Time-lapse Full-waveform Inversion Research Articles

Time-lapse full-waveform permeability inversion: A feasibility study

Time-lapse seismic monitoring necessitates integrated workflows that combine seismic and reservoir modeling to enhance reservoir property estimation. We present a feasibility study of an end-to-end inversion framework that directly inverts for permeability from multiple prestack time-lapse seismic data sets. To assess the method's robustness, we design experiments focusing on its sensitivity to initial models, potential errors in modeling, and crosstalk during multiparameter inversion. Our study leverages the publicly available Compass model to simulate CO2 storage in saline aquifers. This model is derived from well and seismic data from the North Sea in an area that is currently considered for geologic carbon storage.

Assessing Time-Lapse Full-Waveform Inversion Strategies in a Brazilian Pre-Salt Setting

We conducted a comparative study of time-lapse full-waveform inversion (time-lapse FWI) strategies, considering a typical deep-water Brazilian pre-salt setting. This study employed a realistic P-wave model, ocean bottom nodes (OBN) acquisition, noisy data, and a Gaussian anomaly to represent time-lapse model changes. We evaluated the four most commonly used time-lapse FWI schemes. In the first, known as parallel time-lapse FWI, two independent FWI processes are performed from the same initial model, utilizing baseline and monitor datasets. In the second strategy, namely sequential time-lapse FWI, the retrieved baseline model serves as the starting model for inverting monitor data. In both cases, the time-lapse model is derived by subtracting the retrieved baseline model from the retrieved monitor model. The remaining two methods were double-difference and central-difference time-lapse FWI. Our findings demonstrate that all these schemes can detect model variations of 3%. Remarkably, the central-difference time-lapse FWI method demonstrated superior accuracy in producing time-lapse models and, as such, presents itself as a promising strategy for implementation in time-lapse studies within Brazilian pre-salt regions.

Monitoring underground hydrogen storage migration and distribution using time-lapse acoustic waveform inversion

The ongoing global energy shift from fossil fuels to renewable sources highlights the importance of underground hydrogen storage (UHS) as a sustainable mechanism to counterbalance the seasonal inconsistencies of renewable energy. Comparable to geological CO2 sequestration, UHS necessitates precise subsurface imaging and a thorough understanding of hydrogen behavior within geological formations, including its location and migration patterns. Since direct subsurface measurement is unattainable, there is a pronounced need for robust subsurface characterization and monitoring techniques. This research focuses on UHS feasibility in enduring storage scenarios, employing seismic monitoring strategies adapted from CO2 storage practices. Specifically, we integrate Continuous Active Source Seismic Monitoring (CASSM) and Time-Lapse Full Waveform Inversion (TLFWI) to scrutinize UHS. The study employs synthetic crosshole surveys that initially model the coexistence of hydrogen and water within fractured reservoirs, aiming to pinpoint hydrogen-related velocity alterations in acoustic waveforms. Subsequently, we utilize a time-lapse synthetic model of hydrogen injection to emulate CASSM observations. Utilizing TLFWI in conjunction with White's model, we successfully process the CASSM data to discern and quantify temporal variations in velocity and saturation, which effectively maps the spatial and temporal distribution of mobile hydrogen. The results affirm the capabilities of TLFWI and CASSM as proficient monitoring systems for UHS. This study aspires to offer a dependable methodology for the administration of large-scale and long-term geological hydrogen storage.

Bayesian variational time-lapse full waveform inversion

SUMMARY Time-lapse seismic full-waveform inversion (FWI) provides estimates of dynamic changes in the Earth’s subsurface by performing multiple seismic surveys at different times. Since FWI problems are highly non-linear and non-unique, it is important to quantify uncertainties in such estimates to allow robust decision making based on the results. Markov chain Monte Carlo (McMC) methods have been used for this purpose, but due to their high computational cost, those studies often require a pre-existing accurate baseline model and estimates of the locations of potential velocity changes, and neglect uncertainty in the baseline velocity model. Such detailed and accurate prior information is not always available in practice. In this study we use an efficient optimization method called stochastic Stein variational gradient descent (sSVGD) to solve time-lapse FWI problems without assuming such prior knowledge, and to estimate uncertainty both in the baseline velocity model and the velocity change over time. We test two Bayesian strategies: separate Bayesian inversions for each seismic survey, and a single joint inversion for baseline and repeat surveys, and compare the methods with standard linearized double difference inversion. The results demonstrate that all three methods can produce accurate velocity change estimates in the case of having fixed (exactly repeatable) acquisition geometries. However, the two Bayesian methods generate significantly more accurate results when acquisition geometries changes between surveys. Furthermore, joint inversion provides the most accurate velocity change and uncertainty estimates in all cases tested. We therefore conclude that Bayesian time-lapse inversion using a joint inversion strategy may be useful to image and monitor subsurface changes, in particular where variations in the results would lead to different consequent decisions.

