Inverted Velocity Model Research Articles

A Real-Time Inverted Velocity Model for Fault Detection in Deep-Buried Hard Rock Tunnels Based on a Microseismic Monitoring System

Microseismic monitoring is an effective and widely used technology for dynamic fault disaster early warning and prevention in deep-buried hard rock tunnels. However, the insufficient understanding of the distribution of native faults poses a major challenge to yielding precise early warnings of disasters using an MS (Microseismic Monitoring System). Velocity field inversion is a reliable means to reflect fault information, and there is an urgent need to establish a real-time velocity field inversion method during tunnel excavation. In this paper, a method based on an MS is proposed to achieve the inversion of the velocity field in the monitoring area using microseismic event and excavation blasting data. The velocity field inversion method integrates the reflected wave ray-tracing method based on PSO (Particle Swarm Optimization) theory and FWI (Full-Waveform Inversion) theory. The accuracy of the proposed velocity inversion method was verified by various classic numerical simulation cases. In numerical simulations, the robustness of our method is evident in its ability to identify anomalous structural surfaces and velocity discontinuities ahead of the tunnel face.

A fine‐tuning workflow for automatic first‐break picking with deep learning

AbstractFirst‐break picking is an essential step in seismic data processing. For reliable results, first arrivals should be picked by an expert. This is a time‐consuming procedure and subjective to a certain degree, leading to different results for different operators. In this study, we have used a U‐Net architecture with residual blocks to perform automatic first‐break picking based on deep learning. Focusing on the effects of weight initialization on first‐break picking, we conduct this research by using the weights of a pre‐trained network that is used for object detection on the ImageNet dataset. The efficiency of the proposed method is tested on two real datasets. For both datasets, we pick manually the first breaks for less than 10 of the seismic shots. The pre‐trained network is fine‐tuned on the picked shots, and the rest of the shots are automatically picked by the neural network. It is shown that this strategy allows to reduce the size of the training set, requiring fine‐tuning with only a few picked shots per survey. Using random weights and more training epochs can lead to a lower training loss, but such a strategy leads to overfitting as the test error is higher than the one of the pre‐trained network. We also assess the possibility of using a general dataset by training a network with data from three different projects that are acquired with different equipment and at different locations. This study shows that if the general dataset is created carefully it can lead to more accurate first‐break picking; otherwise, the general dataset can decrease the accuracy. Focusing on near‐surface geophysics, we perform traveltime tomography and compare the inverted velocity models based on different first‐break picking methodologies. The results of the inversion show that the first breaks obtained by the pre‐trained network lead to a velocity model that is closer to the one obtained from the inversion of expert‐picked first breaks.

Smoothness: The key factor in well-log information-assisted PINNtomo

Seismic traveltime tomography is popularly used to provide a smooth background model for subsequent depth migration or full waveform inversion (FWI). The core of the traveltime tomography process requires an eikonal solver for seismic traveltime calculation. Most of the conventional eikonal solvers, suffer from first-order convergence errors and difficulties in dealing with irregular topography, which will lead to inaccurate seismic tomography results. To solve these issues, physics-informed neural networks (PINNs) have been developed and demonstrated remarkable success in simultaneous traveltime calculation and velocity construction, which is referred to as PINNtomo. It combines the physics constraint (eikonal equation) and data constraint (traveltime fitting) to form the loss function of the networks. Though PINNtomo can manage to recover a smooth background velocity, it will fail in the inversion for a complicated high-resolution velocity model. We take advantage of the well-log velocity as a prior information to provide an additional model constraint in the loss function to improve the performance of PINNtomo. We found that the well-log information will provide high-resolution components in the inverted velocity model. However, it will destroy the lateral structure of the true model. We propose to use a smoothed version of the well-log velocity as the prior model constraint in PINNtomo. As a result, the accuracy of the inverted background velocity will be improved, which will be beneficial to the subsequent FWI.

