Full Waveform Inversion Method Research Articles

Study on non-destructive visualization identification of concrete internal cracks based on SH array ultrasound

Ultrasonic nondestructive testing (NDT) technology was one of the most frequently used and fastest-developing NDT techniques in detection field. This method had high detection sensitivity, more accurate defect localization, and was harmless to the human body. With the development of ultrasonic testing technology, modern ultrasonic imaging technology generally had automatic data acquisition and processing functions, which allowed for intuitive and clear recognition of internal defects by the human eyes. The overall purpose of this study was to visualize the cracks in concrete by synthetic aperture focusing technique (SAFT) and full-waveform inversion (FWI) algorithms on the basis of ultrasonic nondestructive testing technology. At present, there have been studies on the use of ultrasonic instruments to detect the internal defects of concrete. However, the accuracy and authenticity of this method have not been compared in previous studies. Therefore, in this experiment, four concrete specimens with different buried depths, angles, shapes, and thicknesses of cracks were designed. Based on SH ultrasonic wave NDT technology, two types of operations were performed on the collected ultrasonic wave data: one was the application of SAFT method, and the other was the first application of FWI method for detecting internal cracks in concrete. The study found that both algorithms were most accurate in determining the burial depth of cracks, with error results not exceeding 10 %. They also showed good recognition effects for the angle, shape, and thickness of the buried cracks. This proved that both identification methods had the capability to recognize internal cracks. The Introview software bundled with the ultrasonic instrument could identify cracks using SAFT directly and quickly. When FWI was used with MATLAB computation, the results were more precise and intuitive. The overall purpose of this study was to detect cracks in concrete by SAFT and FWI algorithms on the basis of ultrasonic nondestructive testing technology. Combining the two crack identification techniques could be of great significance for ensuring the long-term safety and stability of concrete structures, providing strong support for structural maintenance and reinforcement.

A global approach to detecting and characterizing water leakage in a concrete bridge deck: Parametric study to validate an adapted full-waveform inversion method

The objective of this study is to address issues related to defects in waterproofing membranes through the use of Ground Penetration Radar to detect water leakage into the concrete layer of bridge decks. Given that processing radar signals based solely on temporal data introduces significant estimation errors, an advanced method optimized from Full-Waveform Inversion (FWI) is employed. This method accounts for several unknown factors, including boundary conditions, antenna positioning inaccuracies, and approximations inherent in 2D modeling during the inversion process. The method is adaptable and capable of reconstructing both the dielectric and geometric parameters of a multilayered structure with any number of layers and unknown parameters using just a few A-scans (up to 10, depending on the number of parameters and layers). In contrast, other methods typically require several hundred A-scans. This efficiency is achieved due to the two-dimensional nature of the layer system. Additionally, the simplicity of the structure facilitates a much faster and more straightforward inversion algorithm, hence making these features especially advantageous for practical applications. The optimized Full-Waveform Inversion approach allows for an accurate determination of unknown parameters within a multilayered medium. The high accuracy of this method is validated through a direct comparison with experiments, wherein the exact parameters are known. Such an approach enables the attainment of a low relative error using the currently available measurement device.

Truncated Newton full waveform inversion method for the human brain imaging

Abstract It has been shown that full-waveform inversion (FWI) method can be a competitive alternative for medical imaging problems. It offers high-resolution results while delivering the advantages of being fast, safe, portable, and affordable, compared to magnetic resonance imaging (MRI) and x-ray computed tomography. However, to the best of our knowledge, FWI applications in medical imaging only use the first-order derivative information. In this case, the high parameter contrasts between different tissues of human body and multi-scatterings problems may lead FWI to local minima. Thus, we present a competitive truncated Newton method for high-resolution imaging of the human brain. This truncated Newton method, based on the efficient linear solver MINRES-QLP, can make full use of multiple scattering wavefield information. Compared with the truncated Newton method based on conjugate gradient, the MINRES-QLP iterative method presents various advantages when solving linear systems, such as the capacity to handle both non-singular and singular systems, less computational cost, and efficiency even for ill-conditioned systems. Numerical experiments for imaging the brain with and without the skull are conducted. Numerical results indicate that, compared with the truncated Newton method based on conjugate gradient, the truncated Newton method based on MINRES-QLP exhibits computational efficiency while maintaining the same level of accuracy.

