Multi-parameter Full Waveform Inversion Research Articles

Asymmetric magma plumbing system beneath Axial Seamount based on full waveform inversion of seismic data

The architecture of magma plumbing systems plays a fundamental role in volcano eruption and evolution. However, the precise configuration of crustal magma reservoirs and conduits responsible for supplying eruptions are difficult to explore across most active volcanic systems. Consequently, our understanding of their correlation with eruption dynamics is limited. Axial Seamount is an active submarine volcano located along the Juan de Fuca Ridge, with known eruptions in 1998, 2011, and 2015. Here we present high-resolution images of P-wave velocity, attenuation, and estimates of temperature and partial melt beneath the summit of Axial Seamount, derived from multi-parameter full waveform inversion of a 2D multi-channel seismic line. Multiple magma reservoirs, including a newly discovered western magma reservoir, are identified in the upper crust, with the maximum melt fraction of ~15–32% in the upper main magma reservoir (MMR) and lower fractions of 10% to 26% in other satellite reservoirs. In addition, a feeding conduit below the MMR with a melt fraction of ~4–11% and a low-velocity throat beneath the eastern caldera wall connecting the MMR roof with eruptive fissures are imaged. These findings delineate an asymmetric shallow plumbing system beneath Axial Seamount, providing insights into the magma pathways that fed recent eruptions.

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.

Subsoil density field reconstruction through 3-D FWI: a systematic comparison between vertical- and horizontal-force seismic sources

SUMMARY Bulk-density (ρ) of soil is an important indicator of soil compaction and type. A knowledge of the spatial variability of in situ soil density is important in geotechnical engineering, hydrology and agriculture. Surface geophysical methods have so far shown limited success in providing an accurate and high-resolution image of 3-D soil-density distribution. In this pursuit, 3-D seismic full-waveform inversion (FWI) is promising, provided the robustness and accuracy of density inversion via this approach can be established in the near-surface scale. However, simultaneous reconstruction of ρ and seismic wave velocities through multiparameter FWI remains a challenging task. Near-surface seismic data are commonly dominated by dispersive surface waves whose velocities are controlled by the value and distribution of shear-wave velocity (VS). One major difficulty in estimating reliably ρ from near-surface seismic data is due to the relatively low sensitivity of the seismic wavefield to ρ compared to seismic velocities. Additionally, the accuracy of the estimated ρ decreases due to error in VS—an issue known as parameter coupling. Parameter coupling makes it difficult to estimate accurately ρ within the framework of conventional gradient-based FWI. More sophisticated optimization approaches (e.g. truncated Newton) can reduce the effect of parameter coupling, but these approaches are commonly not affordable in near-surface applications due to heavy computational burden. In this research, we have investigated how choosing correctly the force direction of the seismic source can contribute to a higher accuracy of ρ estimates through 3-D FWI. Using scattered wavefields, the Hessian, and inversion tests, an in-depth and systematic investigation of data sets corresponding to different force directions has been carried out. A comparison of the scattered wavefields due to a point-localized ρ perturbation for different force directions shows the robustness of the horizontal-force data set to noise compared to the vertical-force data set. Furthermore, for a point-scatterer model, an analysis of the gradients of the misfit function using the Hessian shows that utilizing a horizontal-force source enables one to reconstruct the high-resolution gradient with relatively small parameter coupling. Finally, inversion tests for two different subsoil models demonstrate that 3-D FWI on a horizontal-force-source seismic data set is capable of providing a more accurate 3-D ρ distribution in soil compared to a vertical-force-source data set. Our results show that the use of a horizontal-force source might allow avoiding computationally demanding, costly optimization approaches in 3-D FWI.

