Waveform Energy Focusing Tomography for Passive Sources

Wavefield reconstruction inversion (WRI) mitigates cycle skipping by using an inaccurate initial velocity. This attractive technique is usually implemented with shot records. However, if large numbers of shot records are used, WRI can become computationally burdensome due to the many over-determined linear systems that need to be solved. To alleviate this computational issue, we propose an efficient WRI scheme involving plane-wave encoding (WRI-PW) in the frequency domain. Plane-wave encoding can dramatically reduce the number of relevant datasets by transforming shot records into common ray-parameter gathers with time shifting. Therefore, plane-wave encoding is widely used in many aspects of seismic data processing (e.g. waveform inversion, reverse time migration, etc.). Initially, we performed a simple numerical experiment using a velocity model with a box-shaped anomaly. WRI-PW also could generate scattering wavefields in a homogeneous model. Next, computational efficiency was checked with a modified Marmousi-2 model. The results show that the usage of a sufficient plane-wave angle can achieve satisfactory inversion results. It indicates that WRI-PW requires small datasets compared to WRI. Thus, the computational costs for solving the augmented system can be reduced. Further experiments were conducted to evaluate the robustness of WRI-PW to random noise and to compare WRI-PW and conventional full waveform inversion (FWI) with a modified SEG/EAGE salt velocity model. We verify that WRI-PW is more robust to random noise than WRI, it exhibited less dependency on the accuracy of the initial velocity model than conventional FWI and it is computationally efficient.

Full waveform inversion (FWI) is the combination of the tomography mode and the migration mode. It is essential to emphasize tomographic component during the early stage of inversion when the initial model is far away from the true model. To prevent the inverted model from falling into local minima, we develop a method to update tomographic lowwavenumber components under the frame of FWI with structural shaping regularization. We firstly separate the conventional FWI gradient into tomography and migration modes based on an implicit wavefield decomposition method. Then the tomography mode is used to emphasize low-wavenumber component updates, while the migration mode is used to estimate local-dip information. Then we introduce structural shaping regularization using seislet transform to mitigate the artifacts caused by the leakage of migration component in tomographic updates. Numerical results show that tomography-mode FWI with structural shaping regularization (RSFWI) is stable and effective to recover a background velocity model. The final inverted velocity model is more accurate than the conventional FWI result.

Summary Extended waveform inversion provides an effective way to mitigate cycle skipping that usually occurs in conventional full waveform inversion (FWI), resulting in an inaccurate local minimum model. A matching filter between the predicted and observed data can provide an additional degree of freedom to avoid the cycle skipping. We extend the search space to treat the matching filter as an independent variable that we use to bring the compared data within a half cycle to obtain accurate direction of velocity updates. In this case, the objective function with a reasonable penalty parameter has a larger region of convexity compared to conventional FWI. The normalization of the data can bring us an equivalent normalization of the filter, and a more effective convergence. A Marmousi example demonstrates these features.

Full waveform inversion (FWI) makes full use of the seismic waveforms to find high-resolution velocity and density models by minimising residuals between the calculated and recorded data. Q attenuation widely exists in the subsurface media, leading to weak amplitude and misplacement of reflectors. However, the commonly used Q-compensated FWI (QFWI) based on the second-order wave equation has difficulties in simultaneously inverting velocity and density fields. A QFWI method based on new first-order viscoacoustic quasi-differential equations is proposed to simultaneously produce velocity and density fields. Based on the adjoint state inversion theory, Q-compensated forward-propagated operators, adjoint operators, and gradient equations are derived using the newly derived first-order viscoacoustic quasi-differential wave equations. The time-domain multi-scale decomposition method is introduced to update the velocity and density models from a low to a high wavenumber. Numerical examples on an actual work area model and a modified attenuating Marmousi model show that the proposed QFWI method produces higher-accuracy velocity and density models with iterations by correcting the Q attenuation than the conventional acoustic FWI. Even when the Q model is extremely inaccurate, the proposed QFWI obtains acceptable inversion results. Compared to the conventional QFWI, our QFWI better inverts velocity field in the case of an inaccurate density model. Finally, we verify the adaptability of our QFWI to field data.