Enabling uncertainty quantification in a standard full-waveform inversion method using normalizing flows

To maximize the utility of seismic imaging and inversion results, we need to compute not only a final image but also quantify the uncertainty in the image. Although the most thorough approach to quantify the uncertainty is to use a method such as Markov chain Monte Carlo, which systematically samples the entire posterior distribution, this is often inefficient, and not all applications require a full representation of the posterior. We use normalizing flows (NFs), a machine learning technique to perform uncertainty quantification (UQ) in full-waveform inversion (FWI), specifically for time-lapse data. As with any machine learning algorithm, the NF learns only the mapping from the part of the prior spanned by the training data to the distribution of final models spanned by the training data. Here, we make use of this property to perform UQ efficiently by learning a mapping from the prior to the distribution that characterizes the model perturbations within a specific range. Our approach involves using a range of starting models paired with final models from a standard FWI as training data. Although this does not capture the full posterior of the FWI problem, it enables us to quantify the uncertainties associated with updating from an initial to a final model. Because our target is to perform UQ for time-lapse imaging, we use a local wave-equation solver that allows us to solve the wave equation in a small subset of our entire model, thereby keeping computational costs low. Numerical examples demonstrate that incorporating the training step for NF provides a distribution of model perturbations, which is dependent on a designated prior, to quantify the uncertainty of FWI results.

The importance of data preconditioning strategies for envelope full-waveform inversion methods: Demonstration on marine seismic data

Envelope full-waveform inversion (EI) of seismic data has been proposed to overcome the cycle-skipping issue and recover long-wavelength velocity components for over a decade. However, we are aware of few published successful applications of EI on real data examples (except for some correlation- or phase-based EI methods). We implement EI methods (EI with [Formula: see text], EI with p = 1, and improved EI) on 2D marine seismic data and find that the amplitude mismatching between the modeled and observed data is a critical factor that prevents the successful application of EI methods to real data. To match the amplitude better, we include a data weighting preconditioner in the objective function of the EI methods. The preconditioner term acts as a weighting factor to compensate for the amplitude mismatch between the observed and modeled data. We develop a method for calculating the preconditioner term using the amplitude of the head waves as a reference. Furthermore, we derive the adjoint source and gradient of the EI using the data preconditioning method. We illustrate the successful application of EI methods with the data preconditioning method using the 2D marine seismic data example. In comparison to the EI methods without the data preconditioning method, those using data preconditioning yield much more geophysically reasonable velocity models and Kirchhoff image sections and common-image gathers.

Full waveform inversion of ocean bottom seismometer data from the oceanic Pacific Plate of the Japan trench

SUMMARY The geometrical and seismic structure of the Pacific oceanic Plate of the Japan Trench is essential for the understanding of earthquake activity in the area. Ocean Bottom Seismometer (OBS) data can be used, via ray-based tomography, to obtain estimates of properties such as crust thickness and structure, hydration and depth to the Moho boundary. The spatial resolution of these properties can be substantially improved by using the full waveform inversion (FWI) method. Most OBS data in this area are acquired with a sparse receiver spacing of 5–6 km, whereas FWI is assumed to work best with denser (1–2 km) receiver spacing. We show that FWI can be adapted to sparsely sampled data with better resolution than traveltime tomography. Using a 500 km long OBS longitudinal profile from the Japan Trench we obtain a detailed velocity structure of the crust, a better definition of the Moho boundary, a well-defined low-velocity layer in the lower crust and a clear spatial definition of areas with velocity inversions.

Elastic full-waveform inversion using tools of neural networks

In this paper, we investigate the full-waveform inversion (FWI) for elastic wave equation as training a neural network. The forward modeling of the elastic wave equation in the time domain by the staggered-grid difference schemes can be reformulated as a process of a recurrent neural network (RNN). As a result, the FWI problem is equivalent to neural network training, and the parameter of RNN coincides with the model parameter of inversion. Furthermore, a variety of stochastic optimizers including Adgrad, RMSprop, Adam, Nadam and Admax in neural networks can be applied in the training process. The gradient of the objective function with the model parameters is computed by the technique of automatic differentiation instead of the adjoint-state method in the traditional FWI. A new objective function of FWI is also proposed. Compared to the traditional FWI methods, the developed FWI using tools of neural networks has a relatively good robustness. Numerical computations and comparisons with Marmousi model for two and three parameters simultaneous inversion are completed. The results show that the algorithms except Adgrad can yield good inversion results. The FWI framework developed in this paper has potential applications for other complex partial equations.