Utility tunnel detection by 2D elastic PSV/Rayleigh-wave multi-parameter full waveform inversion

Accurate characterization of the low-velocity anomalies such as utility tunnels in the near-surface by effective geophysical imaging methods has been a valuable but challenging task for urban hazard assessment, underground space development and infrastructure construction. As a current research hotspot, the full waveform inversion (FWI) has been proven to be a promising technique for high-precision imaging of substructures, and has been applied in related practical engineering fields. However, most previous studies have focused on single-parameter (S-wave velocity) or double-parameter (S-wave and P-wave velocities) inversion. So, a complete PSV/Rayleigh-wave multi-parameter (S-wave and P-wave velocities and density) FWI method is developed in this paper to achieve accurate detection of underground utility tunnels. In this approach, the multi-parameter of the model are updated simultaneously during the inversion process to alleviate the negative influence on the S-wave velocity inversion accuracy due to the far deviation of the other two parameters from their true values. We tested the performance of the approach with a synthetic test and a real experiment. In the synthetic test, this method well characterized the position, shape and size of the embedded tunnel in the model, proving its effectiveness. Subsequently, the approach was applied to a field case investigated in Changsha city, China, and the inversion images revealed a tunnel with a burial depth of 4.5 m, height and width of 2 m and 4 m, respectively, which was identified as the detection target. The available borehole data verified the conclusion. The above results demonstrate the validity and time-effectiveness of the approach. It is expected to provide a reference for practical engineering applications at the same scale.

Multi-Constrained Seismic Multi-Parameter Full Waveform Inversion Based on Projected Quasi-Newton Algorithm

The multi-parameter full waveform inversion (FWI) that integrates velocity and density can make full use of the kinematic and dynamic information of the measured data to reconstruct the underground model. However, it faces problems of crosstalk between multiple parameters and strong nonlinearity. This research proposes a multi-constrained, multi-parameter FWI framework based on the projected quasi-Newton algorithm. This framework can introduce multiple types of prior geological information, which can effectively improve the problem of multi-parameter inversion. Additionally, the quasi-Newton method can eliminate the crosstalk phenomenon to further improve the inversion convergence speed. Taking the 1994BP model as an example, the results show that the projected quasi-Newton method has a faster convergence speed than the spectral projected gradient method, and reduces the crosstalk between parameters; multiple constraint sets are uniquely projected onto the intersection to ensure that the estimated values of model parameters meet multiple constraints. We also experiment with the overthrust model, which shows that the framework we proposed can improve the inversion accuracy and has good adaptability. The proposed multi-parameter inversion framework can be compatible with more prior information to obtain an inversion model that conforms to geological understanding and shows great potential in seismic exploration.

Elastic vertically transversely isotropic full-waveform inversion: From synthetic to field data

Representing the earth as an elastic medium leads to a more accurate approximation of the seismic response than can be obtained by assuming an acoustic medium. However, this representation requires a larger number of unknown parameters to be introduced and a more complex seismogram to be considered. Consequently, it is important to carefully deal with two challenging issues, the impact of strong surface waves and the crosstalk among parameters, for land seismic multiparameter full-waveform inversion (FWI). Under the elastic vertically transversely isotropic assumption, a robust FWI approach is developed by combining the optimal transport (OT) misfit function, the Gaussian time window, and the suitable parameterization [Formula: see text]. Without specific preprocessing, surface waves usually dominate the inversion process, leaving the body waves not fully exploited. Correspondingly, the subsurface model is only updated at a shallow depth. The OT misfit function can balance the contributions of surface and body waves to model updates in an automatic manner. In addition, the Gaussian time window further improves the weights of the body waves during inversion. We efficiently exploit the entire seismogram with these two approaches. In this configuration, the performances of several parameterizations chosen from radiation pattern analysis are evaluated. Our inversion strategy is applied to the Middle East model and a field data application. In both cases, it outperforms other inversion strategies. The entire land seismic data are efficiently exploited and multiparameters are simultaneously reconstructed.