CO2 Storage Monitoring via Time-Lapse Full Waveform Inversion with Automatic Differentiation.

In the field of CO2 capture utilization and storage (CCUS), recent advancements in active-source monitoring have significantly enhanced the capabilities of time-lapse acoustical imaging, facilitating continuous capture of detailed physical parameter images from acoustic signals. Central to these advancements is time-lapse full waveform inversion (TLFWI), which is increasingly recognized for its ability to extract high-resolution images from active-source datasets. However, conventional TLFWI methodologies, which are reliant on gradient optimization, face a significant challenge due to the need for complex, explicit formulation of the physical model gradient relative to the misfit function between observed and predicted data over time. Addressing this limitation, our study introduces automatic differentiation (AD) into the TLFWI process, utilizing deep learning frameworks such as PyTorch to automate gradient calculation using the chain rule. This novel approach, AD-TLFWI, not only streamlines the inversion of time-lapse images for CO2 monitoring but also tackles the issue of local minima commonly encountered in deep learning optimizers. The effectiveness of AD-TLFWI was validated using a realistic model from the Frio-II CO2 injection site, where it successfully produced high-resolution images that demonstrate significant changes in velocity due to CO2 injection. This advancement in TLFWI methodology, underpinned by the integration of AD, represents a pivotal development in active-source monitoring systems, enhancing information extraction capabilities and providing potential solutions to complex multiphysics monitoring challenges.

Bayesian Weighted Time-Lapse Full-Waveform Inversion Using a Receiver-Extension Strategy

Bayesian Weighted Time-Lapse Full-Waveform Inversion Using a Receiver-Extension Strategy

Stepsize sharing in time-lapse full-waveform inversion

Full-waveform inversion (FWI) methods can produce high-resolution images of the physical properties of the subsurface. FWI has become a powerful tool for time-lapse or 4D seismic inversion, with applications in the monitoring of reservoir changes with injection and production, and potentially long-term storage of carbon. Current time-lapse FWI strategies include the parallel strategy (PRS), the sequential strategy, the double-difference strategy (DDS), the common-model strategy (CMS), and the central-difference strategy (CDS). PRS time-lapse inversion is affected by convergence differences between the baseline and monitoring inversions, as well as nonrepeatable noise and nonrepeatable acquisition geometries between surveys. The other strategies are largely efforts to fix the sensitivities of PRS, but robust solutions are still sought. We hypothesize that several problems in time-lapse FWI arise from the independence of step lengths during updating. This is supported by synthetic data tests, which indicate that stepsize sharing reduces artifacts caused by the variability in PRS convergence. Two strategies, which we refer to as stepsize-sharing PRS (SSPRS) and stepsize-sharing CMS, are then designed to address these remaining issues. In this paper, we have tested our methods in five scenarios, including noise-free data, nonrepeated noises, nonrepeatable source positions, biased starting models, and a combination of the latter three. The comparisons between the SSPRS and other strategies indicate that the SSPRS can adapt to all tested scenarios well. Especially, except for the DDS which is extremely sensitive to the nonrepeatable source positions, only the SSPRS can provide meaningful results in the latter two scenarios when compared with others. Furthermore, given that SSPRS through its sharing incurs half of the time cost of seeking stepsizes compared with the PRS and DDS, the total computational cost of SSPRS is less than half of that of the CMS and CDS.

