Heterogeneous Velocity Models Research Articles

Near offset reconstruction for marine seismic data using a convolutional neural network

AbstractMarine seismic data is often missing near offset information due to separation between the source and receiver cables. To solve this problem, a convolutional neural network is trained on synthetic seismic data to reconstruct the near offset gap. The synthetic data is created using a two‐dimensional finite difference method within a heterogeneous velocity model. These synthetics are generated with a source‐over‐receiver acquisition geometry so that they contain complete near offset data. The convolutional neural network is then trained on input‐target synthetic pairs where the inputs are common midpoint gathers with the near offset section removed, and the targets are the same gathers with the near offset section retained. Following training, the robustness of the method is investigated with regards to common midpoint data sorting, normal moveout correction and changes in the velocity model. It is found that training on common midpoint‐sorted data results in 2.8 times lower error than training on shot gathers, that normal moveout correction of the training data makes no significant difference in error levels, and that the model can reconstruct realistic near offsets on synthetic data generated 10 km away within the heterogeneous velocity model. In field data testing, first a dataset with source‐over‐cable acquisition geometry from the Barents Sea is used to compare the reconstructed wavefields to ground truth values. Although the reconstructed amplitudes require minor scaling to match the true values, predictions on this dataset yield 2.5 times lower near offset reconstruction error compared to a simple Radon transform interpolation method. Furthermore, amplitude versus offset gradient and intercept sections from the Barents Sea dataset are estimated with half the error when including the convolutional neural network‐predicted near offset data, compared to only using the conventionally‐acquirable portion of the data (beyond 112.5 m of offset). In a secondary field data test, a conventional northern North Sea dataset is used to demonstrate how the method may be applied in practice. Here, the convolutional neural network generates more realistic predictions than the Radon method, and the gradient and intercept sections calculated using the convolutional neural network‐predicted traces have higher signal‐to‐noise ratios than the sections calculated using only the original data. The combination of high‐quality synthetic training data and interpolation in the common midpoint domain enables near offset reconstruction at significant depth (1 s of two‐way traveltime or more), which is demonstrated in both synthetic and field examples.

Synthetic Data Generation for Deep Learning-Based Inversion for Velocity Model Building

Recent years have seen deep learning (DL) architectures being leveraged for learning the nonlinear relationships across the parameters in seismic inversion problems in order to better analyse the subsurface, such as improved velocity model building (VMB). In this study, we focus on deep-learning-based inversion (DLI) for velocity model building, leveraging on a conditional generative adversarial network (PIX2PIX) with ResNet-9 as generator, as well as a comprehensive mathematical methodology for generating samples of multi-stratified heterogeneous velocity models for training the DLI architecture. We demonstrate that the proposed architecture can achieve state-of-the-art performance in reconstructing velocity models using only one seismic shot, thus reducing cost and computational complexity. We also demonstrate that the proposed solution is generalisable across linear multi-layer models, curved or folded structures, structures with salt bodies as well as higher-resolution structures built from geological images through quantitative and qualitative evaluation.

An Inverted Heterogeneous Velocity Model for Microseismic Source Location in Deep Buried Tunnels

An Inverted Heterogeneous Velocity Model for Microseismic Source Location in Deep Buried Tunnels

Imaging and seismic modelling inside volcanoes using machine learning

Despite advances in seismology and computing, the ability to image subsurface volcanic environments is poor, limiting our understanding of the overall workings of volcanic systems. This is related to substantive structural heterogeneities which strongly scatters seismic waves obscuring the ballistic arrivals normally used in seismology for wave velocity determination. Here we address this constraint by, using a deep learning approach, a Fourier neural operator (FNO), to model and invert seismic signals in volcanic settings. The FNO is trained using 40,000+ simulations of elastic wave propagation through complex volcano models, and includes the full scattered wavefield. Once trained, the forward network is used to predict elastic wave propagation and is shown to accurately reproduce the seismic wavefield. The FNO is also trained to predict heterogeneous velocity models given a limited set of input seismograms. It is shown to capture details of the complex velocity structure that lie far outside the ability of current methods available in volcano imagery.