Bayesian inverse scattering theory for multiparameter full-waveform inversion in transversely isotropic media

Full-waveform inversion (FWI) is an effective method that uses kinematic and dynamic information to provide an accurate image of the subsurface target. By applying the Bayesian approaches to FWI workflow, the traditional deterministic solution is replaced with a maximum a posteriori solution. This provides not only a reliable subsurface model for the nonlinear inverse scattering problem but also an uncertainty quantification. The high computational cost of the Bayesian FWI and the complexity of a large-scale anisotropy inversion, however, restrict its application in industrial settings. We have developed an FWI approach for tilted transversely isotropic (TTI) media. The strain field and the particle displacement of the anisotropic media are expressed by an integral method based on the scattering theory and an explicit multiscattering modified Green’s function. To reduce the computational cost, the wavefield is calculated by using the preconditioned generalized minimal residual iterative solver, which approximates the solution in the Krylov subspace. The Fréchet derivatives are expressed by using the distorted Born iterative method. An iterated extended Kalman filter is applied to solve the inverse problem and the posterior covariance matrix frequency-by-frequency. Numerical experiments indicate that the presented methodology can reasonably reconstruct the elastic moduli of the TTI medium. Furthermore, the numerical experiments demonstrate the accuracy and feasibility of our methodology.

Joint towed streamer and ocean-bottom-seismometer data multi-parameter full waveform inversion in acoustic-elastic coupled media

Short-offset towed streamer data, and sparse ocean-bottom seismometer (OBS) data are not conducive to applying multi-parameter full waveform inversion (FWI) in production. It is challenging to reconstruct deep velocity in the former, and the latter suffers from severe acquisition footprints. We developed a joint acoustic-elastic coupled full waveform inversion (J-AEFWI) method, in which towed streamer data and ocean-bottom seismometer data were used jointly to build P-wave and S-wave velocity models. A new joint objective function was established using the least-squares theory, and the joint acoustic-elastic coupled full waveform inversion method on the acoustic-elastic coupled equation was derived. The method can inject the residuals of the towed streamer data and the ocean-bottom seismometer data in time backward propagating to update P-wave and S-wave velocity models. The synthetic experimental results show that joint acoustic-elastic coupled full waveform inversion obtains more accurate results than when using these two types of data alone. Compared to using the towed streamer or ocean-bottom seismometer data alone, the joint acoustic-elastic coupled full waveform inversion method leads to better illumination of the deep background velocities and suppression of acquisition footprints. The results of joint acoustic-elastic coupled full waveform inversion were slightly better than those of the cascaded full waveform inversion strategy. To further demonstrate the benefit of the proposed method, we applied it to the field data, and better results are obtained as expected.

Multiparameter Elastic Full Waveform Inversion Based on Random Source-Encoding and Projection Regularization

Multi-parameter elastic full waveform inversion (FWI) makes full use of the dynamic and kinematic information of all seismic wavefield. Through the mutual constraint and verification of the three parameters of P-wave velocity, S-wave velocity, and density, the joint evaluation is carried out, which is helpful to understand the structural and lithologic information of underground media more comprehensively. The bottleneck restricting the multi-parameter FWI is the large amount of calculation and low efficiency. To improve this problem, multiple shots are directly superimposed to form super shots. While it usually results in an unstable inversion due to that a large amount of crosstalk noise will be easily generated between adjacent shots. In this paper, we introduce the random source-encoding strategy to improve the inversion efficiency and load the total-variation (TV) regularization term to suppress the crosstalk noise, but it also brings the problem of regularization parameters selection for multi-parameter FWI. Thus, the projection method is applied to directly load the regularization term into the model as a constraint, which avoids the unsatisfactory results caused by the improper selection of regularization parameters and effectively improves the ill-posedness of inversion. Finally, three examples of the graben, the 1994BP, and the overthrust model are used to prove that the proposed algorithm based on random source-encoding and projection regularization can effectively improve the inversion efficiency, suppress noise, and has good practicability and adaptability.

