Average‐derivative optimized 21‐point and improved 25‐point forward modelling and full waveform inversion in frequency domain

Summary Full Waveform Inversion (FWI) is a mathematically and computationally challenging inverse problem of finding a quantitative rock-property description of the subsurface to match observed seismogram data. The inversion employs a forward model, which relates the subsurface to the observed seismograms. FWI and other seismic applications require High Performance Computing (HPC) to simulate the dynamics of such complex models. Not a long ago, companies, research institutes, and universities used to acquire clusters of computers to maintain on-premise. Recently, cloud computing has become an alternative posing a challenge to the end-users, who have to decide whether they should execute their applications: on their local clusters or burst them to a remote cloud provider. In this paper, we present a decision support method to choose the correct environment considering trade-offs, such as resource costs, performance, and availability on such heterogeneous execution platforms. We evaluated the system using our FWI application and preliminary results indicate that users of HPC applications can benefit from such a cloud advisory system to reduce costs, turnaround times, and even boost local platforms.

This study investigates the effectiveness and the applicability of full waveform inversion (FWI) method to estimate underwater sound velocity structures. We use a frequency domain full waveform inversion method in this study. We use an adjoint-state method for the calculation of the gradient in an iterative inversion based on a preconditioned conjugate gradient method. We first apply the FWI method to a synthetic dataset that is simulated for a sound velocity structure. The results of our inversion are then compared with those from a conventional ray-based traveltime inversion (TTI) method to evaluate the effectiveness of the method. The results show that the full waveform inversion method could provide more precise image with higher resolution than the ray-based method. The FWI method is also applied to a field dataset acquired by a vertical-cable-seismic (VCS) data acquisition experiment in Lake Biwa. In spite of very limited raypath condition using only direct arrival wave, the full waveform inversion method could reproduce a horizontally stratified velocity structure whose vertical profile showed the existence of a seasonal thermocline in the lake that was to be confirmed by temperature measurements after the VCS experiment. We conclude that the FWI method could be the key success factor for the higher resolution at estimation of underwater sound velocity structure.

This study aims at designing optimal crosshole seismic approach for CO2EOR (enhance oil recovery by CO2 injection) monitoring in Abu Dhabi. It is not easy to perform successful reservoir monitoring for carbonate reservoirs in the Middle East because rock properties may not change much associated with fluid replacement. We investigate advantage of newly available elastic full waveform inversion (FWI) for detection of CO2 flooded zones. To investigate advantage, applicability and future problem of time-lapse FWI for CO2EOR monitoring, we conducted rock physics study, elastic seismic simulation, and test application of FWI to synthetic data. We first made realistic velocity models based on Gassmann's equation and actual well logs obtained before and after CO2 injection at carbonate reservoirs in Abu Dhabi. The in-situ light oil at the target reservoirs was replaced by CO2 (Secondary mode CO2EOR). We prepared models with different width and thickness of CO2 flooded zones and analyzed detectability of seismic waveform change. We also conducted test application of elastic full waveform inversion to synthetic data for delineation of CO2 flooded zones. Results of the rock physics study show 1.6% decrease in P-wave velocity, little change in S-wave velocity and density associated with secondary mode CO2EOR. The small property changes are caused by the rigid rock frame and small density difference in light oil and supercritical CO2 at the reservoir condition. Next we performed synthetic seismic analysis based on the rock property models, available crosshole seismic source and realistic well distances. Because of the small property change, seismic traveltime difference and waveform change are quite small when well distance is 116ft. When well distance is 700 ft or greater, guided waves, or trapped energy inside low velocity layers can be observed; relatively large waveform change can be observed in the guided waves due to CO2 injection. Although guided waves have not been used for reservoir monitoring, they are sensitive to small Vp and thus can be an indicator of the CO2 flooding. The elastic FWI result for a model with well distance of 1160 ft demonstrated good representation of the differential Vp with vertical resolution of 20-30 ft and some horizontal resolution. Although we need further investigation on repeatability and signal transmittability using actual field data, our synthetic study indicates possibility of identifying layers with CO2 using guided waves and elastic FWI.