Neural Eikonal solver: Improving accuracy of physics-informed neural networks for solving eikonal equation in case of caustics

The concept of physics-informed neural networks has become a useful tool for solving differential equations due to its flexibility. A few approaches use this concept to solve the eikonal equation that describes the first-arrival traveltimes of waves propagating in smooth heterogeneous velocity models. However, the challenge of the eikonal is exacerbated by the velocity models producing caustics, resulting in instabilities and deterioration of accuracy due to the non-smooth solution behavior. In this paper, we revisit the problem of solving the eikonal equation using neural networks to tackle caustic pathologies. We introduce the novel Neural Eikonal Solver (NES) for solving the isotropic eikonal equation in two formulations: the one-point problem is for a fixed source location; the two-point problem is for an arbitrary source-receiver pair. We present several techniques which provide stability in the case of caustics: improved factorization; non-symmetric loss function based on Hamiltonian; gaussian activation; symmetrization. In our tests, NES showed the relative mean-absolute error of 0.2-0.4% from the second-order factored Fast Marching Method with a similar inference time, and outperformed existing neural-network solvers giving 10-60 times lower errors and 2-30 times faster training. The one-point NES provides the most accurate solution, while the two-point NES gives slightly lower accuracy but an extremely compact representation with all spatial derivatives. It can be useful in many seismic problems: massive computations of traveltimes for millions of source-receiver pairs in Kirchhoff migration; modeling of ray amplitudes using spatial derivatives; traveltime tomography; earthquake localization; ray multipathing analysis.

Seismic source location using the shortest path method based on boundary discretisation scheme for microseismic monitoring in underground mines

In seismic monitoring at underground mines, the velocity models can be highly complex, particularly in presence of major geological structures . In practice, homogeneous velocity models have been widely used for the purposes of seismic event location in mine seismology . Although heterogeneous velocity models can be incorporated, ray tracing methods need be adopted in these velocity models to compute the travel times for accurately locating seismic events. These methods require each geological unit to be discretised to grids (corner-node or center-node discretisation scheme), which requires large computational capacity. In this research, the Shortest Path Method (SPM) (Moser, 1991) based on a novel Boundary Discretisation Scheme (BDS) is proposed to compute the travel times for seismic event location in heterogeneous velocity models. Only the boundaries of each geological unit are discretised to nodes. The graphical network is constructed by establishing ray paths between discretised nodes on the boundaries of geological units. Dijkstra’s algorithm (Dijkstra et al., 1959) using heap sorting method (Cao et al., 1993) is applied to search for the shortest ray paths with the first arrivals for seismic event location. The accuracy and efficiency of this method are validated using a 2D synthetic example. The seismic events recorded during the field monitoring of a dyke-roadway intersected area are located with the proposed BDS-SPM method. The results demonstrate that, compared with the conventional location method using homogeneous velocity models, the proposed method can provide more accurate seismic event locations for microseismic monitoring in underground mines.

2D Geotechnical site-response analysis including soil heterogeneity and wave scattering

This study describes an approach for modeling wave scattering and the spatial variability of ground motion in geotechnical site-response analysis by modeling soil heterogeneity through 2D correlated random fields. Importantly, the required site-specific inputs to apply the proposed approach in a practical setting are the same as those associated with conventional 1D site-response analysis. The results, which are affected by wave scattering attenuation, are compared to those from conventional laterally homogeneous 1D site-response analyses and 1D analyses with randomized velocity profiles extracted from heterogeneous 2D velocity model realizations. A sensitivity study, involving 5400 2D model realizations, investigates the influence of random field input parameters on wave scattering and site response. The computed ground surface acceleration waveforms and transfer functions show that this method is capable of scattering seismic waves. Multiple ground-motion intensity measures are analyzed to quantify this influence and distinguish between the effects of 1D vertical heterogeneities and averaging across many nodes and realizations, from the effects of wave scattering and 2D ground-motion phenomena. The redistribution of ground-motion energy across wider frequency bands and scattering attenuation of high-frequency waves in the 2D analyses resemble features observed in empirical transfer functions computed in other studies. While analyses with 1D randomized velocity profiles are able to replicate median results from 2D analyses for some low-frequency intensity measures (e.g. transfer functions at [Formula: see text] Hz, and spectral acceleration at the fundamental period), medians and standard deviations of high-frequency intensity measures (e.g. transfer function at [Formula: see text] Hz, [Formula: see text], and Arias intensity), which are influenced by wave scattering, are not appropriately captured. Given the equivalent input information requirements as conventional 1D analysis, and the availability of large computational resources, we advocate that the proposed 2D (and eventually 3D) approach is a fruitful path forward to improve the modeling of site-response physics and realize improved predictive capabilities.

