Acoustic VTI full waveform inversion: Sensitivity analysis and realistic synthetic examples

It is necessary to account for anisotropy in full waveform inversion (FWI) of wide-azimuth and wide-aperture seismic data in most geologic environments, for correct depth positioning of reflectors, and for reliable estimations of wave speeds as a function of the direction of propagation. In this framework, choosing a suitable anisotropic subsurface parameterization is a central issue in monoparameter and multiparameter FWI. This is because this parameterization defines the influence of each physical parameter class on the data as a function of the scattering angle, and hence the resolution of the parameter reconstruction, and on the potential trade-off between different parameter classes. We apply monoparameter and multiparameter frequency-domain acoustic vertical transverse isotropic FWI to synthetic and real wide-aperture data, representative of the Valhall oil field. We first show that reliable monoparameter FWI can be performed to build a high-resolution velocity model (for the vertical, the horizontal, or normal move-out velocity), provided that the background models of two Thomsen parameters describe the long wavelengths of the subsurface sufficiently accurately. Alternatively, we show the feasibility of the joint reconstruction of two wave speeds (e.g., the vertical and horizontal wave speeds) with limited trade-off effects, while Thomsen parameter [Formula: see text] is kept fixed during the inversion. The influence of the wave speeds on the data for a limited range of scattering angles when combined each other can, however, significantly hamper the resolution with which the two wave speeds are imaged. These conclusions inferred from the application to the real data are fully consistent with those inferred from the theoretical parameterization analysis of acoustic vertical transverse isotropic FWI performed in the companion report.

Full-waveform inversion (FWI) has become the centerpiece of velocity model building (VMB) in seismic data processing in recent years. It has proven capable of significantly improving the velocity model and, thus, the migration image for different acquisition types and geologic settings, including complex environments such as salt. With the advent of FWI imaging, the scope of FWI applications has extended further from VMB into the imaging landscape. However, current FWI applications in the industry prevalently employ the acoustic approximation. One common problem of acoustic FWI (A-FWI) is the apparent salt halos at the salt-sediment interface in the resulting FWI velocity and FWI image, the presence of which hinders direct interpretation and imaging focusing around salt bodies. With synthetic and field data examples, we demonstrate that this salt halo is caused mainly by the large mismatch between the elastic recorded data and the acoustic modeled data, particularly at middle to long offsets. To overcome limitations imposed by acoustic assumptions, we developed an elastic FWI (E-FWI) algorithm that combines an elastic modeling engine with the time-lag cost function, which we call elastic time-lag FWI (E-TLFWI). With a more accurate modeling engine, E-TLFWI significantly reduces the salt halo observed in its acoustic counterpart. However, we also observe that the images migrated using the A-FWI and E-FWI velocity models remain similar overall, with some slight improvements around and beneath salt boundaries, particularly near steep salt flanks, as a result of the reduced salt halo. By contrast, FWI images derived from E-TLFWI show considerable benefits over those from acoustic time-lag FWI, such as improved event focusing, better structural continuity, and higher signal-to-noise ratio. The sharpened salt boundaries and enhanced quality of the FWI images reveal the significant value of E-FWI and provide the justification for its greatly increased cost.

<p>The existing conventional inversion algorithm does not provide satisfactory results due to the complexity of propagated wavefield though the gas cloud. Acoustic full waveform inversion has been developed and applied to a realistic synthetic offshore shallow gas cloud feature with Student-t approach, with and without simultaneous sources encoding. As a modeling operator, we implemented the grid based finite-difference method in frequency domain using second order elastic wave equation. Jacobin operator and its adjoint provide a necessary platform for solving full waveform inversion problem in a reduced Hessian matrix. We invert gas cloud model in 5 frequency band selected from 1 to 12 Hz, each band contains 3 frequencies. The inversion results are highly sensitive to the misfit. The model allows better convergence and recovery of amplitude losses. This approach gives better resolution then the existing least-squares approach. In this paper, we implement the full waveform inversion for low frequency model with minimum number of iteration providing a better resolution of inversion results.</p>