Data-assimilated time-lapse visco-acoustic full-waveform inversion: Theory and application for injected CO2 plume monitoring

Continuous seismic monitoring for quantifying CO2 plume migration and detection of any potential leakages in the subsurface is essential for the security of long-term anthropogenic carbon dioxide geologic storage. Traditional time-lapse full-waveform inversion (TLFWI) methods aim to map the CO2 distribution by estimating seismic velocity changes, but recent studies find that CO2-induced attenuation is an important complement to seismic velocity for tracking the CO2 plumes and even quantifying the CO2 saturation. We have developed a novel data-assimilated TLFWI method to construct high-resolution time-lapse velocity and attenuation changes from dense time-lapse monitoring data. This method consists of two theoretical developments: visco-acoustic full-waveform inversion (QFWI) and multiparameter hierarchical matrix-powered extended Kalman filter (mHiEKF). The method is capable of (1) posing temporal constraints to retrieve time-lapse information from dense monitoring data by using mHiEKF, (2) accurately recovering high-spatial-resolution velocity and attenuation perturbations using first-order equation system-based QFWI, and (3) providing the model uncertainty by estimating their model standard deviation. With numerical examples, we first find the effectiveness of the new QFWI on estimating accurate velocity and attenuation models simultaneously. Then, a CO2 leakage case and a realistic Frio-II CO2 monitoring case are presented to find the advantages and applicability of our data-assimilated QFWI method for estimating time-lapse changes using dense time-lapse monitoring surveys. By assimilating time-lapse seismic monitoring data over time, our data-assimilated QFWI method can improve the resolution of velocity and attenuation changes and decrease their model uncertainties.

Weighted-average time-lapse seismic full-waveform inversion

As seismic data can contain information over a large spatial area and are sensitive to changes in the properties of the subsurface, seismic imaging has become the standard geophysical monitoring method for many applications such as carbon capture and storage and reservoir monitoring. The availability of practical tools such as full-waveform inversion (FWI) makes time-lapse seismic FWI a promising method for monitoring subsurface changes. However, FWI is a highly ill-posed problem that can generate artifacts. Because the changes in the earth’s properties are typically small in terms of magnitude and spatial extent, discriminating the true time-lapse signature from noise can be challenging. Different strategies have been proposed to address these difficulties. In this study, we propose a weighted-average (WA) inversion to better control the effects of artifacts and differentiate them from the true 4D changes. We further compare five related strategies with synthetic tests on clean and noisy data. The effects of seawater velocity variation on different strategies also are studied as one of the main sources of nonrepeatability. We tested different strategies of time-lapse FWI (TL-FWI) using the Marmousi and the SEG Advanced Modeling time-lapse models. The results indicate that the WA method can provide the best compromise between accuracy and computation time. This method also provides a range of possible answers of other TL-FWI strategies.

A time-domain multisource Bayesian/Markov chain Monte Carlo formulation of time-lapse seismic waveform inversion

Seismic waveform inversion has been shown to be well-suited for identification and characterization of time-lapse changes in a reservoir. However, the subtle medium variations associated with enhanced oil recovery and/or [Formula: see text] storage problems give uncertainty quantification within such inverse approaches a heightened importance. To analyze both of these features of the time-lapse inverse problem, we formulate a Bayesian full-waveform inversion (FWI) procedure, based on a Markov chain Monte Carlo (MCMC) algorithm. The formulation uses several existing strategies, such as the use of a double-difference time-lapse FWI (DDFWI), incorporation of time-domain multisource data, and application of a local-updating target-oriented inversion. However, it incorporates these within a stochastic framework, involving computation of model covariance with an adaptive Metropolis algorithm, and a method to estimate data error statistics based on the features of time-lapse difference data that is incorporated. A random walk Metropolis-Hastings MCMC is adopted for optimization. In conventional, i.e., deterministic, DDFWI, inversions are carried out for the baseline and monitoring models; in the MCMC approach, a deterministic FWI procedure is carried out for the baseline model, and the MCMC algorithm is applied in the monitoring inversion stage; and the final time-lapse model is the difference between these. A feasibility study is carried out using synthetic 2D acoustic models and data, including time-lapse model estimation and uncertainty quantification. We compare the MCMC approach with conventional deterministic optimization DDFWI and remark on benefits derived, which appear to justify the expanded complexity and cost of a global approach. In addition to the availability of posterior distributions, which are critical for the assessment of the estimations, we observe that the MCMC approach tends to produce monitoring images with clearer edges and fewer coherent errors.

