Multiscale Full-waveform Inversion Research Articles

Integrating U-Nets Into a Multiscale Full-Waveform Inversion for Salt Body Building

Integrating U-Nets Into a Multiscale Full-Waveform Inversion for Salt Body Building

Suppressing position approximation imaging artifacts in full waveform modeling and inversion of marine seismic data

Full-waveform inversion (FWI) is an advanced seismic imaging method for determining high resolution velocity models of different scales, such as in subseafloor geo-hazard monitoring and risk analysis. Among all two-way wave-equation based modeling methods, a mixed-grid finite-difference modeling (FDM) in frequency domain has the advantage of low numerical dispersion errors for mesh size up to 1/4 wave-length. However, irregular source and receiver positions situated away from the FDM nodes introduce position approximation error (PAE) as large as half mesh size. When a source or receiver is situated in strong heterogeneity or near a free surface, the PAE induces imaging artifacts in high frequencies. We propose an imaging artifact suppression method for multi-scale FDM and FWI in marine seismic survey. The delta function of the source or receiver position is approximated by a discrete Kaiser-windowed sinc function in unbounded medium. The free-surface effects to sources and receivers are compensated with the mirror source concept. The final coefficients for delta function approximation and wavefield interpolation are spatially confined tensor products. The results using ocean bottom cable and vertical cable survey layouts in synthetic models validate the accuracy and feasibility of this new FDM and FWI strategy. The FWI tests shows that this strategy has reduced small scale artifacts at high frequencies for survey layouts of good and poor illuminations. The extension of our method to 3-D visco-acoustic model or reverse time migration is straightforward.

Potential of Phase-Amplitude-Based Multi-Scale Full Waveform Inversion with Total-Variation Regularization for Seismic Imaging of Deep-Seated Ores

As the demand for ore resources increases, the target for mineral exploration gradually shifts from shallow to deep parts of the Earth (>1 km). However, for the ore-hosting strata, it is difficult to obtain high-resolution images by using the electromagnetic method. Seismic full waveform inversion (FWI) is an optimization algorithm which aims at minimizing the prestack seismic data residual between synthetic and observed data. In this case, FWI provides an effective way to achieve high-resolution imaging of subsurface structures. However, acquired seismic data usually lack low frequencies, resulting in severe cycle skipping of FWI, when the initial velocity model is far away from the true one. Phase information in the seismic data provides the kinematic characteristics of waves and has a quasi-linearly relationship with subsurface structures. In this article, we propose to use a phase-amplitude-based full waveform inversion with total-variation regularization (TV-PAFWI) to invert the deep-seated ores. The ore-hosting velocity model test results demonstrate that the TV-PAFWI is suitable for high-resolution velocity model building, especially for deep-seated ores.

Multiscale Full-Waveform Inversion with Land Seismic Field Data: A Case Study from the Jizhong Depression, Middle Eastern China

The Jizhong depression contains several geothermal reservoirs that are characterized by localized low-velocity anomalies. In this article, full-waveform inversion (FWI) is used to characterize these anomalies and determine their extent. This is a challenging problem because the reservoirs are quite small and the available data have usable frequencies only down to 5 Hz. An accurate-enough starting model is carefully built by using an iterative travel time tomography method combined with a cycle-skipping assessment method to begin the inversion at 5 Hz. A multiscale Laplace–Fourier-domain FWI with a layer-stripping approach is implemented on the starting model by gradually increasing the maximum offset. The result of overlapping the recovered velocity model on the migrated seismic profile shows a good correlation between the two results. The recovered model is assessed by ray tracing, synthetic seismogram modeling, checkerboard testing and comparisons with nearby borehole data. These tests indicate that low-velocity anomalies down to a size of 0.3 km × 0.3 km at a maximum depth of 2 km can be recovered. Combined with the well log data, the resulting velocity model allows us to delineate two potential geothermal resources, one of which was previously unknown.