Double‐difference constrained reflection tomography in two‐dimensional elastic media

AbstractThe inverted velocity model obtained from the reflection tomography based on the angle domain common‐image gathers has a certain fuzziness. The inverted velocity model's stratigraphic interface is always not clear enough in areas with complex stratigraphic structure. In order to improve the accuracy and resolution of the inverted velocity model, a double‐difference constraint condition is added on the basis of minimizing the absolute travel‐time residual at the subsurface imaging points. This constraint makes the inverted velocity model local structure information more refined by minimizing the differential travel‐time residual at adjacent imaging points (i.e. closely spaced points within the same layer) and makes the variation of velocity model information within a certain range more accurate. The method in this paper is based on angle domain common‐image gathers, the tomography inversion equation is established by using the ray tracing method, and the conversion relationship between the traveltime residual and the residual curvature of the angle domain common‐image gathers. Then, by adding differential constraint and double‐differential constraint conditions and using the least squares QR decomposition method to solve the set of equations, the inverted velocity model can be obtained through multiple iterations, which provides a high‐precision velocity field for the migration and improves the accuracy of seismic imaging. Numerical experiments on both one typical model and a field data example demonstrate the effectiveness of the proposed double‐difference constrained elastic reflection tomography in generating high‐precision velocity models.

Near-Surface Structure Investigation Using Ambient Noise in the Water Environment Recorded by Fiber-Optic Distributed Acoustic Sensing

Near-surface structure investigation plays an important role in studying shallow active faults and has various engineering applications. Therefore, we developed a near-surface structure investigation method using ambient noise in a water environment. This newly developed seismic acquisition technology, fiber-optic distributed acoustic sensing (DAS), was used to acquire ambient noise from the Yangtze River. The recorded data were processed to reconstruct surface waves based on the theory of seismic interferometry. The fundamental-mode dispersion curves were extracted and inverted to obtain a shear-wave velocity model below the DAS line. We compared the inverted velocity model with the subsurface geological information from near the study area. The results from the inverted model were consistent with the prior geological information. Therefore, ambient noise in the water environment can be combined with DAS technology to effectively investigate near-surface structures.

Preconditioned transmission + reflection joint traveltime tomography with adjoint‐state method for subsurface velocity model building

AbstractAdjoint‐state‐based transmission and reflection traveltime inversion are promising approaches for reconstructing a macro velocity field in both shallow and deep depths. However, the contaminated gradient by the uneven illumination impedes the recovery of an optimal velocity model and results in slow convergence rate in inversion. To mitigate this issue, we propose a novel preconditioned transmission + reflection joint traveltime tomography method with transmission and reflection illumination compensation. The proposed illumination compensation operator is theoretically demonstrated as the diagonal elements of the approximated Hessian, which can be efficiently computed in a way similar to gradient calculation. The proposed method can construct a more accurate velocity model compared to the uncompensated counterpart. Convergence is also accelerated by the relatively uniform velocity updates from the shallow to the deep parts. Furthermore, velocity updating and reflector imaging are simultaneously iterated during the inversion. Synthetic numerical example based on the inclusion model indicates that the proposed preconditioned method can result in uniform gradient values of both transmitted and shot/receiver‐side reflected traveltime. The complex foothill model test shows the improved inversion accuracy of the proposed method with an increased convergence rate and improved reflection traveltime predictions using the inverted velocity model. Experiment on the small foothill model indicates that the reflector and velocity can be updated simultaneously, and the inversion accuracy can be significantly improved by selecting multi reflectors. Finally, the effectiveness and practicality of the proposed method are demonstrated by a field data application in East China Sea.

Shallow Ice‐Sheet Composite Structure Revealed by Seismic Imaging Near the West Antarctic Ice Sheet (WAIS) Divide Camp

