High-resolution FWI of converted-wave data — A case study from the Edvard Grieg field

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.

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.

Full-waveform inversion (FWI) has found great success in different geologic settings and has become a must-have tool for velocity model building (VMB), particularly in salt environments where geology and velocity are often highly complex. While still acoustic, FWI has already significantly improved salt models and marked a step change in subsalt imaging compared to conventional VMB workflows driven by manual salt interpretation. Furthermore, the introduction of an innovative imaging method — FWI imaging — has delivered another step change in subsalt imaging, providing subsalt images of greatly improved signal-to-noise ratio (S/N) and better-balanced amplitudes compared to conventional migration methods. Most recently, the evolution of FWI from acoustic (AFWI) to elastic (EFWI) has represented another key breakthrough, yielding velocity models and FWI images with better-defined details and higher S/N, especially in salt provinces where impedance contrasts are large and elastic effects are most pronounced. Our elastic time-lag FWI (E-TLFWI), which integrates an elastic modeling engine with a time-lag cost function, has demonstrated the ability to reduce salt halos, better delineate structures around salt bodies, and enhance subsalt S/N in both velocity models and FWI images. We illustrate these improvements using two ocean-bottom node (OBN) data sets and one streamer data set. Given the proven advantages of EFWI imaging in 3D, it is natural to extend its application from 3D to 4D, particularly for subsalt 4D imaging, which often suffers from weak and imbalanced illumination and poor S/N with conventional 4D processing. The first application of E-TLFWI imaging on 4D data sets over the Atlantis Field in the Gulf of Mexico reveals clearer subsalt 4D signals and more accurate 4D responses that were not previously observed and are confirmed by both well data and production history.

Summary A high-resolution seismic image is of great importance to exploration and production in many ways, such as bypassing drilling hazards and identifying compartmentalized reservoirs. To achieve seismic resolution as high as possible, the conventional seismic imaging process takes more of a linear approach to deal with one or a few specific issues at a time, such as noise and multiple attenuation, source and receiver deghosting, velocity errors, illumination holes, and migration swings. Full-waveform inversion (FWI) Imaging models and uses the full-wavefield data, including primaries and multiples (ghost included) and reflection and transmission waves, to iteratively invert for the reflectivity together with velocity and thus is an elegant solution to resolve those issues in one (iterative) inversion. FWI Imaging has proven to be a superior method for providing seismic images of greatly improved illumination, S/N, focusing, and thus better resolution, over conventional imaging methods. We demonstrate with a towed-streamer data set and an OBN data set that FWI Imaging with a frequency close to the temporal resolution limit of seismic data (100 Hz or higher) can provide seismic images of unprecedented resolution from the recorded seismic data, which has been impossible to achieve with conventional imaging methods.

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.

The East Coast Marine Area (ECMA) of Trinidad and Tobago contains producing gas fields where the imaging of seismic data is known to be challenging. This difficulty has been attributed to the combination of the Dolphin Main Fault, with more than 1 km of throw and large velocity contrasts of up to 30% in magnitude across it, and shallow gas and gas clouds causing very high attenuation. These factors lead to difficulties producing reliable and consistent velocity models. Previous velocity models — generated using traveltime tomography — contained inaccuracies that led to poor imaging and structural positioning, resulting in uncertainty when planning exploration and development drilling programs. In an attempt to reduce these uncertainties, a full-waveform inversion (FWI) feasibility study was performed over the most problematic area, with an initial velocity model built from a combination of legacy prestack time and depth migration velocity models and additional first-break refraction tomography. The geologic complexity near the main fault and the associated poor seismic data quality meant this model gave a poor fit between the synthetic and observed data (from a cycle-skipping point of view) at the lowest usable frequency. This led to the idea of applying a diving-wave-driven, offset-stripping workflow across each frequency band in the FWI, going from 3.5 Hz to 7.5 Hz. After successful application on the test area, the workflow was applied to ∼1400 km2 of 3D seismic over the ECMA. The final velocity model is structurally consistent and highly resolved, containing detailed shallow geologic features such as mud volcanoes, well-defined faults, and potential gas anomalies that were not visible on the legacy tomographic model. A blind test of well-pressure data correlates strongly with velocity drops in the FWI model, showing that FWI models can potentially provide very good input to regional pore-pressure-prediction studies.