Accelerating Bayesian microseismic event location with deep learning

Abstract. We present a series of new open-source deep-learning algorithms to accelerate Bayesian full-waveform point source inversion of microseismic events. Inferring the joint posterior probability distribution of moment tensor components and source location is key for rigorous uncertainty quantification. However, the inference process requires forward modelling of microseismic traces for each set of parameters explored by the sampling algorithm, which makes the inference very computationally intensive. In this paper we focus on accelerating this process by training deep-learning models to learn the mapping between source location and seismic traces for a given 3D heterogeneous velocity model and a fixed isotropic moment tensor for the sources. These trained emulators replace the expensive solution of the elastic wave equation in the inference process. We compare our results with a previous study that used emulators based on Gaussian processes to invert microseismic events. For fairness of comparison, we train our emulators on the same microseismic traces and using the same geophysical setting. We show that all of our models provide more accurate predictions, ∼ 100 times faster predictions than the method based on Gaussian processes, and a 𝒪(105) speed-up factor over a pseudo-spectral method for waveform generation. For example, a 2 s long synthetic trace can be generated in ∼ 10 ms on a common laptop processor, instead of ∼ 1 h using a pseudo-spectral method on a high-profile graphics processing unit card. We also show that our inference results are in excellent agreement with those obtained from traditional location methods based on travel time estimates. The speed, accuracy, and scalability of our open-source deep-learning models pave the way for extensions of these emulators to generic source mechanisms and application to joint Bayesian inversion of moment tensor components and source location using full waveforms.

Estimation of micro-earthquake source locations based on full adjoint P and S wavefield imaging

SUMMARY Locating micro-earthquakes with high resolution and accuracy is a challenge for traveltime inversion, which has uncertainty on the order of a Fresnel zone (many wavelengths). We develop a wave-equation imaging method to increase resolution and reduce location errors to less than a wavelength, but requires very densely deployed receiver arrays with wide aperture and considerable computational cost. Instead of using acoustic data or direct P wave arrivals only, we use elastic multicomponent data and present a new method that uses the full P and S adjoint wavefields to image the microseismic source locations. We separate the P and S waves from the data, and extrapolate the P and S wavefields of each receiver subarray by solving the P and S adjoint wave equations in parallel. We formulate three source imaging conditions by multiplying over subarrays the adjoint P wavefield (IP), S wavefield (IS) and cross-correlated P and S wavefields (IPS). We perform numerical experiments on the highly realistic SEG SEAM4D reservoir model using surface acquisition array geometries. Results for 2-D and 3-D microseismic source estimations show clean images without noisy artefacts at shallow depths. In particular, IPS provides the highest resolution source location image, while IP is limited by the P wavelength and IS is influenced by small coda artefacts. The major-axis alignment and resolution of the source location image are determined by the hypocentral location with respect to the receiver array and illumination-angle coverage, respectively. We discuss the impacts of S-wave attenuation and frequency bandwidth on the source location images. Noise tests indicate that the imaging results are relatively insensitive to ambient noise, as is observed for the surface monitoring data. Using smoothed velocity models, the imaging results are similar to the results using the true realistically heterogeneous velocity model. The 90 per cent confidence ellipse of the source location due to Gaussian-distributed velocity errors shows a larger depth error as the source becomes deeper, while the horizontal error does not change as much.

