Reflection Waveform Inversion Research Articles

One‐way waveform inversion: Real marine data application

AbstractThe reflection waveform inversion is a powerful technique to build a large‐scale velocity model of the subsurface by fitting the reflected recorded seismic waves. The reflection waveform inversion is designed based on the pillar concept of model and data‐scale separation. Therefore, its success is related to the ability of its forward modelling engine to separate reflected events distinctly from other propagation modes (diving waves, multiples, etc.). However, the standard Born modelling based on the two‐way wave equation may generate internal multiples in case of an insufficient smooth background model. These internal multiples may lead to a distorted sensitivity kernel, which adds more non‐linearity to the inverse problem. In addition, simulating the wave equation using two‐way propagators is still an overburden step of the algorithm especially in large three‐dimensional real surveys. In this proposal, we introduce an alternative to the two‐way wave equation by using a one‐way approach for the reflection waveform inversion. The Born modelling based on one‐way propagators significantly reduces the computational cost and I think it should be allows to relax the smooth background velocity model assumption by restricting the forward modelling to primary reflected waves. After a brief theoretical description of the one‐way waveform inversion, we present an application of the algorithm on the real marine dataset to review its promises and pitfalls. Our approach produces an acceptable large‐scale velocity model whose accuracy is confirmed by the migrated image and the offset gathers.

Converted-wave reflection traveltime inversion with free-surface multiples for ocean-bottom-node data

Advancements in ocean-bottom-node (OBN) technologies have enabled the recording of high-quality multicomponent seismic data, which can provide crucial information about subsurface properties through elastic seismic imaging. However, imaging multicomponent data is challenging due to the requirement for P- and S-wave velocity models. Conventional processing relies on estimating the S-wave velocity model using a primary converted wave (C wave) because the pure S-wave primaries are not available if using standard air-gun sources. When a free surface is present, the C waves recorded with geophones can be contaminated by source-side P-wave multiples, especially water-layer reverberations, which are difficult to remove even using state-of-the-art wavefield decomposition methods. These C-wave multiples can cause significant mismatches between synthetic and observed data during reflection traveltime or waveform inversion if only primary P-to-S (PS) conversions are simulated. To address these issues and reliably build an S-wave velocity model for PS imaging, we develop a C-wave reflection traveltime inversion method that takes source-side free-surface multiples into account. The traveltime misfit of C-wave data is extracted using dynamic image warping to ensure a better match between the synthetic and observed data. The functional gradient of the objective function is derived using the adjoint state method. Based on sensitivity kernel analyses, a convenient gradient preconditioning strategy is developed to robustly separate the contribution of primary and multiple C waves during backpropagation. This strategy can effectively mitigate the high-wavenumber crosstalk associated with nonphysical wavepaths in the gradient and thus allow more accurate updating for the S-wave velocity model. The synthetic data and shallow-water OBN data from the East China Sea indicate that this approach can reliably recover the S-wave macrovelocity structures for PS imaging.

Second-order optimization for multiparameter reflection waveform inversion in acoustic VTI media

SUMMARY The seismic wave velocity in subsurface formations typically varies both spatially and directionally, resulting in a heterogeneous and anisotropic medium. To successfully image complex structures and potential reservoirs using multichannel seismic data, high-resolution interval velocity models are required. However, most controlled-source seismic recordings lack wide-angle signals, such as diving and refracted waves that propagate through deep formations. Consequently, geophysicists rely on the traveltimes and waveforms of reflections or back-scatterings in finite-frequency and finite-offset seismograms to estimate velocity and account for possible anisotropy. Recently, wave-equation based reflection waveform inversion (RWI) has emerged as an active research topic due to its ability to recover intermediate-wavelength model components that cannot be retrieved in reflection traveltime tomography. Nevertheless, the widely used gradient-type local optimization suffers from multiparameter trade-off and slow convergence of RWI in anisotropic media. Analysis of the Fréchet derivative reveals that the sensitivity of reflections to changes in long-to-intermediate wavelengths of the anisotropic velocities is jointly controlled by the specular reflection on the interface and the radiation pattern of scattered fields concerning the model parameters along the wave paths. Anatomy of the approximate Hessian reveals characteristics of parameter coupling and spatial resolution in the context of multiparameter RWI, inspiring the development of a matrix-free Gauss–Newton algorithm based on the second-order adjoint-state method for large-scale applications. Synthetic and real data examples demonstrate that the proposed approach can appropriately handle overburden heterogeneities and anisotropies, and thus improve imaging of underlying complex structures such as dipping and small-scale faults in the deep parts.

