Velocity variation coefficient-based angle-dependent gradient conditioning scheme: a new strategy for an enhanced full waveform inversion

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.

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.

In seismic exploration, establishing a reliable velocity model is crucial for seismic migration imaging and reservoir characterization. Full-waveform inversion (FWI) is used to recover subsurface physical parameters by iteratively minimizing the misfit between the observed and synthetic data, theoretically offering the highest modeling accuracy. FWI is a combination of migration imaging and tomography. However, for reflection data, the update of the tomographic component is notably weaker than the migration component. When the gradient is dominated by the migration component, FWI can easily fall into local minima, which leads to bad inversion results. Hence, it is necessary to extract the tomographic component from the original FWI gradient to build a robust background velocity model when the initial model is inaccurate. In this paper, we develop to use the bidimensional empirical mode decomposition (BEMD) method to separate the original FWI gradient into the tomography and migration component. The BEMD method first adaptively decomposes the gradient into different-scale subcomponents. Then, the small-scale bidimensional intrinsic mode functions are combined into the migration component, and the large-scale residual component is considered to be the tomographic component. At the beginning of FWI, the background velocity is updated using the tomographic component, and with iterations, small-scale components are gradually added to update the velocity model. Numerical experiments show that the BEMD method can effectively separate the two components. The BEMD-based FWI can reconstruct the background velocity model, improving the FWI accuracy.

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.

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

Seismic full waveform inversion (FWI) is able to build high-resolution velocity model based on the full information carried by seismic wave. However, FWI requires an accurate enough initial model to ensure convergence. In this paper, we propose a new nonlinear FWI method to mitigate the initial model dependence problem. Specifically, we firstly propose a nonlinear operator within the hybrid model- and data-driven framework based on the frequency controllable envelope operator (FCEO) and a deep learning architecture U-Net. FCEO is used to obtain the envelope of a band-limited data and U-Net realizes the mapping from this envelope to that corresponding to a lower frequency band. The U-Net is trained in a self-supervised manner that avoids the reliance on labeled data and benefits the generalization ability. Based on the nonlinear operator, a nonlinear FWI method is proposed by defining a new misfit function. In addition, the calculation of gradient is derived using the adjoint-state method. Using numerical examples, we investigate the performance of the proposed nonlinear operator and the new nonlinear FWI method. The results clearly demonstrate that the proposed nonlinear operator is effective in obtaining low-frequency envelope data, and the new nonlinear FWI method has advantages over common method in mitigating cycle-skipping and building an initial model for conventional FWI.

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.

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.

Summary Full-waveform inversion (FWI) can capture high-resolution geophysical properties but tends to fall into local minima. We addressed this problem by reducing the degree of freedom in the optimization problem and estimating an initial velocity model from shot gathers; our method comprises three steps. First, we trained a variational autoencoder using synthetic velocity models and created a low-dimensional latent space that represents realistic velocity models. Second, we prepared another encoder model, which estimates the latent features of the corresponding velocity model from shot gathers. Finally, we implemented latent space optimization (LSO) from the initial guess selected by the encoder. In the experiment, LSO reproduced much more accurate and realistic velocity models than the naive FWI, even when the initial guess was considerably different from the ground truth. This implies that with our method the latent space becomes easier to optimize than the original velocity model space. Furthermore, we verified that LSO using an initial guess selected by the encoder could increase the estimation accuracy. Our method also succeeded in accurately estimating the Marmousi2 model, without using any part of the benchmark dataset to directly train the variational autoencoder.

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.

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.

Full waveform inversion (FWI) is a seismic imaging method suitable for wide aperture / azimuth acquisitions thanks to its ability to account for waves propagating over a broad range of incidence angles. Wide aperture / azimuth acquisitions makes, however, the imaging quite sensitive to anisotropy because of the intrinsic difference between vertical and horizontal velocities in vertical transversely isotropic (VTI) media. In this study, we present a numerical procedure to define the best parametrization for acoustic VTI FWI. High-resolution velocity model for either the vertical, the horizontal or the normal move out (NMO) velocity can be developed by monoparameter FWI, when the considered wave speed is combined with the Thomsen’s parameters δ and e in the parametrization, and when available smooth background models of δ and e are kept fixed during FWI. An alternative is to jointly reconstruct two wavespeeds (for example, the vertical and the horizontal velocities) using a model parametrization that combines these two wavespeeds and δ . However, the spatial resolution of the two resulting velocity models is more limited that of the velocity model obtained with the first mentioned parametrization.

High-quality depth images typically require accurate highresolution representations of the earth model. Full-waveform inversion (FWI) has recently justified its value throughout the industry in providing high-resolution velocity models. However, obtaining an accurate FWI velocity model using narrow-azimuth streamer data can still be challenging in complex geologic environments. The uncertainties, often caused by relatively low resolution perpendicular to the shooting direction and weaker illuminations areas, instill less confidence for reservoir delineation and depth mapping. In this case study from offshore Senegal, we present a joint velocity (Vp) and epsilon (ε) multi-azimuth FWI workflow to construct a high-resolution model to overcome severe image distortion. The updated model improved event focusing and gather flatness and demonstrated significant imaging uplifts consistent with our understanding of the geology in the area.

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.

Reflection traveltime information is generally used for producing a kinematically accurate velocity model for seismic imaging. Accurately estimating the traveltime difference between the demigrated and observed data is crucial for data-domain reflection traveltime tomography. To enhance the robustness of signal’s alignment, we propose a new method of segment dynamic image warping (SDIW). It first exploits windowed polynomial fitting for signal processing and then aligns the signals based on point-wise segment-to-segment matching. Compared with the conventional point-to-point matching strategy, our method is more robust and insensitive toward strong random noise. By minimizing the traveltime difference computed by SDIW, data-domain reflection traveltime inversion (DRTI) is then used to find an accurate background velocity model. Synthetic tests show that SDIW provides reliable time shifts between the demigrated and observed data even if the signal-to-noise ratio of input data is rather low. This enables DRTI to automatically reconstruct the deep background velocity model. The subsequent full waveform inversion (FWI) gradually added short-wavelength velocity structures and finally recovers a high-resolution and high-fidelity model. The results demonstrate that the DRTI provides a kinematically accurate background velocity model sufficient for following FWI to fully retrieve the detail of the subsurface structures even when the low frequencies are missing.