Velocity model building and depth imaging are known to be complicated endeavors in numerous onshore areas in the Middle East. Despite recent advancements toward denser, wide-azimuth, and low-frequency seismic acquisitions, the application of full-waveform inversion (FWI) remains challenging. The main difficulties arise from complex near-surface geology that creates wave mode conversions (P to S waves but also strong multiples) and very energetic and complex ground roll overlaying reflected waves and dominating low frequencies, with the diving waves being less energetic and noisier. This paper presents recent progress in land FWI toward higher-resolution velocity models, with successful applications to case studies from the Sultanate of Oman. The first example shows an application of land FWI imaging. It shows that we are able to invert jointly diving and reflected waves in acoustic FWI. With proper input data conditioning and initial model preparation, we successfully ran acoustic FWI up to 45 Hz, resulting in a high-resolution velocity model and derived FWI image that significantly improved subsurface imaging and geologic understanding. The inverted high-frequency velocity could also be more reliably used for subsequent reservoir characterization steps. Given the important role of a good-quality near-surface model for stabilizing high-frequency FWI updates, the second example highlights the creation of a detailed shallow velocity model. We propose using elastic FWI of surface waves for characterization of the near surface in complex geologic settings. Here, we demonstrate the effectiveness of this workflow to enhance imaging of the shallow subsurface. Compared to conventional methods such as surface-wave inversion, elastic FWI of surface waves has the advantage of 3D full-wavefield modeling with no requirement for picking. Our workflow also benefits from the ultra-low frequencies recovered by interferometry to obtain a more stable deeper update.

The Arabian Gulf near-surface geology is complex, with extremely shallow waters and a hard water bottom generating high amplitude short period multiples and thinly bedded high and low velocity layers creating high apparent anisotropy in the bandwidth of seismic surveys. Obtaining an accurate description of the velocity variations in the near-surface and at intermediate depths is a necessity for reliable imaging and positioning of the reservoir layers located underneath. We propose a two-step full-waveform inversion (FWI) of ocean-bottom node (OBN) seismic data from offshore Abu Dhabi. We update a velocity model, using both diving and reflected waves, to reach the required depth of penetration. FWI has become an industry standard for velocity model building. However, due to the oscillatory nature of seismic data, FWI is known to be subject to cycle-skipping, where the inversion process falls into a local minimum. This risk is mitigated by using an accurate enough initial model and the use of low frequencies. In the shallow waters of offshore Abu Dhabi, near-offset data suffer from strong mud-roll and guided-wave energy that are not properly modeled with acoustic FWI. We exclude these offsets from the input data and use diving waves, starting at 3.5Hz, to update the near surface. The diving waves penetration is limited to approximately one kilometer in this area and corresponds to the base of a shallow high velocity layer. To reconcile the kinematics of reflected waves, travelling mostly vertically and used for imaging, and diving waves, travelling mostly horizontally, and used in the velocity update, we need an accurate estimation of the anisotropy. This is obtained using Backus averaging from available well logs. For deeper updates, the data are processed to remove the mud-roll and guided wave energy. This allows for the inclusion of reflections and near offsets. The FWI update is performed to 10Hz and penetrates about 3km into the sub-surface. We applied this FWI workflow to a recent node survey acquired offshore Abu Dhabi. The velocity model obtained follows the main geological structures and accurately describes the velocity variations in the shallow sub-surface. The estimation of anisotropy is important to ensure good convergence of the FWI and for imaging and vertical positioning of the migrated events. The reverse-time migration (RTM) image obtained with the updated model shows improved focusing and simplified depth structures compared to the RTM image obtained with the smooth initial model. To the best of our knowledge, this is the first successful implementation of FWI, here combining diving and reflected waves, on a dataset from offshore Abu Dhabi. It is a step towards resolving buried anomalies such as karst features, that cause imaging distortions at deeper reservoir levels.

In seismic exploration, 3D acoustic full waveform inversion (FWI) is nowadays commonly used to estimate large-to-intermediate scale velocity features with low-frequency and wide-aperture data. Velocity maps estimated with this technique can have higher resolution than the ones obtained by travel-time inversion. However, since full waveform inversion fits both the phases and the amplitudes of seismic data, the acoustic assumption may not be adequate to reproduce the data's amplitude versus offset variations in presence of hard velocity contrasts. This could limit the applications of acoustic FWI and put some constrains on the choice of the initial model reducing model's resolution. To better understand the behaviour of acoustic FWI in presence of hard layers and study the potential elastic effects, we built a synthetic model that mimics the geology of North Oman. Then we inverted the data generated with this model starting from an almost exact initial model and also from a smooth one. We show that acoustic FWI diverges when starting from an initial model with too high resolution. The inversion over-fits the elastic data leading to erroneous velocity updates. This synthetic experiment illustrates the limitations of acoustic FWI when used to obtain a high resolution velocity image in complex geology.