AbstractSmall‐scale polar ice‐sheet composite structures can influence coarse‐grained climate models. For example, surface melting can hydro‐fracture the ice and may eventually lubricate the base. The drainage process will change the petrophysical properties of the subsurface and is predictable from high‐resolution seismic imaging. Ray‐based imaging methods, though limited by the approximations made, have mapped seismic velocities in 1D, but have yet to offer definitive information about the lateral heterogeneity. Here we use the wave‐equation‐based seismic imaging method to estimate shear‐wave velocities and to image an englacial reflector in 2D. We use 7‐day ambient‐noise data recorded by a linear array near the West Antarctic Ice Sheet (WAIS) Divide drilling site to perform the study. We obtain 2D vertical and horizontal shear‐wave velocity models and observe a lateral variation of the radial anisotropy along the acquisition line. The inverted velocity model is further used to estimate the thicknesses of firn‐air and firn layers. We also observe evident SH reflections and calculate the reflector image using robust zero‐offset imaging and a more precise reverse time migration imaging method. The imaged reflector is at about 1,700 m depth and is dipping to the southwest. We anticipate that a porosity change at that depth may cause this englacial seismic discontinuity near WAIS Divide. Our results demonstrate the feasibility of estimating the petrophysical properties of polar ice using seismic methods. We anticipate our work to be further used for understanding ice dynamics and thermodynamics, such as the stability of ice shelves, the retreat of the Antarctic ice sheet, and restoring the paleo‐sedimentary environment.

ML-misfit: A neural network formulation of the misfit function for full-waveform inversion

A robust misfit function is essential for mitigating cycle-skipping in full-waveform inversion (FWI), leading to stable updates of the velocity model in this highly nonlinear optimization process. State-of-the-art misfit functions, including matching filter or optimal transport misfits, are all hand-crafted and developed from first principles. With the growth of artificial intelligence in geoscience, we propose learning a robust misfit function for FWI, entitled ML-misfit, based on machine learning. Inspired by the recently introduced optimal transport of the matching filter objective function, we design a specific neural network architecture for the misfit function in a form that allows for global comparison of the predicted and measured data. The proposed neural network architecture also guarantees that the resulting misfit is a pseudo-metric for efficient training. In the framework of meta-learning, we train the network by running FWI to invert for randomly generated velocity models and update the parameters of the neural network by minimizing the meta-loss, which is defined as the accumulated difference between the true and inverted velocity models. The learning and improvement of such an ML-misfit are automatic, and the resulting ML-misfit is data-adaptive. We first illustrate the basic principles behind the ML-misfit for learning a convex misfit function using a travel-time shifted signal example. Furthermore, we train the neural network on 2D horizontally layered models and apply the trained neural network to the Marmousi model; the resulting ML-misfit provides robust updating of the model and mitigates the cycle-skipping issue successfully.

Autocorrelation R2 on Mars

AbstractA purpose of the Interior Exploration Using Seismic Investigations, Geodesy and Heat Transport (InSight) mission is to reveal the Martian interior structure with seismic data. In this work, ambient noise autocorrelation of the continuously recorded vertical‐component seismic signals has extracted the Rayleigh waves that propagate around Mars for one cycle, R2. The Mars orbiting surface waves are observed at a lag time of ∼6,000 s in the stacked autocorrelation series filtered between 0.005 and 0.01 Hz. Synthetic seismograms from a set of radially concentric velocity models were computed to find the best‐fitting one as the starting model for a Monte Carlo inversion. The starting model was randomly perturbed iteratively to increase the correlation coefficients and reduce the absolute time shifts between the synthetic and observed R2. An S‐wave low‐velocity layer in the inverted velocity model extends to ∼400 km depth, consistent with Marsquake observations, geophysical inversion, and high‐pressure experiments.

Simultaneous Inversion for Surface Wave Phase Velocity and Earthquake Centroid Parameters: Methodology and Application

AbstractBoth the regional earthquake surface wave and seismic ambient noise provide important constraints on the Earth's structure, and yet no study satisfactorily combined them for the best imaging of subsurface seismic structure. In this study, we address this issue by developing a new method to simultaneously determine surface wave phase velocity and earthquake centroid parameters in three steps: (a) preliminary phase velocity inversion based on seismic ambient noise, (b) preliminary earthquake relocation based on earthquake surface wave data, and (c) simultaneous inversion for phase velocity and earthquake centroid parameters with constraints of interstation phase velocity measurements based on seismic ambient noise and event‐station phase velocity measurements based on earthquake surface wave data. Application of the method in the North South Seismic Belt region in China results in high‐resolution Rayleigh wave phase velocity maps and accurate earthquake centroid parameters. The additional earthquake data notably improve resolution of the inverted phase velocity model in west Yunnan and central Tibetan blocks, the regions with sparse seismic station coverage. The inverted phase velocity model exhibits high‐velocity anomalies in cratonic regions and the Emeishan Large Igneous Province, and low‐velocity anomalies in the interior and surrounding regions of the Tibetan Plateau. Relocation places earthquakes in shallow depths with geotherm above the crustal rock's brittle‐ductile transition temperature of , revealing thermal control on thickness of the seismogenic zone. With earthquake centroid parameters constrained, earthquake data are expected to provide further constraints on the deep seismic structure that is beyond the sampling limit of seismic ambient noise.