Multiscale Data-Driven Seismic Full-Waveform Inversion With Field Data Study

Seismic full-waveform inversion (FWI), which uses iterative methods to estimate high-resolution subsurface models from seismograms, is a powerful imaging technique in exploration geophysics. In recent years, the computational cost of FWI has grown exponentially due to the increasing size and resolution of seismic data. Moreover, it is a non-convex problem and can encounter local minima due to the limited accuracy of the initial velocity models or the absence of low frequencies in the measurements. To overcome these computational issues, we develop a multiscale data-driven FWI method based on fully convolutional networks (FCN). In preparing the training data, we first develop a real-time style transform method to create a large set of synthetic subsurface velocity models from natural images. We then develop two convolutional neural networks with encoder-decoder structure to reconstruct the low- and high-frequency components of the subsurface velocity models, separately. To validate the performance of our data-driven inversion method and the effectiveness of the synthesized training set, we compare it with conventional physics-based waveform inversion approaches using both synthetic and field data. These numerical results demonstrate that, once our model is fully trained, it can significantly reduce the computation time, and yield more accurate subsurface velocity models in comparison with conventional FWI.

Numerical Verification of Full Waveform Inversion for the Chang’E-5 Lunar Regolith Penetrating Array Radar

The lunar regolith penetrating array radar (LRPR) carried by Chang’E-5 (CE-5) has explored the subsurface regolith structure of the moon and guided the drill sampling procedures. To evaluate LRPR performance in subsurface imaging and physical-parameter estimation, we apply multiscale full-waveform inversion (FWI) with total variation (TV) regularization to the synthetic CE-5 LRPR data. The time-domain multiscale inversion strategy gives a low-frequency update for the deep region and increases the frequency range for updating the shallow area. The TV regularization reduces the image noise and improves the inversion accuracy of local structures. To mimic the actual scenario, we use an LRPR source wavelet obtained from the LRPR instrument prototype for our FWI test. The LRPR source wavelets include the effect of the antenna radiation patterns and signal scattering from the metallic lander. We test the proposed FWI scheme on two heterogeneous models of the lunar regolith and demonstrate that the scheme effectively reduces the signal scattering from the metallic lander and provides a reliable way to image the lunar regolith structures. These images can be used to estimate the regolith physical parameters.

Multiscale phase inversion for vertical transverse isotropic media

ABSTRACTInanisotropy full waveform inversion, the pseudo‐acoustic approximation is widely used to reduce the computation cost. However, artefacts and inaccurate predictions of amplitudes by the pseudo‐acoustic approximation often result in slow convergence in the full waveform inversion iterations and inaccurate tomograms. To solve this problem, multiscale phase inversion methodology is extended to vertical transverse isotropic media. In multiscale phase inversion, the amplitude spectra of the predicted data are replaced by those of the recorded data to mitigate the amplitude mismatch problem. Moreover, multiscale phase inversion tends to avoid the local minimum problem of full waveform inversion by temporally integrating the traces several times. Numerical tests on synthetic data and field data demonstrate the superiority of this method compared to conventional multiscale full waveform inversion for vertical transverse isotropic media.

Elastic FWI Without Low Frequencies Based on n-th Power Operation and Convolved Wavefields

The elastic full-waveform inversion (FWI) can use the recorded multi-component seismic data to construct high-precision multi-parameter models of the subsurface media such as P- and S-wave velocity models. However, due to the reasons such as data quality and algorithm limitations, there are still many problems in the promotion and application of elastic FWI method. Aiming at alleviating the influence of low-frequency data absence on the inversion results, we propose a robust elastic FWI method based on the n-th power operation. The n-th power of the seismic data can compress the time-domain waveform and expand its frequency-band. The FWI objective function constructed using the n-th power wavefields shows better convexity. By successively lowering the power during the inversion, we can realize a new multiscale FWI strategy, which is also a data-domain layer-stripping strategy. Seismic data will be more sensitive to the source wavelet errors after the n-th power operation. To mitigate this problem, we propose a robust objective function for elastic FWI using the n-th power operation and the convolved wavefields. Finally, the validity of the method is verified by numerical examples.

Full-waveform inversion with borehole constraints for elastic VTI media

The nonlinearity of full-waveform inversion (FWI) and parameter trade-offs can prevent convergence toward the actual model, especially for elastic anisotropic media. The problems with parameter updating become particularly severe if ultra-low-frequency seismic data are unavailable, and the initial model is not sufficiently accurate. We introduce a robust way to constrain the inversion workflow using borehole information obtained from well logs. These constraints are included in the form of rock-physics relationships for different geologic facies (e.g., shale, sand, salt, and limestone). We develop a multiscale FWI algorithm for transversely isotropic media with a vertical symmetry axis (VTI media) that incorporates facies information through a regularization term in the objective function. That term is updated during the inversion by using the models obtained at the previous inversion stage. To account for lateral heterogeneity between sparse borehole locations, we use an image-guided smoothing algorithm. Numerical testing for structurally complex anisotropic media demonstrates that the facies-based constraints may ensure the convergence of the objective function towards the global minimum in the absence of ultra-low-frequency data and for simple (even 1D) initial models. We test the algorithm on clean data and on surface records contaminated by Gaussian noise. The algorithm also produces a high-resolution facies model, which should be instrumental in reservoir characterization.

