A blocky regularization scheme for full waveform inversion

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.

To obtain a physical understanding of gradient-based descent methods in full-waveform inversion (FWI), we find a connection between the FWI gradient and the image provided by reverse time migration (RTM). The gradient uses the residual data as a virtual source, and RTM uses the observed data directly as the boundary condition, so the FWI gradient is similar to a time integration of the RTM image using the residual data, which physically converts the phase of the reflectivity to the phase of the velocity. Therefore, gradient-based FWI can be connected to the classical reflectivity-to-velocity/impedance inversion (RVI). We have developed a new FWI scheme that provides a self-contained and physically intuitive derivation, which naturally establishes a connection among the amplitude-preserved RTM, the Zoeppritz equations (amplitude variation with angle inversion), and RVI, and combines them into a single framework to produce a preconditioned inversion formula. In this scheme, the relative velocity update is a phase-modified and deconvolved RTM image obtained with the residual data. Consistent with the deconvolution, the multiscale approach applies a gradually widening low-pass frequency filter to the deconvolved wavelet at early iterations, and then it uses the unfiltered deconvolved wavelet for the final iterations. Our numerical testing determined that the new method makes a significant improvement to the quality of the inversion result.

ABSTRACTTo obtain a physical understanding of gradient-based descent methods in full-waveform inversion (FWI), we find a connection between the FWI gradient and the image provided by reverse time migration (RTM). The gradient uses the residual data as a virtual source, and RTM uses the observed data directly as the boundary condition, so the FWI gradient is similar to a time integration of the RTM image using the residual data, which physically converts the phase of the reflectivity to the phase of the velocity. Therefore, gradient-based FWI can be connected to the classical reflectivity-to-velocity/impedance inversion (RVI). We have developed a new FWI scheme that provides a self-contained and physically intuitive derivation, which naturally establishes a connection among the amplitude-preserved RTM, the Zoeppritz equations (amplitude variation with angle inversion), and RVI, and combines them into a single framework to produce a preconditioned inversion formula. In this scheme, the relative velocity upd...

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.

Phased array ultrasound is a widely used technique in non-destructive testing. Using piezoelectric elements as both sources and receivers provides a significant gain in information and enables more accurate defect detection. The process is called full matrix capture when all source-receiver combinations are used. The total focusing method (TFM) exploits such datasets and relies on a delay and sum algorithm to sum up the signals on a pixel grid. However, TFM only uses the first arriving p-waves, making it challenging to size complex-shaped defects. By contrast, more advanced methods such as reverse time migration (RTM) and full waveform inversion (FWI) use full waveforms to reconstruct defects. Both methods compare measured signals with ultrasound simulations. While RTM identifies defects by convolving forward and backward wave fields once, FWI iteratively updates material models to reconstruct the actual distributions of material properties. This study compares TFM, RTM, and FWI for six specimens featuring circular defects or Y-shaped notches. The reconstructed results are first evaluated qualitatively by visual assessment, then different defect segmentation approaches are studied, and finally, they are evaluated quantitatively using metrics such as AUPRC, AUROC, and F1-score. The results show that a two-step FWI framework performs best in most of the six samples studied, both qualitatively and quantitatively.

After many years of processing seismic streamer data acquired over the Shenzi field in deep-water Gulf of Mexico (GOM) with the best available technology, the workflows have remained highly interpretive, far from robust, often time-consuming, and ultimately proved inadequate for resolving the complexity of the salt and subsalt velocity models. Recent advances in full-waveform inversion (FWI) algorithms combined with a newly acquired, ocean bottom node (OBN) data set have ushered in a fundamental shift in velocity model building and imaging at Shenzi as we move away from mostly interpretation-driven to more data-driven processes. While the velocity model obtained from Time-lag FWI (TLFWI) using the legacy rich-azimuth (RAZ) streamer data provided significant imaging uplift over the best previous processing, an additional step-change improvement in image quality was achieved by running TLFWI with the OBN data. The OBN TLFWI model combined with the long offsets of the OBN data allowed steeply dipping events along the salt feeder to be seen for the first time on the reverse time migration (RTM) image. However, despite these large improvements, the image still suffers in areas of low illumination. Least-squares RTM (LSRTM) showed some good improvement over the RTM but proved less effective where the starting image was too poor. By running TLFWI to a maximum frequency comparable to the RTM, we were able to generate an FWI Image, an estimation of the reflectivity obtained directly from the FWI velocity model, with good S/N, more balanced amplitudes, and improved steep-dip and fault imaging, making it a direct rival to the RTM and LSRTM images.

Reverse time migration (RTM) is achieved by a forward and reverse time propagation of source and receiver wavefields respectively, followed by an imaging condition. The quality of the image from any RTM implementation depends directly on the method’s ability to separate the true reflection data from the backscattered correlation noise between the source and receiver wavefields. In this paper we demonstrate the application of an inverse scattering imaging condition that significantly reduces this backscattered correlation noise and results in a much higher quality subsurface image than is achieved by typical RTM imaging conditions.