Estimation of shallow VP and VS models in La Reforma Caldera, Baja California Sur, Mexico, using H/V ratios. Preliminary results

We evaluate the subsoil conditions at La Reforma caldera, located inside the Tres Virgenes Volcanic Complex in Baja California Sur, Mexico, using the Horizontal to Vertical Spectral Ratios (HVSR) method. The spatial distribution of the dominant frequencies has a complex pattern, which could be related to the heterogeneities of the zone. There is a good correlation between the inverted velocity models and the caldera lithology proposed in early studies. Our results show significant contrast between VP and VS, resulting in high VP/VS ratios. These high VP/VS ratios suggest a water-saturated material and define a possible water central pathway in La Reforma caldera. The VP/VS values obtained for La Reforma caldera are different from those found in the rest of the Tres Virgenes volcanic complex.

Inversion of velocity models using genetic algorithm method with sigmoidal parameterization

A seismic traveltime inversion method is proposed for building smooth velocity models using traveltime observed on irregular surface. Model parameterization in this study is described by a piecewise constant velocity field on a rectangular grid parameterized by sigmodal functions, which is beneficial for the description of irregular surface with high degree of approximation. The velocity field is defined in the rectangular grid which is used for the description of velocity distribution everywhere in the model sigmoidal interpolation. In addition, we use the simple Genetic Algorithm for the inversion procedure. Through this global scope inversion method, we provide high-resolution estimates of the model parameter and ensure that the results obtained are in accordance with the actual data. Our method is validated with synthetic examples of heterogeneous isotropic media and compared to Simulating Annealing. The inverted velocity models and approximate ray paths obtained coincide well with the trajectories simulated using the seismic ray tracing in synthetic heterogeneous isotropic media.

Deep learning unflooding for robust subsalt waveform inversion

ABSTRACTFull‐waveform inversion, a popular technique that promises high‐resolution models, has helped in improving the salt definition in inverted velocity models. The success of the inversion relies heavily on having prior knowledge of the salt, and using advanced acquisition technology with long offsets and low frequencies. Salt bodies are often constructed by recursively picking the top and bottom of the salt from seismic images corresponding to tomography models, combined with flooding techniques. The process is time consuming and highly prone to error, especially in picking the bottom of the salt. Many studies suggest performing full‐waveform inversion with long offsets and low frequencies after constructing the salt bodies to correct the misinterpreted boundaries. Here, we focus on detecting the bottom of the salt automatically by utilizing deep learning tools. We specifically generate many random one‐dimensional models, containing or free of salt bodies, and calculate the corresponding shot gathers. We then apply full‐waveform inversion starting with salt flooded versions of those models, and the results of the full‐waveform inversion become inputs to the neural network, whereas the corresponding true one‐dimensional models are the output. The network is trained in a regression manner to detect the bottom of the salt and estimate the subsalt velocity. We analyse three scenarios in creating the training datasets and test their performance on the two‐dimensional BP 2004 salt model. We show that when the network succeeds in estimating the subsalt velocity, the requirement of low frequencies and long offsets are somewhat mitigated. In general, this work allows us to merge the top‐to‐bottom approach with full‐waveform inversion, save the bottom of the salt picking time and empower full‐waveform inversion to converge in the absence of low frequencies and long offsets in the data.