Crustal and uppermost mantle structures of the North American Midcontinent Rift revealed by joint full-waveform inversion of ambient-noise data and teleseismic P waves

The Midcontinent Rift (MCR), hosting several world-class ore deposits, is the fossil remnant of a massive Mesoproterozoic rifting event (1.1 Ga) that did not lead to the formation of an ocean basin. To better understand the lithospheric processes associated with the rifting stage and its subsequent failure, we developed a novel full-waveform joint inversion method using ambient noise data and teleseismic P waves for this seismically inactive region. We apply this approach to three years (2011-2013) of seismic recordings from the Superior Province Rifting EarthScope Experiment (SPREE) (~12 km average station spacing) and the USArray Transportable Array (~70 km average station spacing), and obtain a new 3D high-resolution Vs model down to 100 km depth, as well as Vp and density models down to 60 km depth. The model shows major velocity anomalies in agreement with previous seismic studies for the western arm of the MCR. In particular, we observe high density (2.8-3.0 g/cm3), Vp (6.3-6.5 km/s), and Vs (3.6-3.7 km/s) structures in the shallow upper crust within the rift, likely associated with volcanic rocks. Similar to a previously identified underplated layer, we also observe extensive normal-to-high Vs (3.8-4.2 km/s) along the whole rift axis and Vp (6.8-7.5 km/s) beneath the northern segment of the rift within the lower crust. However, the Vs and Vp values are lower than average for typical underplated materials. We suggest that this underplated layer may represent a combination of different intrusive rock types (e.g., gabbro, anorthosite) developed during magma differentiation processes, or contamination of the mafic magma by surrounding crustal material, or intrusions of sills.

Full Dispersion‐Spectrum Inversion of Surface Waves

AbstractNowadays, the most successful applications of full‐waveform inversion (FWI) involve marine seismic data under acoustic approximations. Elastic FWI of land seismic data is still challenging in theory and practice. Here, we propose a full dispersion spectrum inversion method and apply it to seismic data acquired in West Antarctica. Inspired by the conventional surface wave dispersion curve inversion method, we propose to invert the surface wave dispersion spectrum instead of the complicated waveforms. We compare the frequency‐velocity, frequency‐slowness, and frequency‐wavenumber spectra in terms of their ability to resolve dispersion modes and the feasibility of their adjoint updates and conclude that the frequency‐slowness spectrum is the best for our inversion objectives. We test four objective functions, subtraction, zero‐lag crosscorrelation, optimal transport, and the local‐crosscorrelation to quantify the spectrum mismatch and provide the corresponding adjoint source. We then theoretically analyze the convexity of the proposed objective functions and examine their convergence behavior using numerical examples. We also compare the proposed method with the classic FWI method and the traditional surface wave dispersion curve inversion method and discuss the strengths and weaknesses of each method. This technique is employed to evaluate the shallow velocity structures beneath a seismic array stationed in West Antarctica. Our proposed inversion scheme is also useful for more general applications such as imaging the shallow subsurface of the critical zones, like geothermal reservoirs, and CO2 storage sites.

Truncated Gauss-Newton full-waveform inversion of pure quasi-P waves in vertical transverse isotropic media

Full-waveform inversion (FWI) uses the full information of seismic data to obtain a quantitative estimation of subsurface physical parameters. Anisotropic FWI has the potential to recover high-resolution velocity and anisotropy parameter models, which are critical for imaging the long-offset and wide-azimuth data. We develop an acoustic anisotropic FWI method based on a simplified pure quasi P-wave (qP-wave) equation, which can be solved efficiently and is beneficial for the subsequent inversion. Using the inverse Hessian operator to precondition the functional gradients helps to reduce the parameter tradeoff in the multi-parameter inversion. To balance the accuracy and efficiency, we extend the truncated Gauss-Newton (TGN) method into FWI of pure qP-waves in vertical transverse isotropic (VTI) media. The inversion is performed in a nested way: a linear inner loop and a nonlinear outer loop. We derive the formulation of Hessian-vector products for pure qP-waves in VTI media based on the Lagrange multiplier method and compute the model update by solving a Gauss-Newton linear system via a matrix-free conjugate gradient method. A suitable preconditioner and the Eisenstat and Walker stopping criterion for the inner iterations are used to accelerate the convergence and avoid prohibitive computational cost. We test the proposed FWI method on several synthetic data sets. Inversion results reveal that the pure acoustic VTI FWI exhibits greater accuracy than the conventional pseudoacoustic VTI FWI. Additionally, the TGN method proves effective in mitigating the parameter crosstalk and increasing the accuracy of anisotropy parameters.