Velocity model estimation of karstic fault reservoirs using full-waveform inversion accelerated on graphics processing unit

The karstic fault reservoir is a type of hydrocarbon-enriched carbonate reservoir. It is a combination of small-scale caves, vugs, and fractures developing near deep-seated faults, which makes it difficult to delineate using traditional seismic imaging methods. Recent research on geologic characteristics of paleokarst reservoirs facilitates hydrocarbon exploration and exploitation in western China. To interpret karstic fault systems and reservoirs, the seismic image is an effective tool. A high-quality velocity model is essential for high-resolution migration. These seismic results contain crucial information to interpret reservoirs. Full-waveform inversion (FWI) is a powerful method to obtain high-precision velocity models because it makes use of the kinematic and dynamic information in the seismic full wavefield. To image such complicated and irregular fractured-cavity reservoirs accurately, we have applied a multiscale FWI method accelerated on graphics processing unit devices to fault-controlled paleokarst reservoir models. According to the model test results, FWI shows high performance in delineating the boundaries of fault-controlled karstic reservoirs. The proposed method also has the potential to characterize inner structures. Based on the high-precision velocity model provided by FWI, the seismic image obtained by reverse time migration is also improved. These seismic results will show the location, width, and shape of the fault-karst structure, which gives detailed information for fault-controlled paleokarst reservoir interpretation.

An objective function for full-waveform inversion based on frequency-dependent offset-preconditioning.

Full-waveform inversion (FWI) is a powerful technique to obtain high-resolution subsurface models, from seismic data. However, FWI is an ill-posed problem, which means that the solution is not unique, and therefore the expert use of the information is required to mitigate the FWI ill-posedness, especially when wide-aperture seismic acquisitions are considered. In this way, we investigate the multiscale frequency-domain FWI by using a weighting operator according to the distances between each source-receiver pair. In this work, we propose a weighting operator that acts on the data misfit as preconditioning of the objective function that depends on the source-receiver distance (offset) and the frequency used during the inversion. The proposed operator emphasizes information from long offsets, especially at low frequencies, and as a consequence improves the update of deep geological structures. To demonstrate the effectiveness of our proposal, we perform numerical simulations on 2D acoustic Marmousi2 case study, which is widely used in seismic imaging tests, considering three different scenarios. In the first two ones, we have used an acquisition geometry with a maximum offset of 4 and 8 km, respectively. In the last one, we have considered all-offsets. The results show that our proposal outperforms similar strategies, for all scenarios, providing more reliable quantitative subsurface models. In fact, our inversion result has the lowest error and the highest similarity to the true model than similar approaches.

Sparse constrained encoding multi-source full waveform inversion method based on K-SVD dictionary learning

Full waveform inversion (FWI) is an extremely important velocity-model-building method. However, it involves a large amount of calculation, which hindsers its practical application. The multi-source technology can reduce the number of forward modeling shots during the inversion process, thereby improving the efficiency. However, it introduces cross-noise problems. In this paper, we propose a sparse constrained encoding multi-source FWI method based on K-SVD dictionary learning. The phase encoding technology is introduced to reduce crosstalk noise, whereas the K-SVD dictionary learning method is used to obtain the basis of the transformation according to the characteristics of the inversion results. The multi-scale inversion method is adopted to further enhance the stability of FWI. Finally, the synthetic subsag model and the Marmousi model are set to test the effectiveness of the newly proposed method. Analysis of the results suggest the following: (1) The new method can effectively reduce the computational complexity of FWI while ensuring inversion accuracy and stability; (2) The proposed method can be combined with the time-domain multi-scale FWI strategy flexibly to further avoid the local minimum and to improve the stability of inversion, which is of significant importance for the inversion of the complex model.