The impact of heterogeneous salt velocity models on the gross rock volume estimation: an example from the Santos Basin pre-salt, Brazil

The thick and heterogeneous salt section in the Santos Basin, offshore Brazil, imposes great challenges in accessing the pre-salt hydrocarbon reservoirs, especially in relation to seismic imaging, signal quality and depth positioning. Some problems arise from the current velocity models for the salt section, which, for the majority, assume that the salt is a homogeneous halite layer. In the Santos Basin, the commonly assumed salt – halite – only makes up to 80% of the mineral in this section. The inclusion of other salts as stratification in the velocity models, based on seismic attributes, has achieved good results in the last decade, especially for depth resolution. In this work, we analyse the benefits of different velocity models, considering presence/absence of salt stratification and comparing the gross rock volume above the oil–water contact. The results show a significant effect on the depth resolution of the events, as well as on volume estimation, indicating that the greater the reliability captured by the complex velocity models, the greater the confidence in the resulting volumetric information.

Microseismic event detection in large heterogeneous velocity models using Bayesian multimodal nested sampling

Abstract In passive seismic and microseismic monitoring, identifying and characterizing events in a strong noisy background is a challenging task. Most of the established methods for geophysical inversion are likely to yield many false event detections. The most advanced of these schemes require thousands of computationally demanding forward elastic-wave propagation simulations. Here we train and use an ensemble of Gaussian process surrogate meta-models, or proxy emulators, to accelerate the generation of accurate template seismograms from random microseismic event locations. In the presence of multiple microseismic events occurring at different spatial locations with arbitrary amplitude and origin time, and in the presence of noise, an inference algorithm needs to navigate an objective function or likelihood landscape of highly complex shape, perhaps with multiple modes and narrow curving degeneracies. This is a challenging computational task even for state-of-the-art Bayesian sampling algorithms. In this paper, we propose a novel method for detecting multiple microseismic events in a strong noise background using Bayesian inference, in particular, the Multimodal Nested Sampling (MultiNest) algorithm. The method not only provides the posterior samples for the 5D spatio-temporal-amplitude inference for the real microseismic events, by inverting the seismic traces in multiple surface receivers, but also computes the Bayesian evidence or the marginal likelihood that permits hypothesis testing for discriminating true vs. false event detection.

Analysis of the wave propagation paths in numerical reinforced concrete models

The paper aims to study the characteristics of the wave propagation paths in reinforced concrete and to improve the existing velocity models. Therefore, coefficients of reflection and transmission with regard to energy were analyzed for each component of the reinforced concrete (cement matrix, aggregate grains, air voids and reinforcement bars) in case of a free- and joint-material boundary, respectively. The findings were employed to investigate the wave propagation paths in cracked concrete and reinforced concrete. Three-dimensional numerical models to approximate the heterogeneous concrete (numerical concrete model, NCM) and reinforced concrete (numerical reinforced concrete model, NRCM) were implemented in a rotated staggered-grid finite-differences scheme. Numerical simulations of the elastic wave propagation were performed to illustrate the interaction of waves with boundaries. Both velocity models, NCM and NRCM, were applied to localize acoustic emissions (AE). An established source localization estimation method (FastWay) served as a tool to validate the heterogeneous velocity models. FastWay was applied to a synthetic cracked reinforced concrete beam to localize six randomly located AE sources. The influence of non-straight wave propagation paths on the performance of the localization method was discussed.

High-Accuracy Location of Microseismic Events in a Strong Inhomogeneous Mining Environment by Optimized Global Full Waveform Inversion