<p>In the context of seismic imaging, the full waveform inversion (FWI) is more and more popular. Because of its lower numerical cost, the acoustic approximation is often used, especially at the exploration geophysics scale, both for tests and for real data. Moreover, some research domains such as helioseismology face true acoustic medium for which FWI can be useful. In this work, we show that the general acoustic inverse problem based on limited frequency band data is intrinsically non-unique, making any general acoustic FWI impossible. Our work is based on two tools: particle relabelling and homogenization. On the one hand, the particle relabelling method shows it is possible to deform a true medium based on a smooth mapping into a new one without changing the signal recorded at seismic stations. This is a potentially strong source of non-uniqueness for an inverse problem based a seismic data. Nevertheless, in the elastic case, the deformed medium loses the elastic tensor minor symmetries and, in the acoustic case, it implies density anisotropy. It is therefore not a source of non-uniqueness for elastic or isotropic acoustic inverse problems, but it is for the anisotropic acoustic case. On the other hand, the homogenization method shows that any fine-scale medium can be up-scaled into an effective medium without changing the waveforms in a limited frequency band. The effective media are in general anisotropic, both in the elastic and acoustic cases, even if the true media are isotropic at a fine scale. It implies that anisotropy is in general present and needs to be inverted. Therefore, acoustic anisotropy can not be avoided in general. We conclude, based on a particle relabelling and homogenization arguments, that the acoustic FWI solution is in general non-unique. We show, in 2-D numerical FWI examples based on the Gauss-Newton iterative scheme, the effects of this non-uniqueness in the local optimization context. We numerically confirm that the acoustic FWI is in general non-unique and that finding a physical solution is not possible.</p>

Summary Acoustic full waveform inversion (FWI) was applied to the cross-well seismic monitoring data acquired in a carbon capture and storage (CCS) test site in Japan in order to monitor CO2 migration. Thorough parameter tests, related to frequency range and trace selection, were conducted using synthetic data of realistic velocity models created based on the real well-log data. These tests revealed the importance of low frequency data in situations where CO2 injection causes a P-wave velocity decrease and resulting high velocity contrast in the reservoir. Carefully optimized pre-processing includes angle-based trace selection, and eliminating non-acoustic waves using an F-K filter and exponential damping. As a result of these optimizations, a high-resolution P-wave velocity model was obtained from the FWI analysis. The high similarity of the field data and synthetic gathers, which were estimated from the final FWI, confirmed the validity of the results. Data elasticity is a remaining challenge, and we anticipate that the application of elastic FWI may improve the detection of 4D responses.

When reliable a priori information is not available, it is difficult to correctly predict near-surface S-wave velocity models from Rayleigh waves through existing techniques, especially in the case of complex geology. To tackle this issue, we have developed a new method: two-grid genetic-algorithm Rayleigh-wave full-waveform inversion (FWI). Adopting a two-grid parameterization of the model, the genetic algorithm inverts for unknown velocities and densities at the nodes of a coarse grid, whereas the forward modeling is performed on a fine grid to avoid numerical dispersion. A bilinear interpolation brings the coarse-grid results into the fine-grid models. The coarse inversion grid allows for a significant reduction in the computing time required by the genetic algorithm to converge. With a coarser grid, there are fewer unknowns and less required computing time, at the expense of the model resolution. To further increase efficiency, our inversion code can perform the optimization using an offset-marching strategy and/or a frequency-marching strategy that can make use of different kinds of objective functions and allows for parallel computing. We illustrate the effect of our inversion method using three synthetic examples with rather complex near-surface models. Although no a priori information was used in all three tests, the long-wavelength structures of the reference models were fairly predicted, and satisfactory matches between “observed” and predicted data were achieved. The fair predictions of the reference models suggest that the final models estimated by our genetic-algorithm FWI, which we call macromodels, would be suitable inputs to gradient-based Rayleigh-wave FWI for further refinement. We also explored other issues related to the practical use of the method in different work and explored applications of the method to field data.

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.

Generating plausible 3D velocity and anisotropy parameters plays an important role in various seismic analyses such as depth uncertainty estimation. In this paper, we present a 3D stochastic method for generating velocity and anisotropy parameters models in vertical transverse isotropy (VTI) medium that are based on normal moveout (NMO) travel- time calculations and detectability criterion. We provide mathematical derivations of stochastic relations of the properties of the anisotropy parameters and show how to model their realizations and uncertainties. We demonstrate the method using a 3D synthetic example from a sedimentary marine basin. The results of the stochastic modeling provide a recipe for a successful depth uncertainty estimation.

In the early stage of acoustic full-waveform inversion (AFWI), it is important to exploit the long-wavelength features of the gradient and suppress its short-wavelength features to update the background velocity. However, due to strong near-offset PP reflections and multiples within the pressure data, conventional AFWI sometimes primarily reconstructs the short-wavelength features of a given model and fails to converge on a reliable subsurface P-wave velocity model. Therefore, this study, we propose the usage of pseudo-horizontal particle acceleration (pseudo-ax) data for AFWI, rather than the original pressure data. Because the amplitudes of PP reflections are implicitly weighted according to the reflection angle in pseudo-ax data, the near-offset PP reflections and multiples of the pseudo-ax data are much weaker than those of the pressure data. As a result, AFWI using pseudo-ax data focuses on reconstructing the longer-wavelength features of a given model in the early iterations, and then gradually reconstructs short-wavelength features as the inversion process continues. Using synthetic and real data examples for the Volve oilfield in the North Sea, we examined the effects and feasibility of this strategy. In the synthetic data example, the proposed strategy rapidly reduced far-offset data misfits related to long-wavelength feature updates and achieved smaller model misfits than the conventional strategy. The real data example showed that the velocity model reconstructed using the proposed strategy flattened some of the reflectors at the angle-domain common-image gathers (ADCIGs) better than the velocity model obtained using the conventional strategy. These findings demonstrate that our strategy converges closer to the real P-wave velocity model than the conventional strategy by building a hierarchical velocity model from long- to short-wavelength structures.