Full-waveform inversion (FWI) is a highly nonlinear and nonconvex problem. To mitigate the dependence of FWI on the quality of starting model and on the low frequencies in the data, we apply the gradient sampling algorithm (GSA) introduced for nonsmooth, nonconvex optimization problems to FWI. The search space is hugely expanded to have more freedom to accommodate large velocity errors in the starting model. The original implementation of GSA requires explicit calculation of the gradient at each sampled vector, which is prohibitively expensive. Based on the observation that a slight perturbation in the velocity model causes a small spatial shift of the wavefield, we have approximated the sampled gradients by crosscorrelating the space-shifted source- and receiver-side wavefields. Theoretical derivation suggests that the two wavefields should be shifted in the same direction to obtain reasonable low-wavenumber updates. The final descent search direction is obtained by summing all the shifted gradients. For practical implementation, we only take one random space shift at each time step during the gradient calculation. This simplification provides an efficient realization in which the computational costs and memory requirements are the same as conventional FWI. Multiple numerical examples demonstrate that the proposed method alleviates the cycle-skipping problem of conventional FWI when starting from very crude initial velocity models without low-frequency data.

SUMMARY Full waveform inversion (FWI) is a high-precision subsurface imaging technique that inverts subsurface parameter models by minimizing the discrepancy between observed and synthetic seismic data. However, complicated wave propagation mechanisms, non-convexity of the loss function and limited seismic acquisition system necessitate the incorporation of sufficient prior and physical constraints to alleviate the ill-posedness and cycle-skipping. Although the implicit FWI (IFWI) can encode implicit spectral bias (i.e. inverting model parameters from low frequencies to high frequencies) to reduce the dependence on an accurate initial model, its limited high-frequency inversion capability results in thousands of iterations for the final results. In this paper, we indicate that the frequency hyperparameters of the sine activation function in IFWI modulate the spectral bias, making a trade-off between inversion accuracy and stability, that is, lower frequencies yield robust FWI but lower accuracy, while higher frequencies achieve higher accuracy on the premise of an accurate initial model. To improve both the stability and accuracy of IFWI, we propose a novel implicit FWI method with an adaptive Fourier reparametrization strategy (termed FR-IFWI), which explicitly encodes multifrequency information by reparametrizing the network weights using a learnable coefficient matrix and fixed Fourier frequency bases. The role of learnable matrices in neural networks can evolve from determining frequencies in IFWI to actively selecting frequencies from fixed frequency bases through FR-IFWI, which alleviates the dependence on activation function frequency and obtains more robust and accurate inversion results. Extensive numerical experiments on the modified Marmousi, 2-D SEG/EAGE Salt and Overthrust models confirm that FR-IFWI successfully achieves superior inversion efficiency and accuracy compared with conventional FWI and IFWI methods.

Full Waveform Inversion (FWI) is a seismic imaging technique that utilizes the entire content of seismic trace. This method aims to minimizes differences between real and synthetic seismograms. FWI consists of three main steps: forward modelling to simulate synthetic seismograms, adjoint simulation to calculate the gradient misfit, and optimization to obtain an appropriate model perturbation. FWI is an extremely non-linear inversion technique and computationally intensive since it involves many model parameters. In the context of geophysics, finding parameter models that describe the structure of the earth’s subsurface is the main goal. Geophysical measurements in the field only obtain data that is influenced by the parameter model, in this case seismic recording data, therefore mathematical techniques are studied and applied to determine the correct parameter model from the data obtained, also known as the inversion process. In this study, main research area is on optimization step which include mathematical approach to find perturbation model effectively. The Newton method can be used in the optimization step of FWI. However, its implementation is not promising due to high computational cost in calculating Hessian matrix. To reduce computation cost, an identity matrix is chosen to replace the Hessian matrix, as it usually done in the steepest descent method. Since FWI has a high level of non-linearity, steepest descent method requires many iterations to minimize the objective function. Therefore, this study uses a conjugate gradient method to make the data misfit minimized more quickly. Apart from that, the Line search technique is used to find an appropriate step-length at each iteration on both methods. The FWI workflow is applied to the synthetic acoustic velocity model. We conduct FWI using steepest descent and conjugate gradient methods. The results show that the conjugate gradient method requires fewer iterations than the steepest descent method to minimize the objective function. FWI model result using conjugate gradient method is closer with the true model compared to steepest descent method, showed on misfit result and model image. By comparing these methods we can see that conjugate gradient method can be chosen for application on FWI optimization step for better result on seismic imaging. On the industry scale, better results provide less uncertainty on the model parameters that useful for energy exploration or engineering.

