. The established theoretical model can accurately describe the amplitude-frequency characteristics of the seismic wavefield excited by a cylindrical charge with finite length.

Changes in soil conditions before and after earthquakes at a repetitive soil liquefaction site in Taiwan

Beishih Village of Hsinhua Township in southern Taiwan is a unique location for studying soil liquefaction. Soil liquefaction was observed at the same site after earthquakes in 1946, 2010, and 2016, each of which had a Richter magnitude greater than six. This recurrence provides an opportunity for analyzing soil condition variations resulting from soil liquefaction. Seismic data sets were collected in 2011, 2014, 2016, and 2017. We used seismic refraction tomography and the multichannel analysis of surface waves to estimate P- and S-wave velocities. In S-wave velocity profiles, low shear velocity zones were located beneath sand volcanoes shortly after two earthquakes and disappeared 4 years after a 2010 earthquake. However, the P-wave velocity is less sensitive to soil condition changes, possibly because groundwater obscures the effect of soil liquefaction on velocity profiles. In addition, we used seismic wave velocities to determine the importance of soil properties such as Poisson’s ratio, shear modulus, and porosity to identify the cause of the low shear velocity zone. Notably, although porosity decreased after soil grain rearrangement, sand and clay mixing increased the Poisson’s ratio, reducing the shear modulus of the soil. In addition, a soil layer between 2 and 7 m and a deeper layer below 10 m that resulted in sand volcanoes were both liquefied. We also considered how the evaluation of soil liquefaction potential could be affected by long-term variations in soil conditions and changes resulting from liquefaction. The factor of safety was used to evaluate the liquefaction potential of the site. The results revealed that the assessment conducted long after the earthquake underestimated risk because the soil developed shear strength after the earthquake.

Numerical modeling of self-potential in heterogeneous reservoirs

Monitoring water movement toward production wells through downhole measurements of self-potential (SP) was a promising new technology. However, there were uncertainties about its applicability in heterogeneous, multilayered reservoirs. Using numerical modeling, we investigated the likely magnitude and behavior of SP during oil production supported by water injection in two different models of such reservoirs. We found that the magnitude of the SP signal that would be measured along a production well increased as water approached the well, exceeding an assumed noise level of 0.1 mV before water breakthrough. We also found that, in the reservoir models tested, the maximum value of SP at the well skewed toward the fastest waterfront before water breakthrough. The trend of SP increasing at the well with time, together with the shape of the SP profile, were the prime indicators used to investigate water movement. In the reservoir models tested, before water breakthrough the fastest approaching waterfront could be detected approximately 20 m away from the well. However, subsequent waterfronts approaching the well in other layers could not be detected before breakthrough. The effect of these later waterfronts on the SP profile at the well was only detectable at breakthrough. We attributed this to the fact that the SP generated in these layers is masked by the high SP created by the fastest waterfront. Our findings emphasized the importance of an enhanced understanding of reservoir geology and rock electrical properties for better prediction and interpretation of SP.

Innovative application of full-waveform inversion applied to extended wide-azimuth marine streamer seismic in a complex salt environment

We demonstrated the application of full-waveform inversion (FWI) guided velocity model building to an extended wide-azimuth towed streamer (EWATS) seismic data set in the Gulf of Mexico. Field data were collected over a historically challenging imaging area, colloquially called the “grunge zone” due to the formation of a compressional allosuture emplaced between two colliding salt sheets. These data had a poor subsalt image below the suture with conventional narrow-azimuth data. Additional geologic complexities were observed including high-velocity carbonate carapace near the top of salt and multiple intrasalt sedimentary inclusions. As such, improved seismic imaging was required to plan and execute wells targeting subsalt strata. Significant improvements to the velocity model and subsalt image were evident with wide-azimuth towed streamer and later EWATS data using conventional top-down velocity model building approaches. Then, high-impact improvements were made using EWATS data with an FWI velocity model building workflow; this study represented an early successful application of FWI used to update salt body geometries from streamer seismic data, in which many past applications were limited to improving sedimentary velocities. Later petrophysical data verified the new FWI-derived model, which had significantly increased confidence in the structural and stratigraphic interpretation of subsalt reservoir systems below the grunge zone.

A Matlab code package for 2D/3D local slope estimation and structural filtering

Local slope is an important attribute that can help distinguish seismic signals from noise. Based on optimal slope estimation, many filtering methods can be designed to enhance the signal-to-noise ratio (S/N) of noisy seismic data. We present an open-source Matlab code package for local slope estimation and corresponding structural filtering. This package includes 2D and 3D examples with two main executable scripts and related sub-functions. All code files are in the Matlab format. In each main script, local slope is estimated based on the well-known plane wave destruction algorithm. Then, the seismic data are transformed to the flattened domain by utilizing this slope information. Further, the smoothing operator can be effectively applied in the flattened domain. We introduce the theory and mathematics related to these programs, and present the synthetic and field data examples to show the usefulness of this open-source package. The results of both local slope estimation and structural filtering demonstrate that this package can be conveniently and effectively applied to the seismic signal analysis and denoising.