Velocity calibration by incremental pseudomaster events for single-well microseismic monitoring

The velocity model plays a critical role in accurately determining microseismic event locations during hydraulic fracturing. Conventional velocity optimization methods, such as updating the velocity model using perforation shots, have the drawback of weak ray coverage during single-well monitoring. The microseismic events distributed in different areas can broaden the ray coverage and help improve the accuracy of the velocity model, whereas only a few perforation shots are available for a given stage. We have developed an incremental pseudomaster (IPM) method to reduce the velocity errors. The master event location technique is used to determine the positions of representative events in each iteration of the IPM method. These events then act as new pseudomasters to further optimize the velocity model using Bayesian inference. With progressive iterations, the number of pseudomaster events increases and their distribution range expands. The accuracy of the velocity model continuously improves, which means that the final IPM-based velocity model, generated based on the pseudomasters distributed throughout the study area, more accurately locates all microseismic events than the perforation shot alone method. One synthetic example and one field test have been conducted, and the results demonstrate that the IPM method could overcome the drawbacks of weak ray coverage and improve the accuracy of the inverted velocity model and event locations.

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.

Damped wave-equation-based first-arrival traveltime tomography using the embedded boundary method

First-arrival traveltime tomography (FATT) is used to delineate shallow velocity structures to identify static effects in oil exploration as well as to characterize the near surface for geotechnical purposes. Because FATT is generally used for land seismic data processing, it becomes necessary to consider irregular topography especially when performing wave-based tomography. However, the standard Cartesian finite-difference method cannot properly handle irregular topography. Hence, the embedded boundary method (EBM) is incorporated into the frequency-domain damped-wave equation to correctly describe irregular topography. The developed modeling algorithm is used to calculate first-arrival traveltimes and to perform FATT. The EBM-based modeling algorithm accurately describes the irregular surfaces of numerical velocity models on a regular mesh by exploiting the mirror image principle. The accuracy of the EBM-based traveltime calculation is validated by using two homogeneous velocity models with dipping and complex surfaces. The validation results demonstrate that our algorithm is unaffected by the staircase approximation. FATT is then applied to synthetic and real data to demonstrate the applicability of the developed algorithm to velocity models with complex topography. For the real data example, the inverted velocity model is used to apply static corrections. The processing results demonstrate an improvement in the continuity of seismic events, thus confirming the accuracy of the developed FATT method.

Acoustic emission source location from P-wave arrival time corrected data and virtual field optimization method

Acoustic emission (AE) event location plays an important role in structural safety assessments. However, accurately locating an AE event is usually difficult, especially for a small structure. Interestingly, a pencil-lead break (PLB) experiment shows that the P-wave arrival time of a sensor is always significantly different (~260 µs) from that of the other sensors. This time difference is much greater than the P-wave travel time in the range of the experimental sample. Therefore, it can be inferred that there is a P-wave arrival time system error (PATSE) for each sensor. The PATSE may be due to a combined result of the sensor site effect and signal transfer delay time from the sensor to the signal storage. To handle this, a Bayesian inversion framework was built to estimate PATSEs. A synthetic test demonstrated the effectiveness of the proposed Bayesian method for noisy P-wave arrival time data. Then, Bayesian inversion was applied to 15 PLB events, which confirmed the existence of PATSE in an AE experiment for the first time. The average PATSE reached 1.47 µs without considering the P-wave arrival time significantly different sensor. The average location error of 25 PLB events was 14.30 mm and 6.58 mm for PATSE unremoved and removed data, respectively. To achieve this, a high-precision virtual field optimization location method (VFOM) was used. This demonstrates the necessity of removing the PATSEs. Finally, the AE event location performance for the PATSE unremoved and removed data was compared, where the AE events were obtained from the uniaxial compression of a red sandstone sample. The results indicated that there was a higher location detection success rate for the corrected data. The AE locations based on the corrected data were in a better correlation with the rock sample failure mode than that without correction. Moreover, increase the signal sampling frequency for AE event identification, use a real-time inverted 3D velocity model and update the PATSEs in real time could be used to further improve the AE event location accuracy.