Summary Full waveform inversion of full-azimuth broadband ocean bottom nodes is emerging as the go-to strategy for high-resolution seismic imaging in marine settings. The areal extent of node acquisitions and the high signal-to-noise ratio at low frequencies fosters the illumination and undershooting of sought structures by deeply penetrating diving waves and post-critical reflections even in complex environments. In this work, we present full waveform inversion results of a newly provisioned full-azimuth broadband ocean bottom node data from the Gorgon field located off the northwest coast of Australia. We show that even at the first stage of the inversion, using conventional full waveform inversion, the P-wave vertical velocity model is significantly updated and reveals expected structural features in accordance with the geological setting of the Gorgon basin. The enhanced data fit and the excellent match of velocity profiles with well logs validates this result which will serve as baseline for ongoing and future multi-component and multi-parameter FWI of this dataset from offshore North West Australia.

In recent years the elastic full waveform inversion (FWI) was successfully applied to synthetic and field data to compute high resolution velocity models. While seismic velocities are derived from recorded phase information, density models can be estimated from the amplitudes. However, due to the complexity of the inverse problem a long wavelength initial model is required for a good reconstruction of the density. The inclusion of gravity data into the FWI concept can solve this problem. In this study a two-step hierarchic joint inversion of seismic waveforms and gravity data is tested using the Marmousi-II model. In step 1 FWI is performed for all elastic parameters. Gaussian filtered velocity models of the true model and a constant halfspace density model (CDH) are used as initial models. While the velocities can be reconstructed well, the density shows large deviations from the true model. In step 2 joint inversion is applied to optimize only the density model, while the velocity inversion results of the first step and the CDH are used as initial models. The results of this combined approach show a significant improvement of the density model compared to the results of a pure FWI.

Summary Ultra-long offset stationary-receiver acquisitions implemented with multi-component Ocean Bottom Nodes (OBN) are emerging as a suitable technology for deep offshore subsalt imaging by full waveform inversion (FWI). Ultra-long offsets allow to undershoot the deepest targeted structures with diving waves. In this framework, first-arrival traveltime + slope tomography (FASTT) provides a simple and efficient tool to build kinematically-accurate initial velocity model for full waveform inversion (FWI). In particular, the incorporation of slopes in the first-arrival tomography in addition to traveltimes removes artifacts in poorly illuminated areas and better reconstruct structural dips. Either the FASTT or the FWI velocity models can be used as reliable background models for prestack depth migration of co-incident towed-streamer data. However, the high resolution of the FWI velocity model facilitates the integrated interpretation of the reflectivity mapped by migration and the intermediate-scale velocity variations reconstructed by waveform inversion. We illustrate the workflow combining first-arrival tomography + FWI of ultra-long offset OBN data and migration of co-incident towed-streamer data with a challenging deep crustal case study in the eastern Nankai subduction zone.

Seismic full waveform inversion (FWI) is a powerful tool for monitoring subsurface changes during carbon capture and storage (CCS) operations, but its ill-posed nature makes uncertainty quantification (UQ) essential for reliable interpretation. Sampling-based Bayesian methods such as Markov chain Monte Carlo (McMC) provide rigorous UQ but are computationally demanding. In conventional FWI, elastic properties are assigned to densely discretized space-filling cells, resulting in a high-dimensional parameterization that makes large-scale elastic FWI computationally infeasible. To address this challenge, we propose a rock-physics-guided parameter-reduction strategy that compactly represents the CO2 plume geometry using cubic splines controlled by a limited number of nodes. This parsimonious parameterization not only significantly reduces the number of model parameters and the forward simulations required for an effective UQ using sampling methods but also has the potential to improve the practicality and efficiency of other types of UQ methods. Numerical experiments on a cross-well synthetic scenario and a field-scale case based on the Aquistore storage site in Saskatchewan, Canada, demonstrate that the method efficiently reconstructs the plume shape and its extent and that it converges to consistent posterior distributions across multiple Markov chains.