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.

Combining PP-waves with mode-converted PS reflections in migration velocity analysis (MVA) can help build more accurate VTI (transversely isotropic with a vertical symmetry axis) velocity models. To avoid problems caused by the moveout asymmetry of PS-waves and take advantage of efficient MVA algorithms designed for pure modes, here we generate pure SS-reflections from PP and PS data using the PP þ PS ¼ SS method. Then the residual moveout in both PP and SS common-image gathers is minimized during iterative velocity updates. The model is divided into square cells, and the VTI parameters VP0, VS0, e, and δ are defined at each grid point. The objective function also includes the differences between the migrated depths of the same reflectors on the PP and SS sections. Synthetic examples confirm that 2D MVA of PP- and PS-waves may be able to resolve all four relevant parameters of VTI media if reflectors with at least two distinct dips are available. The algorithm is also successfully applied to a 2D line from 3D ocean-bottom seismic data acquired at Volve field in the North Sea. After the anisotropic velocity model has been estimated, accurate depth images can be obtained by migrating the recorded PP and PS data.

Full waveform inversion (FWI) is an established precise velocity estimation tool for seismic exploration. Machine learning-based FWI could plausibly circumvent the long-standing cycle-skipping problem of traditional model-driven methods. The physics-guided self-supervised FWI is appealing in that it avoids having to make tedious efforts in terms of label generation for supervised methods. One way is to employ an inversion network to convert the seismic shot gathers into a velocity model. The objective function is to minimize the difference between the recorded seismic data and the synthetic data by solving the wave equation using the inverted velocity model. To further improve the efficiency, we propose a two-stage training strategy for the self-supervised learning FWI. The first stage is to pretrain the inversion network using a simultaneous source for a large-scale velocity model with high efficiency. The second stage is switched to modeling the separate shot gathers for an accurate measurement of the seismic data to invert the velocity model details. The inversion network is a partial convolution attention modified UNet (PCAMUNet), which combines local feature extraction with global information integration to achieve high-resolution velocity model estimation from seismic shot gathers. The time-domain 2D acoustic wave equation serves as the physical constraint in this self-supervised framework. Different loss functions are used for the two stages, that is, the waveform loss with time weighting for the first stage (simultaneous source) and the hybrid waveform with time weighting and logarithmic envelope loss for the second stage (separate source). Comparative experiments demonstrate that the proposed approach improves both inversion accuracy and efficiency on the Marmousi2 model, Overthrust model, and BP model tests. Moreover, the method exhibits excellent noise resistance and stability when low-frequency data component is missing.

Crustal‐scale imaging by the full‐waveform inversion (FWI) of long‐offset seismic data is inherently difficult because the large number of wavelengths propagating through the crust makes the inversion prone to cycle skipping. Therefore, efficient crustal‐scale FWI requires an accurate starting model and a stable workflow minimizing the nonlinearity of the inversion. Here we attempt to reprocess a challenging 2‐D ocean‐bottom seismometer (OBS) data set from the eastern Nankai Trough. The starting model is built by first‐arrival traveltime tomography (FAT), which is FWI assisted for tracking cycle skipping. We iteratively refine the picked traveltimes and then reiterate the FAT until the traveltime residuals remain below the cycle‐skipping limit. Subsequently, we apply Laplace‐Fourier FWI, in which progressive relaxation of time damping is nested within frequency continuation to hierarchically inject more data into the inversion. These two multiscale levels are complemented by a layer‐stripping approach implemented through offset continuation. The reliability of the FWI velocity model is assessed by means of source wavelet estimation, synthetic seismogram modeling, ray tracing modeling, dynamic warping, and checkerboard tests. Although the viscoacoustic approximation is used for wave modeling, the synthetic seismograms reproduce most of the complexity of the data with a high traveltime accuracy. The revised FWI scheme produces a high‐resolution velocity model of the entire crust that can be jointly interpreted with migrated images derived from multichannel seismic data. This study opens a new perspective on the design of OBS crustal‐scale experiments amenable to FWI; however, a further assessment of the optimal OBS spacing is required for reliable FWI.