Summary Full-waveform inversion (FWI) is a technique which solves the ill-posed seismic inversion problem of fitting our model data to the measured ones from the field. FWI is capable of providing high-resolution estimates of the model, and of handling wave propagation of arbitrary complexity (visco-elastic, anisotropic); yet, it often fails to retrieve high-contrast geological structures, such as salt. One of the reasons for the FWI failure is that the updates at earlier iterations are too smooth to capture the sharp edges of the salt boundary. We compare several regularization approaches, which promote sharpness of the edges. Minimum gradient support (MGS) regularization focuses the inversion on blocky models, even more than the total variation (TV) does. However, both approaches try to invert undesirable high wavenumbers in the model too early for a model of complex structure. Therefore, we apply the Sobolev space norm as a regularizing term in order to maintain a balance between sharp and smooth updates in FWI. We demonstrate the application of these regularizations on a Marmousi model, enriched by a chunk of salt. The model turns out to be too complex in some parts to retrieve its full velocity distribution, yet the salt shape and contrast are retrieved.

In conventional marine seismic surveys, due to the time-delayed reflections from the sea surface on both source and receiver sides, ghosts present in recorded seismograms and lead to both phase and spectrum distortions (especially near certain frequency notches). To achieve a high-quality broad-band image/velocity model with conventional reverse time migration (RTM)/full waveform inversion (FWI) that adopts a synthetic zero-phase source wavelet and absorbing surface condition during wavefield modelling, marine seismic data have to be pre-processed to remove ghost effects. However, seismic deghosting is not a trivial task. Instead of employing an external deghosting process, we propose a strategy to compensate for ghost effects during FWI and RTM, which consists of two parts: first, to address phase distortions due to ghost effects by means of obtaining an accurate source wavelet estimation and adopting an appropriate surface boundary condition in both forward and backward wave propagation to appropriately generate ghosts; secondly, to build a compensation operator in the adjoint state computation to mitigate spectrum distortions caused by dominant ghost effects. To demonstrate the success and robustness of the proposed strategy, we present both synthetic experiments and field examples, which suggest that this strategy can lead to successful applications of FWI/RTM directly on marine seismic data without an extra deghosting process.

In a probabilistic formulation, the solution to an inverse problem can be expressed an a posteriori probability density function (pdf) that combines the independent states of information provided by data and a priori information. Here, we define an a posteriori probability density function that defines the solution to a tomographic full waveform inverse problem, which provides a means of obtaining an uncertainty estimate. Unfortunately, no explicit formulation of the solution to this problem can be defined. Therefore, the a posteriori probability density function has to be sampled. The full waveform inverse problem is known to be computationally very hard and is, traditionally, considered out of reach for Monte Carlo sampling strategies. We show that by means of informative a priori information this problem become tractable for a sampling strategy anyways. We outline the theoretical framework for a full waveform inversion strategy that integrates the extended Metropolis algorithm with sequential Gibbs sampling, which allows for arbitrary complex a priori information to be incorporated. At the same time we show how temporally correlated data uncertainties can be taken into account during the inversion. The suggested inversion strategy is tested on synthetic tomographic crosshole ground penetrating radar full waveform data using multiplepoint based a priori information. This is, to our knowledge, the first example of obtaining a posteriori realizations of a full waveform inverse problem.

Time-lapse seismic analysis plays an essential role in reservoir monitoring. We aim at developing a reservoir monitoring approach using a permanent seismic source “ACROSS” (Accurately Controlled and Routinely Operated Signal System) that can produce repeatable, extremely precise source signature. Both vertical and horizontal single forces are reconstructed by clockwise and counter-clockwise rotations of an asymmetric cylindrical mass. Here, we performed test observation of low-frequency data (3.5-15Hz) at JOGMEC Kashiwazaki test field, Niigata, Japan. We installed the ACROSS source with a horizontal rotation axis that can generate pronounced P-wave energy. With the assumption that one or two ACROSS sources are installed at a CCS (carbon capture and storage) field, we performed 2D simulation study using reverse time migration (RTM) and full waveform inversion (FWI) for delineating temporal change of the P-wave velocity. Since ACROSS precisely controls the sweep source signature, it is possible to discuss application of time-lapse FWI rather than just the first arrival or P-wave reflection traveltime inversion. To simplify the multi-component, multi-parameter problem on elastic FWI, we invert only for P-wave velocity residual using so-called scalar potential of the elastic wavefields. The synthetic FWI result shows sharp delineation of P-wave velocity residual associated with fluid replacement. The superior repeatability of ACROSS and developments of time-lapse imaging methods may bring a breakthrough towards hydrocarbon reservoir monitoring.

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.

Full Waveform Inversion (FWI) is a successful and well-established inverse method for reconstructing material models from measured wave signals. In the field of seismic exploration, FWI has proven particularly successful in the reconstruction of smoothly varying material deviations. By contrast, non-destructive testing (NDT) often requires the detection and specification of sharp defects in a specimen. If the contrast between materials is low, FWI can be successfully applied to these problems as well. However, so far, the method is not fully suitable for reconstructing homogeneous Neumann boundaries such as hidden backsides of walls, crack-like defects, or internal voids, which are characterized by an infinite contrast in the material parameters. Inspired by fictitious domain methods, we introduce a dimensionless scaling function γ to model void regions in the forward and inverse scalar wave equation problem. Applying the scaling function γ to the material parameters in different ways results in three distinct formulations for mono-parameter FWI and one for two-parameter FWI. The resulting problems are solved by first-order optimization, where the gradient is computed using the adjoint state method. The corresponding Fréchet kernels are derived for each approach and the associated minimization is performed using an L-BFGS algorithm. A comparison between the different approaches shows that scaling the density with γ is most promising for parametrizing void material in forward and inverse problems. Finally, in order to consider arbitrary complex geometries known a priori, this approach is combined with an immersed boundary method, the finite cell method (FCM).

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.

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.