GPU Elastic Modeling Using an Optimal Staggered-Grid Finite-Difference Operator

The staggered grid finite difference (SGFD) method has been widely utilised in seismic forward modelling. The accuracy of forward modelling results has a great influence on the results of subsequent seismic imaging and seismic inversion. Numerical dispersion is one of the inherent problems in the SGFD method. To suppress dispersion, we here introduce the truncated window function method, which can get optimised finite difference operators after truncating spatial convolution series of the pseudo-spectral method. The empirical criteria of window functions are the main lobe width that should be as narrow as possible and the side lobe attenuation should be as large as possible. According to these criteria, we propose the combined window function method based on the Gaussian window and Hanning window. The result of the amplitude spectrum response shows that the new combined window has narrower main lobe and greater side lobe attenuation, which results in higher accuracy in numerical simulations with SGFD operators. Numerical tests also illustrate the effectiveness of this new method.

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.

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.

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.

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.

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.

Cost-effective waveform modeling is the key to practical reverse time migration (RTM) and full-waveform inversion (FWI) implementations. We evaluated an explicit time evolution (ETE) method to efficiently simulate wave propagation in acoustic media with high temporal accuracy. We started from the constant-density acoustic wave equation and obtained an analytical time-marching scheme in the wavenumber domain. We then formulated an ETE scheme in the time-space domain by introducing a cosine function approximation. Although the ETE operator appears to be similar to the second-order temporal finite-difference (FD) operator, the exact nature of the ETE formula ensures high accuracy in time. We further introduced a set of optimum stencils and coefficients by minimizing evolution errors in a least-squares sense. Our numerical tests indicated that ETE can achieve similar waveform accuracy as FD with four times larger time steps. Meanwhile, the compact ETE operator keeps the computation efficient. The efficiency and capability to handle complex velocity field make ETE an attractive engine in acoustic RTM and FWI.

Acoustic VTI modeling and pre-stack reverse-time migration based on the time–space domain staggered-grid finite-difference method

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.

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.

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.

Advances in computational capabilities as well as ongoing improvements in storage strategies have made reverse time migration (RTM) a feasible method for capturing images of complex structures. However, large storage requirements still restrict RTM applications, especially in anisotropic media. Utilising a first-order quasi-P-wave equation in vertically transversely isotropic (VTI) media, we investigate anisotropy and deduce an RTM equation for a staggered-grid high-order finite difference (FD) scheme incorporating a perfectly matched layer (PML) boundary in this study. We also develop an improved source wavefield storage strategy via a PML boundary method for VTI medium RTM using graphic processing unit (GPU) accelerated computation. Our proposed method significantly reduces the total volume of data storage required for conventional RTM while increasing calculation time by just a small amount. Checkpoints can be set based on GPU memory size, leading to the generation of high precision and high efficiency subsurface images. We carried out a series of numerical tests on simple anisotropic media and complex Hess 2D VTI models to verify the effectiveness of our proposed method.

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.

Seismic wave forward modelling is a crucial method for studying the propagation characteristics of seismic waves in subsurface media and is a key component of full waveform inversion. Compared to time‐domain forward modelling, frequency‐domain forward modelling offers advantages such as not being constrained by stability limits and reducing the dimension of the solution space. However, forward algorithms based on the rotation coordinate system in the frequency domain cannot adapt to situations with unequal spatial sampling intervals. To enhance the adaptability of the forward modelling algorithm in the frequency domain, we derived a 21‐point finite‐difference scheme based on the average derivative method and calculated the difference coefficients and dispersion conditions. Additionally, to address the significant computational cost in frequency domain forward modelling, we developed an improved 25‐point finite‐difference scheme. The improved 25‐point format is more accurate than the conventional 25‐point format. Building on this foundation, we applied the two derived differential schemes to full waveform inversion to synthesize the shot records of the inversion data. Additionally, we introduced a frequency compensation factor into the gradient processing, which effectively compensates for the deep layer while suppressing noise in the shallow gradient field. Finally, we demonstrated the effectiveness of our approach through a full waveform inversion application on the Marmousi model showcasing its capability in invertig fine subsurface structures.