A Real-Time Permittivity Estimation Method for Stepped-Frequency Ground-Penetrating Radar by Full-Waveform Inversion

Ground-penetrating radar (GPR) has been widely used in estimating the permittivity of mediums. The radar echo amplitude method is an important method used by GPR in this estimation, the basic step of which is to deduce the magnitude of the permittivity according to the relationship between the reflection coefficient and the permittivity. Based on the basic principle of the radar echo amplitude method, this paper proposes a full-wave inversion real-time permittivity estimation method that can be used for stepped-frequency GPR (SFGPR), which offers high efficiency, accuracy, and generalization ability. The characteristics of this method are mainly reflected in the following four aspects: Using the SFGPR system and introducing a layered media detection model, we can complete waveform compensation optimization with high precision. The distance between the antenna and the surface of the reflective medium is extracted from the time domain waveform without manual measurement, avoiding human measurement errors. The inversion of the total reflection waveform at the required height works under the principle of an electromagnetic field, eliminating the need for repeated metal plate calibration experiments and improving work efficiency and waveform accuracy. In a continuous measurement line, the total reflection waveform inversion on each measurement point can be efficiently completed, and the change of permittivity on the measurement line can be obtained. To evaluate the feasibility of the proposed method, we performed experiments on a wall of known thickness, and the permittivity estimation was basically consistent with that of the dielectric probe, physical model calculation, and wall penetration. We also successfully applied this method to the dielectric property analysis of adobe samples. The results indicate that the proposed method can help grasp the condition of a measured medium, which can ensure the accuracy of detection and improve subsequent data processing efficiency.

Wide‐spectrum reconstruction of a velocity model based on the wave equation reflection inversion method and its application

AbstractMost seismic data used for conventional exploration lack far‐offset signals and effective low‐frequency components. This makes it difficult for conventional full waveform inversion methods to recover the low‐wavenumber components of mid‐ and deep‐layer models. To resolve the bottleneck of ray‐theoretical reflection traveltime tomography, wave equations, such as reflection inversion methods, are receiving increasing attention. We reconstructed a wide‐spectrum velocity model based on the multiscale wave‐equation reflection inversion method for model decomposition. First, using the dynamic image warping method to obtain reflection traveltime residuals, the wave‐equation reflection traveltime inversion was used to recover the low‐wavenumber components of the background model, which also solved the cycle‐skipping problem. Second, the medium‐wavenumber component of the model is then supplemented by the reflection waveform inversion, while the reflectivity model is obtained relying on the least‐squares reverse time migration method. Based on this method, the background and perturbation models are updated alternately and iteratively. At the same time, the stratum structural tensor information was extracted using the perturbed model image to construct a preconditioned operator for the stratum structural constraint, suppress unreasonably high‐wavenumber components in the generalized gradient and improve the geological consistency of the inversion results. Testing of the model using the Sigsbee2b model and seismic field data from the East China Sea showed that, compared with the conventional reflection traveltime tomography method based on prestack depth migration, the wave‐equation reflection inversion strategy with well‐matched information from traveltimes to waveforms significantly improved the accuracy of the middle and deep velocity modelling and enhanced the imaging quality of the whole body.