Scale-Aware Edge-Preserving Full Waveform Inversion with Diffusion Filter for Crosshole Sensor Arrays.

Full waveform inversion (FWI) is recognized as a leading data-fitting methodology, leveraging the detailed information contained in physical waveform data to construct accurate, high-resolution velocity models essential for crosshole surveys. Despite its effectiveness, FWI is often challenged by its sensitivity to data quality and inherent nonlinearity, which can lead to instability and the inadvertent incorporation of noise and extraneous data into inversion models. To address these challenges, we introduce the scale-aware edge-preserving FWI (SAEP-FWI) technique, which integrates a cutting-edge nonlinear anisotropic hybrid diffusion (NAHD) filter within the gradient computation process. This innovative filter effectively reduces noise while simultaneously enhancing critical small-scale structures and edges, significantly improving the fidelity and convergence of the FWI inversion results. The application of SAEP-FWI across a variety of experimental and authentic crosshole datasets clearly demonstrates its effectiveness in suppressing noise and preserving key scale-aware and edge-delineating features, ultimately leading to clear inversion outcomes. Comparative analyses with other FWI methods highlight the performance of our technique, showcasing its ability to produce images of notably higher quality. This improvement offers a robust solution that enhances the accuracy of subsurface imaging.

Adaptive structure-based full-waveform inversion

In simultaneous-shot full-waveform inversion (FWI), the re-started limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm can be used to suppress crosstalk, but crosstalk cannot be completely eliminated from the inversion results. To further solve the crosstalk problem caused by the interference among individual shots in simultaneous-shot FWI, adaptive structure-based smoothing is applied to the FWI with the restarted L-BFGS algorithm. Structure-based smoothing can mitigate the crosstalk by highlighting structure boundaries. To perform structure-based smoothing, an implicit anisotropic diffusion equation is solved. We carry out a multiscale inversion strategy. Because the FWI results in the low-frequency band contain less structural information and more crosstalk, structure-based smoothing is applied to the frequency band at frequencies higher than the peak frequency to prevent negative effects from the model structure in the low-frequency band. The estimated structural information is iteratively updated during the inversion process. Furthermore, structure-based smoothing is only added to the iterations with invariant encoding to reduce oversmoothing. The invariant encoding means that the shot encoding remains unchanged between iterations. Numerical experiments with an overthrust model indicate that the proposed adaptive structure-based FWI method can effectively suppress artifacts and provide a high-resolution inversion result, even when the encoded data are contaminated with strong noise. Another advantage of the adaptive structure-based FWI method is that no seismic migration needs to be performed, which makes it more efficient for real data.

The method for precise seismic detection of geological structures in underground coal mines and application

The occurrence of major accidents such as water inrush in coal mines and coal-gas outbursts is closely correlated with the unclear exploration of underground geological structures. Seismic exploration in underground coal mines is not limited by ground conditions and close to the detected target, so it has advantages with respect to the detection of underground geological structures. However, the geological structures leading to accidents are usually characterized by small size and diverse combinations, making it difficult to detect. In coal mine working faces, the use of transmission observation systems, combined with full waveform inversion methods, represents a new attempt at finely detecting geological structures. Therefore, a three-dimensional numerical model of an abnormal combination of faults and collapse columns was established, a physical simulation model of a multi-collapse column combination was built, and transmission and detection experiments were carried out. The results show that the morphology and locations of 1 fault and 4 collapse columns obtained by the FWI algorithm are consistent with the data from the actual numerical model. According to physical simulation results, the background velocity of the model after inversions and the velocity of 5 anomalies are consistent with the actual values. Field experiments were conducted in the actual underground coal mines. After verification, the average error ratios of the long axis, short axis and intersection angle of the 4 collapse columns were 0.19, 0.15 and 0.02. The detection findings and comparison results confirm the feasibility of precise detection of geological structures by transmissive seismic waves based on the FWI method.