Imaging ahead of and around the bit in a desert environment: DrillCAM field trial with wireless geophones and top-drive sensor

Advanced seismic-while-drilling (SWD) technologies are being utilized to steer drilling operations and provide high-resolution subsurface images around and ahead of the bit. We present a case study of SWD imaging using a recently acquired field data set from a desert environment with a complex near surface. Data acquisition is performed with wireless geophones and top-drive sensors using continuous real-time recording. The drill-bit noise data are analyzed while continuously recording in real time by using a specialized workflow that combines elements of SWD and conventional vertical seismic profiling processing with controlled seismic sources. First, the workflow enhances the direct wavefield to retrieve accurate first-break picks for traveltime tomographic inversion along east–west- and north–south-striking walkaway lines. Then, it extracts and enhances upgoing reflection events, illuminating parts of the subsurface around and ahead of the bit. During the final step, these upgoing reflections are imaged using the inverted velocity model to reconstruct a migrated subsurface image around the well. As is the case for land surface seismic in the presence of a complex near surface, we observe a significant variation of data quality for the orthogonal receiver lines. As a result, each line provides a robust image of a different part of the subsurface. The east–west-striking line's migrated image delineates a major shallow reflector that serves as a marker for predicting the drilling depth of a deeper horizon. Likewise, migrating upgoing reflections from the north–south line accurately maps a deeper target horizon ahead of the bit. The obtained SWD images assist in setting the casing points accurately and provide a more precise ahead-of-the-bit depth for different horizons with significantly less uncertainty than surface seismic.

The Community Velocity Model V.1.0 of Southwest China, Constructed from Joint Body- and Surface-Wave Travel-Time Tomography

Abstract Southwest China, located at the southeastern margin of the Tibetan plateau, plays an important role for the plateau growth and its material extrusion. It has complicated tectonic environment and strong seismic activities including the 2008 Wenchuan great earthquake. Numerous geophysical studies have been conducted in southwest China. However, a community velocity model (CVM) in this region is still not available, which makes it difficult to have a consistent catalog of earthquake locations and focal mechanisms and a consistent velocity model for simulating strong ground motions and evaluating earthquake hazards. In this study, we aim at building a high-resolution CVM (both VP and VS) of the crust and uppermost mantle in southwest China along with earthquake locations by joint inversion of body- and surface-wave travel-time data. In total, we have assembled 386,958 P- and 372,662 S-wave first arrival times and nearly 8100 Rayleigh-wave dispersion curves in the period band of 5–50 s. A multigrid strategy is adopted in the joint inversion. A coarser horizontal grid interval of 0.5° is first used and then a finer grid interval of 0.25° is used with initial models interpolated from the coarser-grid inverted velocity models. The spatial resolution of both VP and VS models can reach up to 0.5° horizontally and 10 km vertically according to the checkerboard tests. The comparisons of our inverted VP and VS models with those from other studies show general consistency in large-scale features. The inverted models are further validated by P-wave arrival times from active sources and Rayleigh-wave data. In general, our velocity models show two low-velocity zones in the middle-lower crust and a prominent high-velocity region in between them. Our new models have been served as the first version of the CVM in southwest China (SWChinaCVM-1.0) for future studies.

Full-waveform inversion strategies using common-receiver gathers for ocean-bottom cable data

Full-waveform inversion (FWI), which is among the most powerful seismic data processing techniques for imaging subsurface geological structures, has a huge computational cost in proportion to the number of sources. To increase the speed of FWI, we explored the use of common-receiver gathers (CRGs) as an alternative to common-shot gathers (CSGs) as observed data. This approach has the potential to reduce the computational cost of FWI significantly, particularly for ocean-bottom cable (OBC) acquisition. As we match modelled and observed CSGs in CSG-based FWI, we match observed CRGs with modelled CSGs of switched source–receiver geometry in CRG-based FWI. According to the reciprocity principle, CRG FWI based on the steepest descent or Gauss–Newton method yields the same inverted velocity models as CSG FWI for an identical and known source signature applied over whole source positions. However, when the source wavelet is unknown, and changes from one source position to another, each trace of a CRG contains a different source signature, making it difficult to apply conventional source estimation or source-independent methods to CRG FWI. Therefore, in this study, we proposed inversion strategies for CRG FWI in both the time and frequency domains to deal with errors arising from different source wavelets between CRG traces. Then, we used a synthetic example for the Marmousi-II model and a real data example from the North Sea to demonstrate that our strategies for CRG FWI provide very similar inverted velocity models to those obtained from CSG FWI, at a lower computational cost.