Newton optimization and the Hessian matrix in scale-separation waveform inversion problems with reflected and transmitted waves

Summary Full waveform inversion (FWI) is often utilized for determining the medium parameters of the Earth by minimizing the misfit between observed and modelled waves. The conventional formulation of FWI is well suited to utilize transmitted waves to determine long-to-intermediate wavelength properties of the medium. Hovewer, the penetration depth of transmitted waves may be limited for a given acquisition. As a remedy, reflection waveform inversion (RWI) exploits the kinematic information in reflected waves to retrieve these long-wavelength properties, particularly below the maximum illumination depth of transmitted waves. Previous works have demonstrated the benefits of utilizing both transmitted and reflected waves, thereby considering a reconciliation of conventional FWI and RWI. One such formulation is known as joint full waveform inversion (JFWI), where reflected and transmitted waves are separately compared in the misfit functional. A disadvantage of gradient-based optimization schemes in RWI and JFWI is the presence of strong crosstalk due to mapping of reflected data residuals along the entire reflection wavepaths. Because RWI and JFWI require frequent least-squares migration, we are incentivized to determine well-focused search directions that allow large movements between the migration steps. Thus, we propose an improvement to RWI and JFWI by utilizing Newton methods to directly account for crosstalk between parameters. The crosstalk effects are described by the second-order sensitivities of the misfit functional, i.e. the Hessian matrix. We adopt the adjoint-state method to compute the first- and second order sensitivities of the misfit functional for any of these waveform inversion procedures in a unified framework and for arbitrary misfit functionals. Furthermore, we conceptually study the Hessian matrix in least-squares based full-, reflection- and joint full waveform inversion from a data-domain point of view. Synthetic examples and a three-dimensional field data example demonstrate that the truncated Gauss-Newton method is effective in attenuating artefacts due to crosstalk between spatially separated variables, thus substantially improving the spatial focusing of the search directions.

Automated salt model building: From compaction trend to final velocity model using waveform inversion

Conventional seismic velocity model building in complicated salt-affected areas requires the explicit identification of salt boundaries in migrated images and typically involves testing of possible subsurface scenarios through multiple generations. The resulting velocity models are slow to generate and may contain interpreter-driven features that are difficult to verify. We show that it is possible to build a full final velocity model using advanced forms of full-waveform inversion applied directly to raw field data, starting from a model that contains only a simple 1D compaction trend. This approach rapidly generates the final velocity model and migrates processed reflection data at least as accurately as conventionally generated models. We demonstrate this methodology using an ocean-bottom-node data set acquired in deep water over Walker Ridge in the Gulf of Mexico. Our approach does not require exceptionally long offsets or the deployment of special low-frequency sources. We restrict the inversion so it does not use significant energy below 3 Hz or offsets longer than 14 km. We use three advanced forms of waveform inversion to recover the final model. The first is adaptive waveform inversion to proceed from models that begin far from the true model. The second is nonlinear reflection waveform inversion to recover subsalt velocity structure from reflections and their long-period multiples. The third is constrained waveform inversion to produce salt- and sediment-like velocity floods without explicitly identifying salt boundaries or velocities. In combination, these three algorithms successively improve the velocity model so it fully predicts the raw field data and accurately migrates primary reflections, though explicit migration forms no part of the workflow. Thus, model building via waveform inversion is able to proceed from field data to the final model in just a few weeks. It entirely avoids the many cycles of model rebuilding that may otherwise be required.

Elastic Reflection Waveform Inversion With a Nonlinear Born Scattering Operator for Multiparameter Reconstruction

Elastic full waveform inversion (FWI) is one of the most popular tools in recovering the subsurface P- and S-velocity models with high resolution. However, it requires either a good starting model or low-frequency data to avoid the cycle-skipping issue. Elastic reflection waveform inversion (ERWI) uses the migration/demigration process to compute the low-wavenumber gradient. One drawback of conventional ERWI is that it mainly relies on the first-order Born scattering and only utilizes primary reflection wave paths, providing limited wavenumber illumination in the update. In this letter, a nonlinear Born scattering operator is incorporated with ERWI for multiparameter reconstruction to mitigate the drawback of the conventional linear Born approximation. Finally, we use numerical examples to show that the nonlinear Born scattering operator allows us to take advantage of the multiples and enlarge the wavenumber illumination in ERWI results.