An extended Gauss-Newton method for full-waveform inversion

Full-waveform inversion (FWI) is a large-scale nonlinear ill-posed problem for which computationally expensive Newton-type methods can become trapped in undesirable local minima, particularly when the initial model lacks a low-wavenumber component and the recorded data lack low-frequency content. A modification to the Gauss-Newton (GN) method is developed to address these issues. The standard GN system for multisource multireceiver FWI is reformulated into an equivalent matrix equation form, with the solution becoming a diagonal matrix rather than a vector as in the standard system. The search direction is transformed from a vector to a matrix by relaxing the diagonality constraint, effectively adding a degree of freedom to the subsurface offset axis. The relaxed system can be explicitly solved with only the inversion of two small matrices that deblur the data residual matrix along the source and receiver dimensions, which simplifies the inversion of the Hessian matrix. When used to solve the extended-source FWI objective function, the extended GN (EGN) method integrates the benefits of model and source extension. The EGN method effectively combines the computational effectiveness of the reduced FWI method with the robustness characteristics of extended formulations and offers a promising solution for addressing the challenges of FWI. It bridges the gap between these extended formulations and the reduced FWI method, enhancing inversion robustness while maintaining computational efficiency. The robustness and stability of the EGN algorithm for waveform inversion are demonstrated numerically.

Wasserstein distance-based full waveform inversion method for density reconstruction

Reliable density information is an essential factor in lithologic interpretation and reservoir evaluation. However, density reconstruction is hampered by a lack of long-wavelength information and the crosstalk between different parameters. The powerful nonlinearity in density inversion constrains the multi-parameter full waveform inversion application. This paper introduces the Wasserstein distance into the full waveform inversion for velocity and density based on the optimal transport theory. We construct an objective function with better convexity to avoid the cycle-skipping caused by the poor initial model. Furthermore, due to the sensitivity of the quadratic Wasserstein distance to low-frequency, we add the low-wavenumber component absent in the conventional density inversion. We acquire a long-wavelength density background using optimal transport inversion and then apply it as an initial model for least-squares inversion. Numerical examples show that our optimal transport inversion effectively builds a reasonable density background model for FWI. Density inversion can be improved by incorporating optimal transport and least-squares theory, leading to a reliable quantitative description for petroleum exploration and development.

Robust joint adaptive multiparameter waveform inversion with attenuation compensation in viscoacoustic media

Full-waveform inversion (FWI) has been proven as an effective method to estimate subsurface parameters by iteratively reducing the data residual between the predictions and the observations. Nevertheless, FWI is greatly dependent on the initial model, and a poor initial model will lead to an incorrect solution. Furthermore, owing to the anelasticity of the earth, seismic waves will attenuate during propagation, which results in an attenuated gradient and makes the convergence rate of FWI even worse in viscoacoustic medium. Commonly, multiparameter (e.g. velocity and Q) waveform inversion can be used to mitigate these problems. Benefiting from the theory of Q-compensated wavefield propagation, we develop a Q-compensated joint multiparameter waveform inversion method to weaken the nonlinearity of the FWI objective function, which enables it to cope with challenges related with attenuation-induced gradient energy loss and cycle skipping simultaneously. We refer to our Q-compensated joint multiparameter FWI scheme as QJMFWI. The main contributions of QJMFWI are as follows: (1) given the difficulty associated with the estimation of velocity and Q simultaneously in viscoacoustic media, QJMFWI provides a straightforward waveform inversion method for velocity and Q model construction, by which we can obtain velocity and Q information with improved accuracy and resolution; and (2) compared with conventional FWI methods, QJMFWI relaxes the requirement for a good initial velocity and Q model, which can avoid trapping into local minima. Numerical and field data examples demonstrate that QJMFWI is an effective method to invert for accurate subsurface parameters in viscoacoustic media.

