Geophysical Problems Research Articles

Seismic Velocity Model Building Using Recurrent Neural Networks: A Frequency-Stepping Approach

Data-driven artificial neural networks (ANNs) demonstrably offer numerous advantages over conventional deterministic methods in a wide range of geophysical problems. For seismic velocity model building, judiciously trained ANNs offer the possibility of estimating subsurface velocity models; however, there are substantial challenges with effective and efficient network training. Motivated by the multi-scale approach commonly used to address FWI non-linearity challenges, we develop a frequency-stepping velocity model building approach that uses a sequence-to-sequence recurrent neural network (RNN) with built-in long short-term memory (LSTM). The input sequences to the LSTM-RNN consist of the frequency-domain seismic data ordered by frequency from lowest available to highest usable or chosen, while the corresponding output sequences are frequency-dependent smoothed velocity models. We compare models recovered using the trained RNN to the true models qualitatively and quantitatively. The normalized root-mean-square (NRMS) misfit between the true and predicted models has a mean of 6%, which confirms that the network recovers highly accurate models.

Semi-supervised learning seismic inversion based on Spatio-temporal sequence residual modeling neural network

The Spatio-temporal sequence residual modeling neural network (STSRM-net) is built to address the geophysical problem of obtaining P-impedance of the subsurface from the zero-offset seismic data and initial model of P-impedance. The initial model is used as the initial value of STSRM-net, and the modification value of the initial model and the residual between the modified initial model and true P-impedance are learned during the training. The Spatio-temporal characteristics of the data could be fully dug by STSRM-net. Limited by the inadequacy of labeled data, the semi-supervised learning inversion framework is constructed to train the STSRM-net. The performance of the STSRM-net and some deep learning inversion methods are compared on the synthetic dataset. The test results indicate that STSRM-net has higher inversion accuracy, stronger continuity, and better anti-noise performance. In addition, the robustness experiments indicate that the STSRM-net has excellent fault tolerance to the initial model. Finally, the STSRM-net is applied to the field data and compared with the sparse pulse inversion method, which also proves high inversion resolution, inversion accuracy and robustness to the choice of training wells of the proposed method.

Uncertainty quantification in stochastic inversion with dimensionality reduction using variational autoencoder

Estimating rock and fluid properties in the subsurface from geophysical measurements is a computationally and memory-intensive inverse problem. For nonlinear problems with non-Gaussian variables, analytical solutions are generally not available, and the solutions of those inverse problems must be approximated using sampling and optimization methods. To reduce the computational cost, model and data can be reparameterized into low-dimensional spaces where the solution of the inverse problem can be computed more efficiently. Among the potential dimensionality reduction methods, deep-learning algorithms based on deep generative models provide an efficient approach to reduce the dimension of the model and data vectors. However, such dimension reduction might lead to information loss in the reconstructed model and data, reduction of the accuracy and resolution of the inverted models, and under- or overestimation of the uncertainty of the predicted models. To comprehensively investigate the impact of model and data dimension reduction with deep generative models on uncertainty quantification, we compare the prediction uncertainty in nonlinear inverse problem solutions obtained from Markov chain Monte Carlo and ensemble-based data assimilation methods implemented in lower dimensional data and model spaces using a deep variational autoencoder. Our workflow is applied to two geophysical inverse problems for the prediction of reservoir properties: prestack seismic inversion and seismic history matching. The inversion results consist of the most likely model and a set of realizations of the variables of interest. The application of dimensionality reduction methods makes the stochastic inversion more efficient.

A new technique for remote location of unknown caves and deep-seated faults by unmanned aerial systems (UAS)

Here, for the first time in Bulgaria, we demonstrate that aerial survey of the terrain with a coaxial thermal and visible camera mounted on an UAS can detect much larger number of entrances to underground cavities and deep seated faults than a detailed systematic ground survey by experienced personnel. Thus geophysical problems are solved with these remote sensing methods. It is extremely promising and reveals great opportunities for improving techniques for location of unknown caves and deep seated faults to a much higher level. Obtained results are a significant step forward in the state-of-the art.