Seismic reflection waveform inversion based on Gauss–Newton optimization

Abstract Owing to the lack of long-offset signals and effective low-frequency components, it is extremely difficult for classical full-waveform inversion (FWI) to obtain the long-wavelength components of medium and deep elastic parameter models. Considering ray theory, reflection traveltime tomography is restricted by resolution, and the reflection waveform inversion (RWI) method of the wave equation, and its practicability, has received greater attention. However, previous studies into RWI have primarily used first-order optimization methods, in which convergence and resolution still need substantial improvement. Based on the second-order optimization inversion theory, we deduced the reflection wave-sensitive kernel, objective function gradient and Hessian operator of background and perturbation model. Additionally, we revealed the de-fuzzification effect of the Hessian matrix on the gradient of inversion and the working mechanism of background velocity updating on direction optimization and inversion resolution improvement. Experiments on the SEG/EAGE overthrust model showed that an RWI with the Gauss–Newton method using an approximate Hessian matrix significantly improved convergence and wide-spectrum modeling capability compared with the conjugate gradient method. On the streamer seismic data of the East China Sea, the second-order optimization RWI method surpassed the commonly used reflection traveltime tomography based on pre-stack depth migration. In addition, the RTM of inversion model can depict the complex fault system in the Changjiang sag with a high resolution, which improves the imaging quality of the deep basement.

Reflection-based traveltime and waveform inversion with second-order optimization

Reflection-based inversion that aims to reconstruct the low-to-intermediate wavenumbers of the subsurface model, can be a complementary to refraction-data-driven full-waveform inversion (FWI), especially for the deep target area where diving waves cannot be acquired at the surface. Nevertheless, as a typical nonlinear inverse problem, reflection waveform inversion may easily suffer from the cycle-skipping issue and have a slow convergence rate, if gradient-based first-order optimization methods are used. To improve the accuracy and convergence rate, we introduce the Hessian operator into reflection traveltime inversion (RTI) and reflection waveform inversion (RWI) in the framework of second-order optimization. A practical two-stage workflow is proposed to build the velocity model, in which Gauss-Newton RTI is first applied to mitigate the cycle-skipping problem and then Gauss-Newton RWI is employed to enhance the model resolution. To make the Gauss-Newton iterations more efficiently and robustly for large-scale applications, we introduce proper preconditioning for the Hessian matrix and design appropriate strategies to reduce the computational costs. The example of a real dataset from East China Sea demonstrates that the cascaded Hessian-based RTI and RWI have good potential to improve velocity model building and seismic imaging, especially for the deep targets.

Adaptive Feedback Convolutional‐Neural‐Network‐Based High‐Resolution Reflection‐Waveform Inversion

AbstractFull‐waveform inversion (FWI) applies non‐linear optimization to estimate the velocity model by fitting the observed seismic data. With a smooth starting velocity model, FWI mainly inverts for the shallower background velocity model by fitting the observed direct, diving and refracted data, and updates the interfaces by fitting the observed reflected data. As the deeper parts of background velocity model cannot be effectively updated by fitting the reflected data in FWI, the deeper interfaces are less accurate than the shallower interfaces. To update the deeper background velocity model, many reflection‐waveform inversion (RWI) algorithms were proposed to separate the tomographic and migration components from the reflection‐related gradient. We propose a convolutional‐neural‐network‐based reflection‐waveform inversion (CNN‐RWI) to repeatedly apply the iteratively updated convolutional neural network (CNN) to predict the true velocity model from the smooth starting velocity model (the tomographic components), and the high‐resolution migration image (the migration components). The CNN is iteratively updated by the more representative training data set, which is obtained from the latest CNN‐predicted velocity model by the proposed spatially constrained divisive hierarchical k‐means parcellation method. The more representative the training velocity models are, the more accurate the CNN‐predicted velocity model becomes. Synthetic examples using different portions of the Marmousi2 P‐wave velocity model show that CNN‐RWI inverts for both the shallower and deeper parts of velocity models more accurately than the conjugate‐gradient FWI (CG‐FWI). Both the CNN‐RWI and the CG‐FWI are sensitive to the accuracy of the starting velocity model and the complexity of the unknown true velocity model.