Direct building background velocity field by plane-wave multi-source multi-scale full-waveform inversion

ABSTRACTFull-waveform inversion (FWI) is one of the most promising inversion methods in geophysics due to its theoretical completeness and high resolution. However, the inversion ability of FWI strongly relies on the accuracy of the initial model and the quality of the low-frequency data. For FWI, it is important to accurately recover low and middle wavenumber components (the background model). In order to invert for the background model, we use a new strategy to compose the plane-wave using reference source points. With the new algorithm, more plane-waves can be composed for a single ray parameter to obtain the background model by plane-wave multi-scale full-waveform inversion (PMFWI) method. By controlling the ray parameter in this method, the low to middle wavenumber components can be recovered in sequence. Composing several plane-waves for a single ray parameter enables the illumination to be significantly improved, even for incomplete data. As only a small number of plane-waves are needed in this method, the computation burden greatly decreases. Analysis of numerical tests also verifies that the proposed inversion strategy is robust, to a certain extent, for high-frequency or noisy data. Application of this method on a modified portion of a SigsBee 2A model illustrates that, combined with conventional FWI, PMFWI has suitable model accuracy, even for coarse initial model data and high-frequency data.

Accelerating 2D frequency-domain full-waveform inversion via fast wave modeling using a model reduction technique

Full-waveform inversion (FWI) is widely used to infer earth structures and rock properties. In FWI, most of the computation arises from the repeated simulations of wave propagation. Although frequency-domain implementations have several advantages, solving the Helmholtz equation incurs a major computational cost associated with the inversion of large matrices. Hence, we have used a new model reduction technique called the generalized multiscale finite-element method (GM FEM) to perform this task rapidly for forward and backward simulations. This in turn leads to the acceleration of the FWI. In addition, the multiscale finite-element approach allows flexible, adaptive selection of modeling parameters (i.e., grid size, number of basis functions) for different target frequencies, providing further speed up. We apply this frequency-domain, multiscale FEM approach to the Marmousi-2 model, and the FWI results indicated how varying the number of basis functions can control the trade-off between the accuracy and computational speed. In addition, we introduced FWI examples applied to field data from the Gulf of Mexico. These field data examples indicate that applying our multiscale FWI with a relatively small number of basis functions can quickly construct a macrovelocity model using low frequencies. We also evaluate a strategy to optimize the FWI procedure by using frequency-adaptive multiscale basis functions based on the target frequency group. In general, we can reduce the run time by up to 30% through the application of GM FEM wave modeling in FWI.

Multiscale Full-Waveform Dual-Parameter Inversion Based on Total Variation Regularization to On-Ground GPR Data

Full-waveform inversion (FWI) in the time domain of ground-penetrating radar (GPR) data involves a vast number of calculations; thus, it requires a large amount of memory and is difficult to calculate on a personal computer (PC). In this paper, GPR data are analyzed with multiscale FWI using two parameters (permittivity and conductivity) based on total variation (TV) regularization, which is implemented on a PC using a graphics processing unit (GPU) parallel acceleration strategy. The inverse problem is considered to be a nonlinear optimization problem and is solved with limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) process, which is a quasi-Newton method. The gradient of the objective function is calculated using the adjoint-state method, and the finite-difference method is required to solve the forward problem many times. A multiscale serial inversion strategy is applied to optimize the inversion algorithm and to decompose the inversion problem into 2–3 frequency bands to search in the direction of the global minimum point instead of local minimums. Taking the complex model as an example, experiments are carried out to assess the parameter adjustment factor and regularization parameter. The appropriate parameter adjustment factor and regularization parameter can effectively guarantee the convergence speed and stability of dual-parameter inversion method and improve the accuracy of GPR data inversion. Finally, FWI of the noise-free and 25-dB signal-to-noise ratio (SNR) noise data of the overthrust model is performed. The results show that the multiscale and dual-parameter inversion method proposed in this paper can provide reliable constraints, has better adaptability to noisy data, and can reliably and accurately reconstruct the dielectric properties distribution of the subsurface.

Frequency Controllable Envelope Operator and Its Application in Multiscale Full-Waveform Inversion

Full-waveform inversion (FWI) attempts to find optimal models of subsurface by using full information of the observed data. One difficulty in conventional FWI is that the misfit function has many local minima because of cycle skipping. Envelope inversion (EI), which uses the envelope operator (EO)-based misfit function, has been proven to be effective in mitigating cycle skipping and recovering long-wavelength velocity model. However, EI ignores the fact that the information within different frequency bands plays different roles in inversion. In this paper, a frequency controllable EO, which can control the frequency components being used to construct envelope, is proposed. We propose a new misfit function and a multiscale FWI method. Using synthetic experiments based on the Marmousi model, we demonstrate that the proposed method is better than EI in mitigating cycle skipping and in building an accurate initial model for conventional FWI to significantly improve its final result. In addition, this method can tolerate a wide range of noise levels. Its effectiveness has also been successfully demonstrated using a field data set.