Unilateral Alignment: An interpretable machine learning method for geophysical logs calibration

Most of the existing machine learning studies in logs interpretation do not consider the data distribution discrepancy issue, so the trained model cannot well generalize to the unseen data without calibrating the logs. In this paper, we formulated the geophysical logs calibration problem and give its statistical explanation, and then exhibited an interpretable machine learning method, i.e., Unilateral Alignment, which could align the logs from one well to another without losing the physical meanings. The involved UA method is an unsupervised feature domain adaptation method, so it does not rely on any labels from cores. The experiments in 3 wells and 6 tasks showed the effectiveness and interpretability from multiple views.

Two optimization methods for solving the inverse gravimetrical problem

Mineral exploration, in particular, increasing the accuracy of calculations up to now is one of the urgent problems of geophysics. It is necessary to restore the density of a given inhomogeneity after considering the results of measuring the potential and its gradient on the surface of the earth. One of the measured values, the potential or the gradient of the gravity field, is chosen beyond the boundary condition, and the second corresponds to the minimized functional, i.e. one in-verse problem can be put in correspondence two different optimization problems. Both problems are solved based on the same gradient method. Based on the numerical analysis, two methods for solving the inverse problem are compared.

Discretization of equations Gelfand-Levitan-Krein and regularization algorithms

The paper considers the initial-boundary-value inverse problem of acoustics for onedimensional and multidimensional cases. The inverse problems are to reconstruct the coefficients using one-dimensional and multidimensional analogues of the Gelfand-Levitan-Krein integral equations. It is known that such equations are linear integral Fredholm equations of the first kind, which are ill-posed. The aim of the work is to find a numerical solution of the Gelfand-Levitan-Krein equation using iterative regularizing algorithms. Using the specifics of these equations (the kernel of the equation depends on the difference of arguments) it is possible to create highly efficient iterative regularizing algorithms. The implemented algorithms can be successfully applied in solving such problems as reconstruction of blurred and defocused images, inverse problem of gravimetric, linear programming problem with inaccurately given matrix of constraints, inverse problem of Geophysics, inverse problems of computed tomography, etc. The main results of the work are the discretization of the one-dimensional and multidimensional Gelfand-Levitan-Krein equation and the construction of iterative regularization algorithms.

Robust Lp-Norm Inversion for High-Resolution Fluid Contents from Nuclear Magnetic Resonance Measurements

Fluid content computed from nuclear magnetic resonance (NMR) has proved to be an accurate and reliable tool for petrophysical property estimation. To overcome the limitations of conventional NMR measurements, high spatial resolution NMR (HSR-NMR) has been introduced to achieve the desired resolution for cores of any size. However, inversion of fluid contents from HSR-NMR data suffers from nonreliable measurements at the ends of the detection coil due to the heterogeneities of the magnetic fields caused by the relatively small size of the coil. A robust Lp-norm inversion algorithm, developed for geophysical inverse problems, has been implemented and applied on the inversion of NMR measurements. The estimated fluid content from Lp inversion matches well with the kerogen content in the cores both visually and quantitively. The resolution of the inverted fluid contents is as high as 1 inch. Further testing on the raw data with large derivations demonstrated that reliable results can only be achieved by using Lp inversion with low p’s values within the range of (1, 1.1).

Innovation: Complex Geophysics in the Field of Archaeology (South Bulgarian Black Sea Coastline)

The study examines the results of complex geophysical research of threearchaeological sites located near the southern part of the Black Sea coastline in Bulgaria:Propadnalata Voda, Atiya, and Alepu. The authors discuss the use of complex geophysical methodsin archaeology depending on the objectives of archaeological research, on the one hand, and thelikely properties of the archaeological sites, on the other. As known, the methods of appliedgeophysics involve reverse geophysical problems, which do not have definitive solutions. Toovercome potential ambiguities in this regard, the study demonstrates how the complementary useof different methods makes the interpretation of the final results easier.

Implicit approximate decoupling procedure withCrank–Nicolsonscheme for bandpass symmetric rotationally geophysical problems

To efficient simulate symmetric rotationally geophysical problems, implicit Crank–Nicolson (CN) scheme incorporated with approximate decoupling procedure is proposed in the body of revolution (BOR) finite-difference time-domain (FDTD) algorithm. For further absorption of large number of low-frequency waves in bandpass simulation, complex envelope method is incorporated with the perfectly matched layer implementation. To be more specific, the proposed implementation shows advantages in terms of improved efficiency, considerable accuracy, and remarkable absorption. To demonstrate effectiveness and efficiency of the proposed implementation, geophysical numerical examples are carried out in the BOR-FDTD domain. Through different numerical examples, it can be concluded from simulation results that the proposed implementation can obtain admirable entire performance in bandpass geophysical simulation. In addition, it can also be illustrated that it can keep stable when time step surpasses far beyond the Courant–Friedrichs- Levy condition.