Joint Traditional and Reflection Envelope Inversion

The envelope inversion (EI) is an effective method to recover low-wavenumber components, which helps to produce a good initial model for full-waveform inversion (FWI). However, when the initial model is not capable of generating reflections, it brings enormous challenges for EI to invert deep low-wavenumber components, especially for short offset data. In contrast, reflection waveform inversion (RWI) uses demigration data to fit the observed reflection, which focuses on the transmission information with short offset seismic data. However, the cycle skipping and high nonlinearity of the RWI misfit still exist when the low-frequency information is absent. In this letter, we develop a joint traditional and reflection envelope inversion (JREI) that utilizes both reflection and transmission waves with envelope low-frequencies to recover low-wavenumber components in the shallow and deep regions simultaneously. We then use the FWI with high-frequency seismic data to obtain the high-wavenumber components. Applications to the modified Marmousi and Overthrust models demonstrate that the JREI can invert a better starting velocity model for the FWI to achieve a high-resolution inversion result.

Two-step full waveform inversion of diving and reflected waves with the diffraction-angle-filtering-based scale-separation technique

SUMMARYFull waveform inversion (FWI) is a highly non-linear optimization problem that aims to reconstruct high-resolution subsurface structures. The success of FWI in reflection seismology relies on appropriate updates of low-wavenumber background velocity structures, which are generally driven by the diving waves in conventional FWI. On the other hand, the reflected waves mainly contribute to updating high-wavenumber components rather than low-wavenumber components. To extract low-wavenumber information from the reflected waves in addition to the diving waves, we propose a two-step FWI strategy that separates a given model into the reflectivity and background velocity models and then alternately update them using the scale-separation technique based on diffraction-angle filtering (DAF; which was proposed to effectively control wavenumber components of the FWI gradient). Our strategy first inverts the high-wavenumber reflectivity model by suppressing energy at large diffraction angles, which are necessary to compute the reflection wave paths (i.e. the rabbit-ears-shaped kernels) for low-wavenumber updates in the subsequent stage. Then, we extract low-wavenumber components due to the diving (banana-shaped kernels) and reflected waves (rabbit-ears-shaped kernels) from the gradient by suppressing energy at small diffraction angles. Our strategy is similar to reflection waveform inversion (RWI) in that it separates a given model into high- and low-wavenumber components and uses the rabbit-ears-shaped kernels for low-wavenumber updates. The main difference between our strategy and RWI is that our strategy adopts the DAF-based scale-separation technique in the space domain, which makes our algorithm of using both the banana-shaped and rabbit-ears-shaped kernels computationally attractive. By applying our two-step inversion strategy to the synthetic data for the Marmousi-II model and the real ocean-bottom cable data from the North sea, we demonstrate that our method properly reconstructs low-wavenumber structures even if initial models deviate from the true models.

Hessian-based reflection waveform inversion: Theory and applications to synthetic and field data

Wave-equation reflection waveform inversion (RWI) is a promising method to reconstruct the background velocity model with reflection data. But it is difficult to precondition this highly nonlinear inverse problem for efficient convergence and reliable model updating. In the context of full-waveform inversion (FWI), the second-order derivative of the objective function with respect to the model parameters (i.e., the Hessian operator) can be used with the second-order optimization to overcome similar difficulties. To our knowledge, however, there are few such studies for RWI. This motivates us to derive and investigate the Hessian operator using the Born approximation in the context of RWI. For the same experimental setup with a toy model, we observe that the Hessian matrix of RWI exhibits a more compact structure than its counterpart in the context of FWI because they are constructed with the sensitivity kernels of very different spatial distribution features. Accordingly, we have developed a truncated Gauss-Newton RWI method consisting of two nested loops: An outer loop updates the background model in the manner of nonlinear waveform inversion, and an inner loop aims to iteratively estimate the background model update in a matrix-free manner by solving the Gauss-Newton equation. The workflow consists of alternating estimation of the perturbation and the background velocity model components, of which the former is done with a linear least-squares reverse time migration using the conjugate-gradient method. A synthetic example on the overthrust model and a field data example demonstrate that the Hessian-based RWI can significantly improve the estimation of intermediate-wavenumber components and promote velocity model building and seismic imaging with precritical reflection data.