Source-independent time-lapse full-waveform inversion for anisotropic media

Time-lapse full-waveform inversion can provide high-resolution information about changes in the reservoir properties during hydrocarbon production and CO2 injection. However, the accuracy of the estimated source wavelet, which is critically important for time-lapse FWI, is often insufficient for field-data applications. The so-called “source-independent” FWI is designed to reduce the influence of the source wavelet on the inversion results. We incorporate the convolution-based source-independent technique into a time-lapse FWI algorithm for VTI (transversely isotropic with a vertical symmetry axis) media. The gradient of the modified FWI objective function is obtained from the adjoint-state method. The algorithm is tested on a model with a graben structure and the modified VTI Marmousi model using three time-lapse strategies (the parallel-difference, sequential-difference, and double-difference methods). The results confirm the ability of the developed methodology to reconstruct the localized time-lapse parameter variations even for a strongly distorted source wavelet. The algorithm remains robust in the presence of moderate noise in the input data but the accuracy of the estimated time-lapse changes depends on the model complexity.

Time-lapse full waveform inversion based on curvelet transform: Case study of CO2 storage monitoring

Full waveform inversion (FWI) has high accuracy in predicting reservoir elastic parameters. Prediction of changes in reservoir elastic parameters is an effective method for CO2 storage monitoring. Therefore, FWI is of great significance in CO2 storage monitoring, however, it relies on low-frequency information and data quality and its use incurs substantial computational costs. To alleviate this problem, a multi-scale time-lapse inversion method based on the curvelet transform was proposed. Using the high sparsity of the curvelet transform, the original shot gather data can be separated into multiple scales. A multi-scale inversion process based on the curvelet transform was introduced, and a coarse to fine scale inversion was conducted. According to the multi-scale inversion strategy, the P- and S-wave velocities and densities of the reservoirs in multiple periods were obtained. The test results of Marmousi II and the manual model show that the inversion method based on the curvelet transform exhibits high accuracy in predicting reservoir elastic parameters and can clearly determine the local changes in the reservoir. The calculation time shows that the multi-scale inversion based on the curvelet transform does not reduce the calculation efficiency. In summary, the time-lapse full waveform inversion method based on the curvelet transform is highly accurate, and is therefore promisingly effective for CO2 storage monitoring.

CO2 storage monitoring based on time-lapse seismic data via deep learning

CO2 geological storage is an effective way of reducing atmospheric CO2 concentration. The physical characteristics of the reservoir and the feasibility of CO2 flooding were analyzed based on the carbon capture, utilization, and storage (CCUS) project in Yanchang Oilfield, China. The heterogeneity of the reservoir indicates variation in the shape of the CO2 plume. A CO2 storage monitoring method based on a full convolutional neural network (FCN) that applies time-lapse difference seismic data is proposed for the geological task of CO2 storage monitoring. A total of 2800 sets of forward simulation time-lapse difference data and corresponding velocity changes were used to train the network. These data include noisy and noise-free data, which help improve the noise immunity of the network. The prediction accuracy of the network under different samples of training data, noise levels, and velocity changes is discussed. Furthermore, 100 sets of noisy data and 100 sets of noise-free data were used to verify the predictive ability of the network. The test results of the synthetic data show that the FCN-based CO2 storage monitoring method exhibits relatively high efficiency and high precision compared with time-lapse full waveform inversion.