Old abandoned coal working create major hazards in the form of subsidence of the coalfields. To avoid such hazards, there is need to detect these cavities prior to start of deeper seam mining. There are number of geophysical techniques available for detecting subsurface cavity. High-resolution seismic survey is one such technique which provides accurate results as compared to others. Usually, most of the seismic processing and interpretation of these cavity detection was performed based on stacked data only. To understand these signatures more precisely, in our study, an attempt has been made to image these cavities with the help of Reverse Time Migration (RTM) combined with Full Waveform Inversion (FWI). RTM mostly used for hydrocarbon exploration targets with low central frequency as source. Application of this method to shallow subsurface exploration is still in research stage. Like the same way for velocity model updating, FWI gives mostly appropriate optimization results as compare to other techniques, but it also has the limitation to application of low frequency only. In this paper we first develop a 2D realistic Water Filled Cavity (WFC) model with a work flow of RTM combined with FWI in a high-frequency Ricker source wavelet as 100 Hz. In order to provide a velocity model with high accuracy for RTM, we apply FWI to estimate the subsurface velocity by considering an initial smooth velocity model with addition of 30 % Gaussian noise. The conventional RTM fails to image the cavities and yield a large amount of low frequency back scattered noise at shallow depth during the time of cross correlation due to time/space lag. To avoid these situation, we introduced an automatic shift operator at the time of imaging condition that operates automatically both in time or space. It leads to reduce the lag and improve the results by minimizing the noises at shallow subsurface. By comparing both the results it is observed that most of the noises in the migrated section of conventional method were eliminated by the improved form of RTM with the help of FWI velocity model estimation.

We assessed 3D frequency-domain (FD) acoustic full-waveform inversion (FWI) data as a tool to develop high-resolution velocity models from low-frequency global-offset data. The inverse problem was posed as a classic least-squares optimization problem solved with a steepest-descent method. Inversion was applied to a few discrete frequencies, allowing management of a limited subset of the 3D data volume. The forward problem was solved with a finite-difference frequency-domain method based on a massively parallel direct solver, allowing efficient multiple-shot simulations. The inversion code was fully parallelized for distributed-memory platforms, taking advantage of a domain decomposition of the modeled wavefields performed by the direct solver. After validation on simple synthetic tests, FWI was applied to two targets (channel and thrust system) of the 3D SEG/EAGE overthrust model, corresponding to 3D domains of 7×8.75×2.25km and 13.5×13.5×4.65km, respectively. The maximum inverted frequencies are 15 and 7Hz for the two applications. A maximum of 30 dual-core biprocessor nodes with 8GB of shared memory per node were used for the second target. The main structures were imaged successfully at a resolution scale consistent with the inverted frequencies. Our study confirms the feasibility of 3D frequency-domain FWI of global-offset data on large distributed-memory platforms to develop high-resolution velocity models. These high-velocity models may provide accurate macromodels for wave-equation prestack depth migration.

Seismic velocity modeling is a crucial step in seismic processing that enables the use of velocity information from both seismic and wells to map the depth and thickness of subsurface layers interpreted from seismic images. The velocity can be obtained in the form of normal moveout (NMO) velocity or by an inversion (optimization) process such as in full-waveform inversion (FWI). These methods have several limitations. These limitations include enormous time consumption in the case of NMO due to manual and heavy human involvement in the picking. As an optimization problem, it incurs high cost and suffers from nonlinearity issues. Researchers have proposed various machine learning (ML) techniques including unsupervised, supervised, and semi-supervised learning methods to model the velocity more efficiently. The focus of the studies is mostly to automate the NMO velocity picking, improve the convergence in FWI, and apply FWI using ML directly from the data. In the purview of the digital transformation roadmap of the petroleum industry, this paper presents a chronologic review of these studies, appraises the progress made so far, and concludes with a set of recommendations to overcome the prevailing challenges through the implementation of more advanced ML methodologies. We hope that this work will benefit experts, young professionals, and ML enthusiasts to help push forward their research efforts to achieving complete automation of the NMO velocity and further enhancing the performance of ML applications used in the FWI framework.