Frequency-domain reflection waveform inversion with generalized internal multiple imaging

Full-waveform inversion (FWI) has the potential to provide a high-resolution detailed model of the earth’s subsurface, but it often fails to do so if the starting model differs significantly from the true one. Reflection waveform inversion (RWI) is a popular method for building a sufficiently accurate initial model for FWI. In traditional RWI, the low-wavenumber updates are always computed and captured by smearing the data misfit along the reflection path with the help of migration/demigration. However, the success of RWI relies heavily on accurately reproducing the data in demigration. Thus, we have introduced a new generalized internal multiple imaging-based RWI (GIMI-RWI) implementation, in which we avoid the Born modeling and update the primary reflection kernel directly. In GIMI-RWI, we store one reflection kernel for each source-receiver pair, preserving the unique wavepath for every single source-receiver trace. Subsequently, the convolution between the data residuals and the corresponding reflection kernel can build the tomographic velocity updates. In this situation, the long-wavelength tomographic updates are free of migration footprints and will contribute a smoother background velocity to reduce the cycle-skipping risk and stabilize the followed FWI process. In addition, the GIMI-RWI method is source independent because it entirely relies on the data. Using a synthetic example extracted from the Sigsbee2A model, we find the reliable performance of the GIMI-RWI technique.

Reflection Full Waveform Inversion With Second‐Order Optimization Using the Adjoint‐State Method

AbstractIn controlled‐source seismology, the standard full waveform inversion (FWI) can't reliably recover the macrovelocity structure in the deep part, if the surface seismic data lack of ultra‐long offsets and very low frequencies. Reformulating the FWI for pre‐critical reflections based on model scale separation leads to reflection waveform inversion (RWI), which aims to improve the reconstruction of low‐to‐intermediate model wavenumbers. However, the state‐of‐art RWI approaches rely on the gradient‐type optimization, resulting in slow convergence and inaccurate recovery of the deep macrovelocities. Therefore, we present a Hessian‐based second‐order optimization in the context of RWI. Based on the reflection Fréchet derivative with respect to the background model, the approximate Hessian and the point spread functions (PSFs) on toy models with two and three layers are constructed to gain physical insights about parameter coupling and spatial resolution at the scale of low‐to‐intermediate wavenumbers for finite‐offset and band‐limited data. The high‐velocity anomaly and checkerboard experiments demonstrate the benefit of incorporating the inverse approximate Hessian effect on the functional gradient. Accordingly, for large‐scale applications, we propose a matrix‐free Gauss‐Newton RWI approach, in which the Hessian‐vector product is formulated with the second‐order adjoint‐state method and an optimal updating direction is estimated in the nested inner loop to accelerate the convergence. A synthetic example and an application to the real data from East China Sea demonstrate that the proposed method can improve velocity model building and seismic imaging, especially for the deep targets.

A reflection-based efficient wavefield inversion

Full-waveform inversion (FWI) is popularly used to obtain a high-resolution subsurface velocity model. However, it requires either a good initial velocity model or low-frequency data to mitigate the cycle-skipping issue. Reflection-waveform inversion (RWI) uses a migration/demigration process to retrieve a background model that can be used as a good initial velocity in FWI. The drawback of conventional RWI is that it requires the use of least-squares migration, which is often computationally expensive, and it is still prone to cycle skipping at far offsets. To improve the computational efficiency and overcome cycle skipping in the original RWI, we have incorporated it into a recently introduced method called efficient wavefield inversion (EWI) by inverting for the Born-scattered wavefield instead of the wavefield itself. In this case, we use perturbation-related secondary sources in the modified source function. Unlike conventional RWI, the perturbations are calculated naturally as part of the calculation of the scattered wavefield in an efficient way. Because the sources in the reflection-based EWI (REWI) are located in the subsurface, we are able to update the background model along the reflection wavepath. In the background velocity inversion, we calculate the background perturbation by a deconvolution process at each frequency. After obtaining the REWI inverted velocity model, a sequential FWI or EWI is needed to obtain a high-resolution model. We determine the validity of our approach using synthetic data generated from a section of the Sigsbee2A model. To further demonstrate the effectiveness of our approach, we test it on an ocean-bottom cable data set from the North Sea. We find that our methodology leads to improved velocity models as evidenced by flatter angle gathers.