Two-phase SPH modelling of a real debris avalanche and analysis of its impact on bottom drainage screens

Rapid flow-like landslides, particularly debris flows and debris avalanches, cause significant economic damage and many victims worldwide every year. They are usually extremely fast with the capability of travelling long distances in short times, sweeping away everything in their path. The principal objective of this paper is to test the ability of the ‘GeoFlow-SPH’ two-phase model developed by the authors, to reproduce the complex behaviour of natural debris avalanches where pore-water pressure evolution plays a key role. To reach this goal, the model is applied to reproduce the complex dynamic behaviour observed in Johnsons Landing debris avalanche including the observed bifurcation caused by the flowing out of part of the moving mass from the mid-channel. Initial thickness deposit trim-line, distribution of deposit volume, and the average velocities were provided for this real case, making it an appropriate case to validate the developed model. The paper also contributes to evaluate the SPH-FD model’s potentialities to simulate the structural countermeasure, like bottom drainage screens, used to reduce the impact of debris flows. The analysis of the results shows the adequacy of the proposed model to solve this complicated geophysical problem.

Improved Modified Symbiosis Organisms Search (IMSOS): A New and Adaptive Approach for Determining Model Parameters from Geoelectrical Data

Symbiotic Organisms Search (SOS) is a global optimization algorithm inspired by the natural synergy between the organisms in an ecosystem. The interactive behavior among organisms in nature simulated in SOS consists of mutualism, commensalism, and parasitism strategies to find the global optimum solution in the search space. The SOS algorithm does not require a tuning parameter, which is usually used to balance explorative and exploitative search by providing posterior sampling of the model parameters. This paper proposes an improvement of the Modified SOS (MSOS) algorithm, called IMSOS, to enhance exploitation along with exploration strategies via a modified parasitism vector. This improves the search efficiency in finding the global minimum of two multimodal testing functions. Furthermore, the algorithm is proposed for solving inversion problems in geophysics. The performance of IMSOS was tested on the inversion of synthetic and field data sets from self-potential (SP) and vertical electrical sounding (VES) measurements. The IMSOS results were comparable to those of other global optimization algorithms, including the Particle Swarm Optimization, the Differential Evolution and the Black Holes Algorithms. IMSOS accurately determined the model parameters and their uncertainties. It can be adapted and can potentially be used to solve the inversion of other geophysical data as well.

Workshop Review: Joint DGG-SEG Scientific Drilling Workshop a success

SEG and the German Geophysical Society (DGG) held their first joint workshop in early March at DGG's 2021 Annual Meeting. The workshop was part of a new cooperative aim between DGG and SEG to promote engagement between the societies, to foster growth in geophysics, and to expand the community of scientists and engineers tackling important geophysical problems. The 2021 workshop theme, “Scientific Drilling,” was chosen because scientific drilling provides access to rocks and fluids in the subsurface that are essential for ground truthing interpretations from geophysical data and geologic interpretation, for providing samples and in-situ data for detailed characterization, and for providing inputs to models. Consequently, the workshop aimed to attract interest across many subfields of geophysics.

Flower Pollination Algorithm for the Inversion of Schlumberger Sounding Curve

Inversion of schlumberger sounding curve is non-linear, and multi-minimum. All linear inversion strategies can produce local optimum, and depend on the initial model. Meanwhile, the non-linear bionic method for inversion problems does not require an initial model, simple, flexible, derivation-free mechanism and can avoid local optimum. One of the new algorithm of the non-linear bionic method for geophysical inversion problem is the Flower Pollination Algorithm (FPA). The FPA is used for the inversion of schlumberger sounding curve. This algorithm was stimulated by the pollination process for blooming plants. The applicability of the present algorithm was tested on synthetic models A-type and KH-type curve. Numerical tests in MATLAB R2013a for the synthetic data and the observed data show that FPA can find the global minimum. For further study, inverted results using the FPA are contrasted with the damped least-square (DLSQR) inversion program, Particle Swarm Optimization (PSO), and Grey Wolf Optimizer (GWO). The outcomes of the comparison reveal that FPA performs better than the DLSQR inversion program, PSO, and GWO.