Conventional seismic imaging methods rely on the single-scattering assumption, where only primary reflections contribute to the reflectivity, neglecting the additional illumination provided by multiples. These methods also depend on a velocity model obtained through a separate workflow—such as tomography or full waveform inversion (FWI)—that focuses on recovering the low- to mid-wavenumber components governing wavefield kinematics. On the other hand, FWI imaging takes advantage of the full wavefield to recover both the velocity model and reflectivity image within a single framework. This approach updates low-, mid-, and high-wavenumber components, therefore enhancing image illumination and resolution. In this work, we demonstrate the benefits of this methodology by comparing recent FWI-based imaging results from the Brazil Santos Basin with those from traditional approaches.

Historically, velocity model building for PS imaging has been done sequentially, starting with estimation of P-velocity and anisotropic parameters using PP data alone, followed by updates of S-velocity to match PS and PP depth images. A better option is to include both PP and PS data in model building from the start and find the model that satisfies both data types, producing flat events on gathers and PP and PS images with consistent depths. We implemented a new method for joint PP/PS tomography in which moveout picks on PP and PS depth gathers are combined with floating event constraints between PP and PS images to simultaneously solve for Vp, Vs, and anisotropic parameters (Mathewson et al, 2013). Our method is an improvement on previous approaches that require separate treatment of PP and PS data in the early stages of model building, allowing the use of combined PP and PS data throughout the model-building process. Benefits of the joint PP/PS tomography include improved efficiency, reduced uncertainty, and better resolution of anisotropy.

Full waveform inversion using a decomposed single frequency component from a spectrogram

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.

Although full-waveform inversion (FWI) has shown significant promise in reconstructing heterogeneous velocity fields, most existing methodologies are limited to acoustic models. We extend FWI to multicomponent (PP and PS) data from anisotropic media, with the current implementation limited to a stack of horizontal, homogeneous VTI (transversely isotropic with a vertical symmetry axis) layers. The algorithm is designed to estimate the interval vertical P- and S-wave velocities ([Formula: see text] and [Formula: see text]) and Thomsen parameters [Formula: see text] and [Formula: see text] from long-spread PP and PSV reflections. The forward-modeling operator is based on the anisotropic reflectivity technique, and the inversion is performed in the time domain using the gradient (Gauss-Newton) method. We employ nonhyperbolic semblance analysis and Dix-type equations to build the initial model. To identify the medium parameters constrained by the data, we perform eigenvalue/eigenvector decomposition of the approximate Hessian matrix for a VTI layer embedded between isotropic media. Analysis of the eigenvectors shows that the parameters [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] (density is assumed to be known) can be resolved not only by joint inversion of PP and PS data, but also with PP reflections alone. Although the inversion becomes more stable with increasing spreadlength-to-depth ([Formula: see text]) ratio, the parameters of the three-layer model are constrained even by PP data acquired on conventional spreads ([Formula: see text]). For multilayered VTI media, the sensitivity of the objective function to the interval parameters decreases with depth. Still, it is possible to resolve [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] for the deeper layers using PP-waves, if the ratio [Formula: see text] for the bottom of the layer reaches two. Mode-converted waves provide useful additional constraints for FWI, which become essential for smaller spreads. The insights gained here by examining horizontally layered models should help guide the inversion for heterogeneous TI media.