Full-waveform inversion of pure quasi-P waves in titled transversely isotropic media based on different parameterizations

Full-waveform inversion (FWI) builds subsurface parameter models by minimizing the residuals between the modeled and observed data. Accounting for the effects of anisotropy is critical for high-resolution imaging of complex structures. We develop an acoustic anisotropic FWI method based on a pure quasi-P-wave (qP-wave) equation. The equation coefficients and their derivatives with respect to Thomsen’s anisotropy parameters ([Formula: see text] and [Formula: see text]) are estimated by least-squares optimization. We derive and analyze the radiation patterns for six parameter classes: the velocity along the symmetry axis [Formula: see text], [Formula: see text], and [Formula: see text]; the normal moveout velocity [Formula: see text], the anisotropy parameter [Formula: see text], and [Formula: see text]; the horizontal velocity [Formula: see text], [Formula: see text], and [Formula: see text]; [Formula: see text], [Formula: see text], and [Formula: see text]; [Formula: see text], [Formula: see text], and [Formula: see text]; and [Formula: see text], [Formula: see text], and [Formula: see text]. The parameterization [Formula: see text] has significant trade-off between [Formula: see text] and [Formula: see text] at the intermediate and wide scattering angles. The anisotropy parameters [Formula: see text] and [Formula: see text] are resolvable at the short scattering angles for the parameterizations [Formula: see text] and [Formula: see text], respectively. The parameter crosstalk for the parameterizations [Formula: see text] and [Formula: see text] is more serious than that for other types of parameterizations. We perform FWI of pure qP-waves in vertical transversely isotropic (VTI) and titled transversely isotropic (TTI) media. Inversion results on the overthrust VTI model and the modified BP TTI model show that the velocity, anisotropy parameters, and tilt angle can be individually reconstructed when other parameters are sufficiently accurate. The multiparameter FWI cannot obtain reliable tilt angles for each type of parameterization. The inversion with the parameterization [Formula: see text] produces [Formula: see text], [Formula: see text], and [Formula: see text] models with modest accuracy, whereas the parameterization [Formula: see text] helps to improve the accuracy of [Formula: see text] and [Formula: see text] models.

A Source-Independent TV-Regularized Full Waveform Inversion Method for Peripheral Imaging Around a Borehole

A Source-Independent TV-Regularized Full Waveform Inversion Method for Peripheral Imaging Around a Borehole

High-Precision Corrosion Detection via SH1 Guided Wave Based on Full Waveform Inversion.

Corrosion detection for industrial settings is crucial for safe and efficient operations. Due to its high imaging resolution, the guided-wave full-waveform inversion tomography technique has significant potential for corrosion detection of plate metals. Limited by the long wavelengths of A0 and S0 mode waves, this method exhibits inadequate detection resolution for the earlier shallow and small corrosion defects. Based on the relatively short wavelength characteristics of the SH1 mode wave, we propose a high-precision corrosion detection method via SH1 guided wave using the full waveform inversion algorithms. By conducting finite element simulations of ultrasonic-guided waves on aluminum plates with varying corrosion defects, a comparison was made to assess the detection precision across A0, S0, and SH1 modes. The comparison results showed that, whether for regular or irregular defects, the SH1 mode wave always exhibited higher imaging accuracy than the A0 and S0 mode waves for shallow and small-sized defects. The corresponding experiments were conducted on an aluminum plate with simple or complex defects. The results of the experiments reconfirmed that the full waveform inversion method using SH1 guided wave can effectively reconstruct the shape and size of small and shallow corrosion defects within aluminum plates.

Robust Elastic Full-Waveform Inversion Based on Normalized Cross-Correlation Source Wavelet Inversion

The elastic full-waveform inversion (EFWI) method efficiently utilizes the amplitude, phase, and travel time information present in multi-component seismic recordings to create detailed parameter models of subsurface structures. Within full-waveform inversion (FWI), accurate source wavelet estimation significantly impacts both the convergence and final result quality. The source wavelet, serving as the initial condition for the wave equation’s forward modeling algorithm, directly influences the matching degree between observed and synthetic data. This study introduces a novel method for estimating the source wavelet utilizing cross-correlation norm elastic waveform inversion (CNEWI) and outlines the EFWI algorithm flow based on this CNEWI source wavelet inversion. The CNEWI method estimates the source wavelet by employing normalized cross-correlation processing on near-offset direct waves, thereby reducing the susceptibility to strong amplitude interference such as bad traces and surface wave residuals. The proposed CNEWI method exhibits a superior computational efficiency compared to conventional L2-norm waveform inversion for source wavelet estimation. Numerical experiments, including in ideal scenarios, with seismic data with bad traces, and with multi-component data, validate the advantages of the proposed method in both source wavelet estimation and EFWI compared to the traditional inversion method.