Summary Onshore, the application of full waveform inversion (FWI) for imaging is challenged by the surface waves. Commonly, after their removal, it is possible to approximate the background velocities by inverting the diving/transmitted waves with low-frequency, wide-angle seismic data. However, the surface waves provide information on the near surface that is difficult to obtain from the body waves. A straight forward application of an elastic FWI on land data solely focuses on interpreting the surface waves with more pronounced energy footprints. In this study, we tested an approach based on simultaneous inversion of the surface and diving/transmitted waves, balanced through a time-space weighting scheme. The long-offset data also allows for inversion of the higher modes of the surface waves. Additionally, a novel pre-processing of the acquired seismic data aims at the elimination of the interfering secondary surface waves originating from human activities during the acquisition. Even with a relatively crude initial model, the inverted earth parameters obtained with the elastic FWI show a spectacularly good match with the well logs up to a depth of 1200 m. This study emphasizes the significance and the complementary role of both surface and diving waves in retrieving elastic earth parameters.

A developed nearly analytic discrete method for forward modeling in the frequency domain

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 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 an inverse problem for estimating the wave velocity distribution in a given domain, based on observed data on the boundaries. The inversion is computationally demanding because we are required to solve multiple forward problems, either in time or frequency domains, to simulate data that are then iteratively fitted to the observed data. We consider FWI in the frequency domain, where the Helmholtz equation is used as a forward model, and its repeated solution is the main computational bottleneck of the inversion process. To ease this cost, we integrate a learning process of an Encoder-Solver preconditioner that is based on convolutional neural networks (CNNs). The Encoder-Solver is trained to effectively precondition the discretized Helmholtz operator given velocity medium parameters. Then, by re-training the CNN between the iterations of the optimization process, the Encoder-Solver is adapted to the iteratively evolving velocity medium as part of the inversion. Without retraining, the performance of the solver deteriorates as the medium changes. Using our light retraining procedures, we obtain the forward simulations effectively throughout the process. We demonstrate our approach to solving FWI problems using 2D geophysical models with high-frequency data.

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.

In most full-waveform inversion (FWI) problems, sufficient prior information is available to constrain the velocity of certain parts of the model, e.g., the water column or, in some cases, near-surface velocities. We take advantage of this situation and develop a fast Schur-complement-based forward modeling and inversion approach by partitioning the velocity model into two parts. The first part consists of the constrained zone that does not change during the inversion, whereas the second part is the anomalous zone to be updated during the inversion. For this decomposition, we partially factorize the governing system of linear equations by computing a Schur complement for the anomalous zone. The Schur complement system is then solved to compute the fields in the anomalous zone, which are then back substituted to compute the fields in the constrained region. For each successive modeling steps with new anomalous zone velocities, the corresponding Schur complement is easily computed using simple algebra. Because the anomalous part of the model is comparatively smaller than the whole model, considerable computational savings can be achieved using our Schur approach. Additionally, we showed that the Schur complement method maintains the accuracy of standard frequency-domain finite difference formulations, but this comes at a slightly higher peak memory requirement. Our FWI workflow shows reduced runtime by 15%–57% depending upon the depth of the water column without losing any accuracy compared to the standard method.