Central-difference time-lapse 4D seismic full-waveform inversion

Repeated seismic surveys contain valuable information regarding time-lapse (4D) changes in the subsurface. Full-waveform inversion (FWI) of seismic data can provide high-resolution estimates of 4D change. We have adopted a new time-domain 2D acoustic time-lapse FWI method based on the central-difference scheme with higher order mathematical accuracy and reasonable computational cost. The method is rigorously tested on the SEG Advanced Modeling 4D time-lapse model and ocean-bottom-node data set. High-resolution 4D velocity estimates are obtained, which show strong (approximately 25%) velocity increases in a 75 m thick gas layer, as well as weaker (5%) changes due to geomechanical effects, the latter of which are poorly recovered by the conventional parallel 4D FWI method. We also perform the bootstrap 4D FWI method, and the result is contaminated by strong artifacts in the underburden, whereas the proposed central-difference method has fewer underburden artifacts allowing more reliable interpretations. In this realistic case study, acoustic FWI erroneously overfits some of the elastic scattered waves, and it cannot fit the strong elastic 4D coda waves well. The results show that the proposed central-difference 4D FWI method within the acoustic approximation may be a practical solution for time-lapse seismic velocity inversion.

Towards real-time monitoring: data assimilated time-lapse full waveform inversion for seismic velocity and uncertainty estimation

SUMMARYRapid development of time-lapse seismic monitoring instrumentations has made it possible to collect dense time-lapse data for tomographically retrieving time-lapse (even continuous) images of subsurface changes. While traditional time-lapse full waveform inversion (TLFWI) algorithms are designed for sparse time-lapse surveys, they lack of effective temporal constraint on time-lapse data, and, more importantly, lack of the uncertainty estimation of the TLFWI results that is critical for further interpretation. Here, we propose a new data assimilation TLFWI method, using hierarchical matrix powered extended Kalman filter (HiEKF) to quantify the image uncertainty. Compared to existing Kalman filter algorithms, HiEKF allows to store and update a data-sparse representation of the cross-covariance matrices and propagate model errors without expensive operations involving covariance matrices. Hence, HiEKF is computationally efficient and applicable to 3-D TLFWI problems. Then, we reformulate TLFWI in the framework of HiEKF (termed hereafter as TLFWI-HiEKF) to predict time-lapse images of subsurface spatiotemporal velocity changes and simultaneously quantify the uncertainty of the inverted velocity changes over time. We demonstrate the validity and applicability of TLFWI–HiEKF with two realistic CO2 monitoring models derived from Frio-II and Cranfield CO2 injection sites, respectively. In both 2-D and 3-D examples, the inverted high-resolution time-lapse velocity results clearly reveal a continuous velocity reduction due to the injection of CO2. Moreover, the accuracy of the model is increasing over time by assimilating more time-lapse data while the standard deviation is decreasing over lapsed time. We expect TLFWI-HiEKF to be equipped with real-time seismic monitoring systems for continuously imaging the distribution of subsurface gas and fluids in the future large-scale CO2 sequestration experiments and reservoir management.

Integrated kinematic time-lapse inversion workflow leveraging full-waveform inversion and machine learning

We demonstrate that a workflow combining emergent time-lapse full-waveform inversion (FWI) and machine learning technologies can address the demand for faster time-lapse processing and analysis. During the first stage of our proposed workflow, we invert long-wavelength velocity changes using a tomographically enhanced version of multiparameter simultaneous reflection FWI with model-difference regularization. Short-wavelength changes are inverted during the second stage of the workflow by a specialized high-resolution image-difference tomography algorithm using a neural network. We discuss application areas for each component of the workflow and show the results of a West Africa case study.

Combining reflection and transmission information in time-lapse velocity inversion: A new hybrid approach

Full-waveform inversion (FWI) uses the information of the full wavefield to deliver high-resolution images of the subsurface. Conventional time-lapse FWI primarily uses the transmitted component (diving waves) of the wavefield to reconstruct the low-wavenumber component of the velocity model. This requires large-offset surveys and low-frequency data. When the target of interest is deep, diving waves cannot reach the target and FWI will be dominated by the reflected component of the wavefield. Consequently, the retrieved model resembles a least-squares migration instead of a velocity model. Image-domain methods, especially image-domain wavefield tomography (IDWT), have been developed to obtain a model of time-lapse velocity changes in deeper targets using reflected waves. The method is able to recover models of deep targets. However, it also tends to obtain smeared time-lapse velocity changes. We have developed a form of time-lapse waveform inversion that we call dual-domain time-lapse waveform inversion (DDWI), whose objective function joins FWI and IDWT, combining information from the diving waves in the data-domain FWI term with information from the reflected waves in the image-domain IDWT term. During the nonlinear inversion, the velocity model is updated using constraints from both terms simultaneously. Similar to sequential time-lapse waveform inversion, we start the time-lapse inversion from a baseline model recovered with FWI. We test DDWI on a variety of synthetic models of increasing complexity and find that it can recover time-lapse velocity changes more accurately than when both methods are used independently or sequentially.