Discrete cosine transform for parameter space reduction in Bayesian electrical resistivity tomography

ABSTRACTElectrical resistivity tomography is a non‐linear and ill‐posed geophysical inverse problem that is usually solved through gradient‐descent methods. This strategy is computationally fast and easy to implement but impedes accurate uncertainty appraisals. We present a probabilistic approach to two‐dimensional electrical resistivity tomography in which a Markov chain Monte Carlo algorithm is used to numerically evaluate the posterior probability density function that fully quantifies the uncertainty affecting the recovered solution. The main drawback of Markov chain Monte Carlo approaches is related to the considerable number of sampled models needed to achieve accurate posterior assessments in high‐dimensional parameter spaces. Therefore, to reduce the computational burden of the inversion process, we employ the differential evolution Markov chain, a hybrid method between non‐linear optimization and Markov chain Monte Carlo sampling, which exploits multiple and interactive chains to speed up the probabilistic sampling. Moreover, the discrete cosine transform reparameterization is employed to reduce the dimensionality of the parameter space removing the high‐frequency components of the resistivity model which are not sensitive to data. In this framework, the unknown parameters become the series of coefficients associated with the retained discrete cosine transform basis functions. First, synthetic data inversions are used to validate the proposed method and to demonstrate the benefits provided by the discrete cosine transform compression. To this end, we compare the outcomes of the implemented approach with those provided by a differential evolution Markov chain algorithm running in the full, un‐reduced model space. Then, we apply the method to invert field data acquired along a river embankment. The results yielded by the implemented approach are also benchmarked against a standard local inversion algorithm. The proposed Bayesian inversion provides posterior mean models in agreement with the predictions achieved by the gradient‐based inversion, but it also provides model uncertainties, which can be used for penetration depth and resolution limit identification.

Novel technique for the interpretation of gravity anomalies over geologic structures with idealized geometries using the Manta ray foraging optimization

In this study, the potential and efficacy of adapting the bioinspired Manta ray foraging optimization algorithm (MRFO) as a tool for estimating model parameters of two-dimensional gravity profile anomalies is presented. The process of implementing the MRFO algorithm for accurate estimation of shape/depth defining parameters over geometric geologic structures was assessed. The experimental data comprised synthetically generated gravity anomalies that were later corrupted with white Gaussian noise at levels of 5, 10, and 15%, and then, case examples were taken from mining sites across different parts of the world. The algorithm was found to be fast, stable, and consistent in its search for the global best solution to each of the geophysical inverse problems. Its performance was excellent when confronted with constrained multi-parameter non-linear inversion problems and exhibited admirable stability even in the presence of noise. The consistency of the estimated results, when compared to actual values, affirmed the reliability of the procedure. It is, therefore, a stable and efficient tool for performing geophysical data inversion and is recommended for use in inverting geophysical data with higher complexities like seismic reflection, self-potential and magnetic data, which require many corrections to be performed before reliable geological interpretations can be made.

Using deep generative neural networks to account for model errors in Markov chain Monte Carlo inversion

SUMMARY Most geophysical inverse problems are non-linear and rely upon numerical forward solvers involving discretization and simplified representations of the underlying physics. As a result, forward modelling errors are inevitable. In practice, such model errors tend to be either completely ignored, which leads to biased and over-confident inversion results, or only partly taken into account using restrictive Gaussian assumptions. Here, we rely on deep generative neural networks to learn problem-specific low-dimensional probabilistic representations of the discrepancy between high-fidelity and low-fidelity forward solvers. These representations are then used to probabilistically invert for the model error jointly with the target geophysical property field, using the computationally cheap, low-fidelity forward solver. To this end, we combine a Markov chain Monte Carlo (MCMC) inversion algorithm with a trained convolutional neural network of the spatial generative adversarial network (SGAN) type, whereby at each MCMC step, the simulated low-fidelity forward response is corrected using a proposed model-error realization. Considering the crosshole ground-penetrating radar traveltime tomography inverse problem, we train SGAN networks on traveltime discrepancy images between: (1) curved-ray (high fidelity) and straight-ray (low fidelity) forward solvers; and (2) finite-difference-time-domain (high fidelity) and straight-ray (low fidelity) forward solvers. We demonstrate that the SGAN is able to learn the spatial statistics of the model error and that suitable representations of both the subsurface model and model error can be recovered by MCMC. In comparison with inversion results obtained when model errors are either ignored or approximated by a Gaussian distribution, we find that our method has lower posterior parameter bias and better explains the observed traveltime data. Our method is most advantageous when high-fidelity forward solvers involve heavy computational costs and the Gaussian assumption of model errors is inappropriate. Unstable MCMC convergence due to non-linearities introduced by our method remain a challenge to be addressed in future work.