Multi-Scale Full Waveform Inversion based on Curvelet Transform

Full waveform inversion (FWI) is a rapidly developed inversion method in recent years, and the resolution is much higher than traditional inversion methods, such as tomography and migration velocity analysis. However, FWI is much dependent on starting model and low frequency information, and easy to fall into local minima because of cycle skipping issue. We proposed Curvelet transform multi-scale strategy to improve the effect of bad starting model by selecting different scale information of observed data during inversion. Test of frequency domain FWI on Marmousi model shows that the result of inversion has a better stability and convergence with Curvelet transform multi-scale method than traditional methods.

High-Resolution Characterization of Near-Surface Structures by Surface-Wave Inversions: From Dispersion Curve to Full Waveform

Surface waves are widely used in near-surface geophysics and provide a noninvasive way to determine near-surface structures. By extracting and inverting dispersion curves to obtain local 1D S-wave velocity profiles, multichannel analysis of surface waves (MASW) has been proven as an efficient way to analyze shallow-seismic surface waves. By directly inverting the observed waveforms, full-waveform inversion (FWI) provides another feasible way to use surface waves in reconstructing near-surface structures. This paper provides a state of the art review of MASW and shallow-seismic FWI and a comparison of both methods. A two-parameter numerical test is performed to analyze the nonlinearity of MASW and FWI, including the classical, the multiscale, the envelope-based, and the amplitude-spectrum-based FWI approaches. A checkerboard model is used to compare the resolution of MASW and FWI. These numerical examples show that classical FWI has the highest nonlinearity and resolution among these methods, while MASW has the lowest nonlinearity and resolution. The modified FWI approaches have an intermediate nonlinearity and resolution between classical FWI and MASW. These features suggest that a sequential application of MASW and FWI could provide an efficient hierarchical way to delineate near-surface structures. We apply the sequential-inversion strategy to two field data sets acquired in Olathe, Kansas, USA, and Rheinstetten, Germany, respectively. We build a 1D initial model by using MASW and then apply the multiscale FWI to the data. High-resolution 2D S-wave velocity images are obtained in both cases, whose reliabilities are proven by borehole data and a GPR profile, respectively. It demonstrates the effectiveness of combining MASW and FWI for high-resolution imaging of near-surface structures.

Automated Large‐Scale Full Seismic Waveform Inversion for North America and the North Atlantic

AbstractWe present a new anisotropic seismic tomography model based on a multiscale full seismic waveform inversion for crustal and upper‐mantle structure from the western edge of North America across the North Atlantic and into Europe. The gradient‐based inversion strategy utilizes the adjoint state method coupled with an L‐BFGS quasi‐Newton optimization scheme. To improve the handling of large data quantities in the context of full seismic waveform inversions, we developed a workflow framework automating the procedure across all stages, enabling us to confidently invert for waveforms from 72 events recorded at 7,737 unique stations, resulting in a total of 144,693 raypaths, most of them with three‐component recordings. The final model after 20 iterations is able to explain complete waveforms including body as well as surface waves of earthquakes that were not used in the inversion down to periods of around 30 s. The model is complemented by a detailed resolution analysis in the form of 3‐D distributions of direction‐dependent resolution lengths.

Multiscale full-waveform inversion based on shot subsampling

Conventional full-waveform inversion is computationally intensive because it considers all shots in each iteration. To tackle this, we establish the number of shots needed and propose multiscale inversion in the frequency domain while using only the shots that are positively correlated with frequency. When using low-frequency data, the method considers only a small number of shots and raw data. More shots are used with increasing frequency. The random-in-group subsampling method is used to rotate the shots between iterations and avoid the loss of shot information. By reducing the number of shots in the inversion, we decrease the computational cost. There is no crosstalk between shots, no noise addition, and no observational limits. Numerical modeling suggests that the proposed method reduces the computing time, is more robust to noise, and produces better velocity models when using data with noise.