Seismic acquisitions in urban areas represent a challenge due to the noisy environment during the recording of the data. This often prevents obtaining high-resolution images of the subsurface in the area of interest. One way to achieve better results, despite the challenging circumstances, is full-waveform inversion (FWI). This method iteratively updates a starting model until the simulated data and the observed field data matches to a satisfactory level. This eventually yields the desired subsurface model. However, FWI comes with some major limitations. Because each iteration requires a calculation of the wave propagation several times for each shot, it is highly computationally expensive. Furthermore, due to storage limitations, especially if high performance computing (HPC) clusters are not available, the model size is restricted as well. This work aims to find a solution for these limitations in an elastic 2D case by implementing the random-shot workflow (RSW). In a conventional FWI workflow which is called full-shot workflow (FSW) in this work, each iteration uses all shots of the recorded data before updating the whole model at once which leads to the high computational and storage costs. RSW randomly picks only one shot, applies FWI within the area of the shot and its corresponding receivers and then updates the model only within this subset. This should, in my expectation, split the workload into several smaller subsets without sacrificing the effectiveness of FWI. After the implementation, I compare RSW to FSW in a synthetic benchmark where I verify the performance. Afterwards, the workflows are compared to each other by using a fraction of a field data set that was acquired in Salt Lake City. These data represents a large urban seismic land data set with a low signal-to-noise ratio. They also have suboptimal conditions such as the end-on spread geometry due to the use of a land streamer and occasionally bad coupling of the geophones. This turns out to be a big challenge for the FWI algorithm. The starting model used for the field data inversion is based on the multichannel analysis of surface waves which deals with the inversion of surface-wave dispersion curves. It is a cost-efficient way to obtain an initial model for FWI.With a subset of this model and the data, I investigate the influence of traces near the sources which suffer heavily from the suboptimal acquisition conditions, and if more iterations can improve the results. Removing such traces improve the major part of the results, while more iterations are not beneficial with this particular data set. At the end I show a final comparison of both workflows by applying them to the complete Salt Lake City field data set. An application of FWI on such a large-scale land streamer acquisition with such a large number of shots has, to the best of my knowledge, not been done yet, most likely because of the large computational costs, even in 2D. The comparisons and investigations show that while RSW has a major computational advantage in storage usage and per-CPU performance, it is too sensitive to bad traces and shots which significantly degrade the final model. Therefore, it is unsuitable for field data with a low signal-to-noise ratio or that have not been preprocessed well. Furthermore, RSW cannot utilise the whole power of HPC clusters while FSW is able to do so by optimal shot parallelisation. Thus, FSW could potentially outperform RSW by raw computing power if such excessive power is available.

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

Geophysical imaging utilising the Ground Penetrating Radar (GPR) is a staple for observing the subsurface in high resolution. It produces images of the distribution of dielectric permittivity and electrical conductivity of the surveyed subsurface region. To produce these images, the data is supplied to an inversion algorithm. This algorithm iteratively improves the estimates of what the subsurface looks like. Each iteration is based on how close the response produced by the estimate is to the data.To evaluate the response from estimate models, we require an efficient forward solver of the Maxwell's equations. It can be performed in time-domain, as very capably done via gprMax, or in frequency-domain. Working in frequency-domain allows for spectral analysis of subsurface response, choosing particular frequencies of interest, and unique parallelisation and inversion strategies. For wide-band antennas used in a GPR survey, we are developing an efficient frequency domain forward modelling code in 3D. Simulating in 3D allows us to account for the antenna's complete radiation pattern. Moreover, to account for the wide band data, the forward solver will be equipped with a custom meshing algorithm that creates separate meshes for different frequency ranges of the data spectrum. Care needs to be taken that adequate boundary conditions are implemented in the forward solver for accurate domain truncation.We will present the capabilities and features of the forward solver with synthetic test cases. Supplying our forward engine to a suitable Full Waveform Inversion (FWI) strategy that maximises the adaptable meshing and frequency domain evaluations could result in high performance. The exact strategy for such an FWI will be defined and tested such that it leads to accurate and efficient reconstruction of the electrical subsurface properties.

Summary The waveform inversion method based on full wave field is limited by the quality of seismic data. In practical application, due to the shortcomings of low signal-to-noise ratio at low frequency, short offset and large spatial variation of wavelet in onshore seismic data, the application of full waveform inversion in onshore data will generally face great challenges. This paper relies on the onshore data of Bohai Bay Basin to carry out acoustic full waveform inversion processing, including seismic data pre-processing, wavelet estimation and full waveform inversion iterative processing, and finally updates the velocity model of the subsurface shallow layer to obtain a velocity model that well matches the logging velocity, effectively improving the imaging quality of pre-stack depth migration.