Pre-conditioned BFGS-based uncertainty quantification in elastic full-waveform inversion

SUMMARYFull-waveform inversion has become an essential technique for mapping geophysical subsurface structures. However, proper uncertainty quantification is often lacking in current applications. In theory, uncertainty quantification is related to the inverse Hessian (or the posterior covariance matrix). Even for common geophysical inverse problems its calculation is beyond the computational and storage capacities of the largest high-performance computing systems. In this study, we amend the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm to perform uncertainty quantification for large-scale applications. For seismic inverse problems, the limited-memory BFGS (L-BFGS) method prevails as the most efficient quasi-Newton method. We aim to augment it further to obtain an approximate inverse Hessian for uncertainty quantification in FWI. To facilitate retrieval of the inverse Hessian, we combine BFGS (essentially a full-history L-BFGS) with randomized singular value decomposition to determine a low-rank approximation of the inverse Hessian. Setting the rank number equal to the number of iterations makes this solution efficient and memory-affordable even for large-scale problems. Furthermore, based on the Gauss–Newton method, we formulate different initial, diagonal Hessian matrices as pre-conditioners for the inverse scheme and compare their performances in elastic FWI applications. We highlight our approach with the elastic Marmousi benchmark model, demonstrating the applicability of pre-conditioned BFGS for large-scale FWI and uncertainty quantification.

A MODULE OF A GEOINFORMATION SYSTEM BASED ON NUMERICAL MODELING OF INVERSE PROBLEMS OF GEOCHEMISTRY BY REGULARIZING ALGORITHMS

Currently, due to the rapid development of computer technology in geology, methods and approaches of scientific visualization based on additional data analysis are being intensively developed. The general concept is that the main data field on the daily surface and additional conditions are set at the input. Further, methods of mathematical geophysics are used for their analysis and processing, as a result of which new information is obtained for deep surveys. Then, in the information system, visualization tools are applied to the new information received and to the main data field. Thus, the information system is based on the synthesis of visual representation methods and methods of mathematical geophysics, computational mathematics from different branches of knowledge. This paper presents a description of the software module of the geoinformation system, based on the methods of intelligent detection of anomalies of hidden deposits, for deep predictive and search modeling of deposits. The functioning of the software module is based on the application of the theory of inverse problems of mathematical geophysics with elements of artificial intelligence using geological data on the earth's surface, geophysical measurements and geochemical analyses as input data. The program module for the inverse problem of the continuation of potential fields in the direction of disturbing masses is used for real data of a specific mineral deposit.

A three‐dimensional hybrid finite element — spectral boundary integral method for modeling earthquakes in complex unbounded domains

AbstractWe present a 3D hybrid method which combines the finite element method (FEM) and the spectral boundary integral method (SBIM) to model nonlinear problems in unbounded domains. The flexibility of FEM is used to model the complex, heterogeneous, and nonlinear part— such as the dynamic rupture along a fault with near fault plasticity—and the high accuracy and computational efficiency of SBIM is used to simulate the exterior half spaces perfectly truncating all incident waves. The exact truncation allows us to greatly reduce the domain of spatial discretization compared to a traditional FEM approach, leading to considerable savings in computational time and memory requirements. The coupling of FEM and SBIM is achieved by the exchange of traction and displacement boundary conditions at the computationally defined boundary. The method is suited to implementation on massively parallel computers. We validate the developed method by means of a benchmark problem. Three more complex examples with a low velocity fault zone, low velocity off‐fault inclusion, and interaction of multiple faults, respectively, demonstrate the capability of the hybrid scheme in solving problems of very large sizes. Finally, we discuss potential applications of the hybrid method for problems in geophysics and engineering.