Elastic reflection traveltime inversion with pure-wave propagators

Elastic full-waveform inversion (EFWI) updates high-resolution model parameters by minimizing the misfit function between the observed and modeled data. EFWI possesses strong nonlinearity and is likely to converge to a local minimum when the inversion begins with inaccurate initial models. Elastic reflection waveform inversion (ERWI) recovers the low-wavenumber components of P- and S-wave velocities along the “rabbit ear” wavepaths to provide initial velocity models for EFWI. However, every iteration of ERWI requires six times as many forward calculations with elastic-wave equations, which can be computationally expensive. Hence, we have developed a pure-wave reflection waveform inversion (PRWI) approach, which sequentially inverts low-wavenumber components of P- and S-wave velocity models. In our PRWI, we decompose elastic-wave operators into background and perturbed pure-wave parts and derive PRWI gradients using pure-wave operators. The background and perturbed wavefields in PRWI gradients are vector wavefields with a single wave mode. PRWI can remove the high-wavenumber noise caused by S-wave stress decomposition and reduce the computational cost of ERWI by almost 70%. Under the framework of PRWI, we have further developed the pure-wave reflection traveltime inversion (PRTI) approach to alleviate the issue of cycle skipping caused by waveform mismatch. To ensure the recovery of low-wavenumber components, we mute out the contribution of wavefields with small opening angles to PRTI gradients. Numerical examples have demonstrated that our PRTI method can efficiently provide good initial velocity models for EFWI.

Regularized elastic passive equivalent source inversion with full-waveform inversion: Application to a field monitoring microseismic data set

One of the key goals of microseismic processing is accurate estimation of the source location. Using full-waveform information in passive-source data sets can potentially delineate microseismic sources. The accuracy of the compressional-wave and shear-wave velocities has a strong influence on the estimation of source locations and hence the reliability of the fracture detection. We have adopted a methodology for passive source and velocity inversion, in which the conventional source term of the elastic wave equation is represented by an equivalent source. The equivalent source term is composed of source images and source functions because it is inspired by elastic reflection waveform inversion. Thus, we update the source locations, source functions, and velocities simultaneously by using a waveform inversion scheme. In the 2D isotropic case, the source terms are defined by two source image components and three source function components. They provide an alternative representation of the source mechanism, usually defined by the moment tensor. Waveform inversion of passive events has severe nonlinearity due to the unknown source locations in space and their functions in time. We have thus used a source-independent objective function, based on convolving reference traces with modeled and observed data, to avoid cycle skipping caused by the unknown sources. We first synthetically examined our method on a modified Marmousi model. Then, by applying a nested inversion for these variables, our method also produces good estimation of the source and background velocity for real microseismic monitoring data. We use a ball-drop event to test the accuracy because the inverted source location should match the ball-seat location. For the uncontrolled events, the estimated source distribution using waveform inversion agrees with the local stress potential information. Although our method has a higher computational cost than traveltime- or migration-based methods, the estimated event locations have significantly improved accuracy.

Efficient reflection waveform inversion using a locally normalized zero‐lag correlative objective function

ABSTRACTFull‐waveform inversion is characterized by cycle‐skipping when the starting background model differs significantly from the true model and low‐frequency data are unavailable. To mitigate this problem, reflection waveform inversion is applied to provide a background velocity model for full‐waveform inversion. This technique attempts to extract background velocity updates along the reflection wavepath by matching the reflection waveforms. However, two issues arise during the implementation of reflection waveform inversion: amplitude and efficiency. The amplitude is always underestimated due to the complex subsurface parameter (i.e. the source signature, density, attenuation etc.). This makes it unreasonable to match the reflection amplitude involved in waveforms, especially in the filed data cases. In addition, generating the background velocity gradient requires the simulation of the reflection wavefield. However, simulating the reflection wavefield is time‐consuming. To address the former, we introduced a locally normalized objective function, while for the latter, we used an efficient strategy by avoiding the explicit generation of the reflection wavefield. Results show that applying the proposed method to both synthetic and field data can provide a good background velocity model for full‐waveform inversion with high efficiency.