High-accuracy determination of a microseismic (MS) location is the core task in MS monitoring. In this study, a 3D multi-scale grid Green’s function database, depending on recording wavefield frequency band for the target mining area, is pre-generated based on the reciprocity theorem and 3D spectral element method (SEM). Then, a multi-scale global grid search strategy is performed based on this pre-stored Green’s function database, which can be effectively and hierarchically processed by searching for the spatial location. Numerical wavefield modeling by SEM effectively overcomes difficulties in traditional and simplified ray tracing modeling, such as difficult wavefield amplitude and multi-path modeling in 3D focusing and defusing velocity regions. In addition, as a key step for broadband waveform simulation, the source-time function estimated from a new data-driven singular value decomposition averaged fractional derivative based wavelet function (DD-SVD-FD wavelet) was proposed to generate high-precision synthetic waveforms for better fitting observed broadband waveform than those by simple and traditional source-time function. Combining these sophisticated processing procedures, a new robust grid search and waveform inversion-based location (GSWI location) approach is integrated. In the synthetic test, we discuss and demonstrate the importance of 3D velocity model accuracy to waveform inversion-based location results for a practical MS monitoring configuration. Furthermore, the average location error of the 3D GSWI location for eight real blasting events is only 15.0 m, which is smaller than error from 3D ray tracing-based location (26.2 m) under the same velocity model. These synthetic and field application investigations prove the crucial role of 3D velocity model, finite-frequency travel-time sensitivity kernel characteristics and accurate numerical 3D broadband wavefield modeling for successful MS location in a strong heterogeneous velocity model that are induced by the presence of ore body, host rocks, complex tunnels, and large excavations.

Depth dependent azimuthal anisotropy in Madagascar island from ambient noise tomography

To gain better insight into the structure and complex deformation pattern of Madagascar island, we derived a 3-D heterogeneous and anisotropic velocity model of its crust and uppermost mantle based on ambient noise analyses. The data set comprises ~1 year of seismic ambient noise recorded by 63 broad-band seismic stations deployed in and around the island. Data from Ocean Bottom Seismometers were treated for tilt and compliance noise before applying the standard noise processing routine followed by cross-correlation, dispersion measurement, Rayleigh-wave phase-velocity tomography in period range 5–40 s, and 3-D shear wave velocity modelling to 70 km depth. At shallow to mid-crustal depths, our results show fast velocities all over the Precambrian shield of the eastern two-thirds of the island in contrast to the adjacent west coast that is delineated by slow speeds that correlate with the sedimentary basins. In the lower crust and uppermost mantle, relatively fast velocities preponderate the western third of the island indicating a thinned crust and uplifted mantle. We found complex spatial and depth variation in patterns of azimuthal anisotropy across the island. The orientation of fast azimuth is relatively similar in the upper and middle crust. Aligning mostly N-S in the south and approximately NE-SW in the northern areas, it is attributed to alignment of cracks and metamorphic layering that pervades the Precambrian basement. The fast polarization axis in many sub-regions in the lower crust differs from that in the upper to middle crust and uppermost mantle. Apart from the dominant NE-SW fast axis observed in the uppermost mantle consistent with mantle flow, a semi-circular pattern of anisotropy coinciding with widespread intense slow velocities is observed beneath the central Antananarivo terrane. A delaminating lower crust that is initiated by an upwelling asthenosphere hypothesized for this region is invoked to explain our observation.

Microseismic Event Location by Considering the Influence of the Empty Area in an Excavated Tunnel

The velocity model is a key factor that affects the accuracy of microseismic event location around tunnels. In this paper, we consider the effect of the empty area on the microseismic event location and present a 3D heterogeneous velocity model for excavated tunnels. The grid-based heterogeneous velocity model can describe a 3D arbitrarily complex velocity model, where the microseismic monitoring areas are divided into many blocks. The residual between the theoretical arrival time calculated by the fast marching method (FMM) and the observed arrival time is used to identify the block with the smallest residual. Particle swarm optimization (PSO) is used to improve the location accuracy in this block. Synthetic tests show that the accuracy of the microseismic event location based on the heterogeneous velocity model was higher than that based on the single velocity model, independent of whether an arrival time error was considered. We used the heterogeneous velocity model to locate 7 blasting events and 44 microseismic events with a good waveform quality in the Qinling No. 4 tunnel of the Yinhanjiwei project from 6 June 2017 to 13 June 2017 and compared the location results of the heterogeneous-velocity model with those of the single-velocity model. The results of this case study show that the events located by the heterogeneous velocity model were concentrated around the working face, which matched the actual conditions of the project, while the events located by the single-velocity model were scattered and far from the working face.