An accurate earth model is key to any successful depth imaging effort. Full waveform inversion is an advanced velocity model building process which uses the full two way wave equation. Existing methods use a ray tracing approach to distribute velocity errors within the model. In this presentation, we will show examples of seismic data processed with the latest technology, including earth model building with full waveform inversion. Introduction The industry has moved to using two-way wave equation migrations(commonly known as reverse time migration), especially in areas of complex geology such as the salt bodies in the Gulf of Mexico and offshore Brazil. The velocity model, including velocity anisotropy, is key to any depth migration effort. The natural next step is to use the two-way wave equation for velocity model building. One of the most advanced tools for velocity model building using the two-way wave equation is Full Waveform Inversion(FWI). Full-waveform inversion uses computer intensive forward modeling of the seismic measurement combined with residual wavefield back propagation to iterate to a final velocity model, which can provide greater detail than tomographic ray tracing approaches. Velocity inversion using full waveform inversion has been used on a number of projects around the world including the GOM, Brazil and the North Sea.

A good starting model is imperative in full-waveform inversion (FWI) because it solves a least-squares inversion problem using a local gradient-based optimization method. A suboptimal starting model can result in cycle skipping leading to poor convergence and incorrect estimation of subsurface properties. This problem is especially crucial for salt models because the strong velocity contrasts create substantial time shifts in the modeled seismogram. Incorrect estimation of salt bodies leads to velocity inaccuracies in the sediments because the least-squares gradient aims to reduce traveltime differences without considering the sharp velocity jump between sediments and salt. We have developed a technique to estimate velocity models containing salt bodies using a combination of global and local optimization techniques. To stabilize the global optimization algorithm and keep it computationally tractable, we reduce the number of model parameters by using sparse parameterization formulations. The sparse formulation represents sediments using a set of interfaces and velocities across them, whereas a set of ellipses represents the salt body. We use very fast simulated annealing (VFSA) to minimize the misfit between the observed and synthetic data and estimate an optimal model in the sparsely parameterized space. The VFSA inverted model is then used as a starting model in FWI in which the sediments and salt body are updated in the least-squares sense. We partition model updates into sediment and salt updates in which the sediments are updated like conventional FWI, whereas the shape of the salt is updated by taking the zero crossing of an evolving level set surface. Our algorithm is tested on two 2D synthetic salt models, namely, the Sigsbee 2A model and a modified SEG Advanced Modeling Program (SEAM) Phase I model while fixing the top of the salt. We determine the efficiency of the VFSA inversion and imaging improvements from the level set FWI approach and evaluate a few sources of uncertainty in the estimation of salt shapes.

plex shallow subsurface. This workflow incorporates dispersion curve inversion, traveltime tomography and full waveform inversion into a single framework to optimize the advantages of each. An accurate near-surface velocity is derived using the dispersion curve inversion technique that overcomes limitations of traditional traveltime tomography. This velocity is then incorporated into layer-stripping full waveform or RMO inversion schemes by “freezing” the ultra-shallow part of the model in order to retrieve the deeper velocity structure. We illustrate the workflow on a test data set from Inner Mongolia, China, whose long-offsets and low-frequency content provide the necessary input for both the dispersion curve and full waveform inversion techniques. Using this data set, we demonstrate the efficacy of the integrated methodology in determining both the macro-velocity model and near-surface velocities in structurally complex geological setting.

Summary Offset Vertical Seismic Profile (VSP) is often used for time-lapse seismic monitoring in oil/gas exploration or CO2 geosequestration. Standard offset VSP processing technologies allow the imaging and qualitative interpretation of time-lapse changes in the medium. However, quantification of the observed time-lapse anomalies is often needed. We suggest using Full Waveform Inversion (FWI) for quantitative interpretation of the offset VSP data. We apply conventional time-lapse processing and time-lapse FWI to the offset VSP dataset acquired in the Otway field and compare the results. We observe a match in the images of the CO2 plume obtained by both methods and suggest that using FWI increases the value of offset VSP data.