Application of time-lapse full waveform inversion of vertical seismic profile data for the identification of changes introduced by CO2 sequestration

Seismic methods are frequently used for the purpose of monitoring of time-lapse changes introduced by CO2 sequestration. Surface seismic is often considered as the main tool for monitoring. Vertical Seismic Profile (VSP) is occasionally applied as an auxiliary method. Standard VSP data processing workflow does not provide a quantitative estimate of the time-lapse changes in the physical properties. However, full waveform inversion (FWI) may be used for the purpose of quantitative interpretation. Its ability to employ the whole seismic wavefield (including transmitted, reflected and converted waves) for the purpose of building the models of physical properties can be considered one of its main advantages.We show that time-lapse elastic FWI of VSP data is capable of providing quantitative estimates of time-lapse changes in the medium. A feasibility study is carried out on 2D and 3D synthetic datasets created using full-earth models of the CO2CRC Otway CO2 sequestration site. The inversion workflow obtained from the feasibility study is successfully applied to a field single-offset time-lapse VSP dataset. As a result, FWI provides an image of the time-lapse changes introduced by the injection of supercritical CO2.

Time-lapse full-waveform inversion as a reservoir-monitoring tool — A North Sea case study

Full-waveform inversion (FWI) has become an enabling tool for 3D velocity-model building, especially in the shallow part of the seismic image that is well probed by diving waves. Given that FWI provides direct access to P-wave velocities, its application to time-lapse (4D) studies is of obvious interest. Can 4D FWI give fast access to small reservoir production-related velocity changes and compete with traditional 4D time-shift results based on fully processed and imaged reflection data? Also, what algorithmic developments may be needed to achieve robust 4D FWI results? Time-lapse data sets acquired with highly repeatable permanent-reservoir-monitoring (PRM) acquisition systems, such as the one deployed over the Grane Field in the Norwegian North Sea, are well suited to help address these questions. We demonstrate the success of the 4D FWI technique using a synthetic study involving 3D elastic modeling through a highly realistic earth model akin to the actual Grane PRM data. This study indicates there is minimal sensitivity of the method to various residual uncertainties in the data and in the modeling for this acquisition configuration. The 4D FWI results using real time-lapse Grane PRM data acquired in the field with a six-month acquisition interval between vintages show changes at the reservoir level that correlate with both injecting and producing wells. We also find good agreement when comparing the velocity differences from 4D FWI to 4D time shifts and time strains from the fully processed and imaged seismic reflection data. Given that the FWI updates are driven mainly by diving waves, whereas the time-strain analysis uses reflection data, this gives increased confidence in both sets of results. Overall, this case study demonstrates the potential of FWI as a reservoir-monitoring tool.

Time-lapse full-waveform inversion with ocean-bottom-cable data: Application on Valhall field

Knowledge of changes in reservoir properties resulting from extracting hydrocarbons or injecting fluid is critical to future production planning. Full-waveform inversion (FWI) of time-lapse seismic data provides a quantitative approach to characterize the changes by taking the difference of the inverted baseline and monitor models. The baseline and monitor data sets can be inverted either independently or jointly. Time-lapse seismic data collected by ocean-bottom cables (OBCs) in the Valhall field in the North Sea are suitable for such time-lapse FWI practice because the acquisitions are of a long offset, and the surveys are well-repeated. We have applied independent and joint FWI schemes to two time-lapse Valhall OBC data sets, which were acquired 28 months apart. The joint FWI scheme is double-difference waveform inversion (DDWI), which inverts differenced data (the monitor survey subtracted by the baseline survey) for model changes. We have found that DDWI gave a cleaner and more easily interpreted image of the reservoir changes compared with that obtained with the independent FWI schemes. A synthetic example is used to demonstrate the advantage of DDWI in mitigating spurious estimates of property changes and to provide cross validations for the Valhall data results.