Solving fractional Laplacian visco-acoustic wave equations on complex-geometry domains using Grünwald-formula based radial basis collocation method

We propose a radial basis function collocation method (RBF method) to solve fractional Laplacian visco-acoustic wave equation for the Earth media having heterogeneous velocity model and complex geometry. Unlike the fractional Laplacian wave equation proposed in Zhu and Harris (2014), the wave equation we consider has a different definition for the fractional Laplacian. Specifically, spectral and Riesz fractional Laplacians are considered in Zhu and Harris (2014) and the present paper, respectively. Accordingly, the Fourier pseudospectral method (FPS method) and the RBF method are employed to solve the spectral and the Riesz fractional Laplacian wave equations. The two wave equations are observed to produce obviously different wavefields. We demonstrate the validity and flexibility of the proposed RBF method by considering five benchmarks of seismic forward modeling: (1) two-dimensional Earth media with four types of velocity models (homogeneous, two-layer, homogeneous but complex-geometry, and heterogeneous models) and (2) a spherical medium with homogeneous velocity model. We make a three-way comparison among numerical solutions to the Riesz fractional Laplacian, the spectral fractional Laplacian, and the integer-order visco-acoustic wave equations, and observe that when wave attenuation is weak the Riesz wave equation yields more similar wavefield to that of the integer-order wave equation than the spectral wave equation does. Furthermore, uniform and quasi-uniform layouts for collocation points of the RBF method are considered, and the latter layout turns out to be economical since it can preserve the solution accuracy with the minimum number of collocation points. The RBF method is truly mesh-free and dimension-free and can easily handle high-dimensional, irregular domains. Additionally, the method is easier to implement than element-based methods, such as finite element and spectral element methods, for discretizing the Riesz fractional Laplacian.

Comparison of ray-matrix and finite-difference methods in a simple 1-D velocity model

The ray-matrix method can extend the applicability of ray methods to 3-D heterogeneous velocity models containing thin stacks of fine isotropic or anisotropic layers. Ray-matrix synthetic seismograms are compared with finite-difference synthetic seismograms in a simple 1-D velocity model, consisting of a low velocity layer covering a homogeneous halfspace. The agreement between the ray-matrix and finite-difference synthetic seismograms is very good. Moreover, the ray-matrix seismograms do not suffer from extremely thin layers, from anisotropy, and from reflections from the non-reflecting boundaries typical for finite differences.

Targeted location of microseismic events based on a 3D heterogeneous velocity model in underground mining

The accurate location of induced seismicity is a problem of major interest in the safety monitoring of underground mines. Complexities in the seismic velocity structure, particularly changes in velocity caused by the progression of mining excavations, can cause systematic event mislocations. To address this problem, we present a novel construction method for an arbitrary 3D velocity model and a targeted hypocenter determination method based on this velocity model in underground mining. The method constructs a velocity model from 3D geological objects that can accurately express the interfaces of geologic units. Based on this model, the block corresponding to the minimum difference between the observed arrival times and the theoretical arrival times computed by the Fast Marching Method is located. Finally, a relocation procedure is carried out within the targeted block by heuristic algorithms to improve the performance. The accuracy and efficiency of the proposed method are demonstrated by the source localization results of both synthetic data and on-site data from Dongguashan Copper Mine. The results show that our proposed method significantly improves the location accuracy compared with the widely used Simplex and Particle Swarm Optimization methods.

Surrogate regression modelling for fast seismogram generation and detection of microseismic events in heterogeneous velocity models

This work has been supported by the Shell Projects and Technology. The Wilkes high performance GPU computing service at the University of Cambridge has been used in this work.

Travel time computations using a compact eikonal equation for vertical transverse isotropic media

ABSTRACTEikonal solvers often have stability problems if the velocity model is mildly heterogeneous. We derive a stable and compact form of the eikonal equation for P‐wave propagation in vertical transverse isotropic media. The obtained formulation is more compact than other formulations and therefore computationally attractive. We implemented ray shooting for this new equation through a Hamiltonian formalism. Ray tracing based on this new equation is tested on both simple as well as more realistic mildly heterogeneous velocity models. We show through examples that the new equation gives travel times that coincide with the travel time picks from wave equation modelling for anisotropic wave propagation.