Superior resolution through multiparameter FWI imaging: A new philosophy in seismic processing and imaging

Seismic processing and imaging workflows have been refined over many decades to attenuate aspects of the recorded wavefield which would be improperly mapped into the image domain by legacy migration algorithms such as Kirchhoff prestack depth migration. These workflows, which include techniques such as deghosting, designature, demultiple, and regularization, have become increasingly complex and time-consuming due to the sequential fashion in which they must be tested and applied. The single-scattering (primary-only) preprocessed data are then migrated and used in extensive model building workflows, including reflection residual moveout tomography, to refine low-frequency subsurface models. Obtaining optimal results at each stage requires subjective assessment of a wide range of parameter tests. Results can be highly variable, with different decisions resulting in very different outcomes. Such workflows mean that projects may take many months or even years. Full-waveform inversion (FWI) imaging offers an alternative philosophy to this conventional approach. FWI imaging is a least-squares multiscattering algorithm that uses the raw field data (transmitted and reflected arrivals as well as their multiples and ghosts) to determine many different subsurface parameters, including reflectivity. Because this approach uses the full wavefield, the subsurface is sampled more completely during the inversion. Here, we demonstrate the application of a novel multiparameter FWI imaging technique to generate high-resolution amplitude variation with angle reflectivity simultaneously with other model parameters, such as velocity and anisotropy, directly from the raw field data. Given that these results are obtained faster than the conventional workflow with a higher resolution, improved illumination, and reduced noise, we highlight the potential of multiparameter FWI imaging to supersede the conventional workflow.

Multi-parameter full waveform inversion using only the streamer data based on the acoustic-elastic coupled wave equation

The ocean seismic pressure data observed by hydrophones contain the elastic information of the subsurface medium, although few studies of full waveform inversion (FWI) regard the pressure data as generated from elastic media. Based on the acoustic-elastic coupled equation, which can directly obtain the elastic pressure component, we propose an acoustic-elastic FWI (AEFWI) method to use elastic pressure data. First, we illustrated the similarities and differences in wave propagation in acoustic and elastic media using ocean-bottom models. Furthermore, we compared the effect of pressure data with different degrees of elastic effects on acoustic FWI (AFWI) and AEFWI. It was found that the S-wave velocity at the seabed interface had a significant effect on the AFWI. When the seabed is soft, the results of AFWI are acceptable, whereas when the seabed is hard, the results of AFWI are nearly wrong, and the presence of elastic effects has to be considered in the inversion at this time. Contrastingly, the proposed method can obtain more accurate P- and S-wave velocities using only pressure data. Finally, the proposed method was applied to a real streamer dataset of the East China Sea, and high wavenumber P- and S-wave velocities were obtained. The RTM images illustrated the accuracy of the inversion results.

A sequential inversion with outer iterations for the velocity and the intrinsic attenuation using an efficient wavefield inversion

Full-waveform inversion (FWI) has become a popular method to retrieve high-resolution subsurface model parameters. It is a highly nonlinear optimization problem based on minimizing the misfit between the observed and predicted data. For intrinsically attenuating media, wave propagation experiences significant loss of energy. Thus, for better data fitting, it is sometimes crucial to consider attenuation in FWI. Viscoacoustic FWI aims at achieving a joint inversion of the velocity and attenuation models. However, multiparameter FWI imposes additional challenges including expanding the null space and facing parameter trade-off issues. Theoretically, an ideal way to mitigate the trade-off issue in multiparameter FWI is to apply the inverse Hessian operator to the parameter gradients. However, it is often not practical to calculate the full Hessian and its matrix inverse because this will be extremely expensive. To improve the computational efficiency and mitigate the trade-off issue, we have used an efficient wavefield inversion (EWI) method to invert for the velocity and the intrinsic attenuation. This approach is implemented in the frequency domain, and the velocity, in this case, is complex-valued in the viscoacoustic EWI. We evaluate a sequential update strategy for the velocity and the intrinsic attenuation, and we repeat the separate optimizations, which we refer to as outer iterations, until the convergence is achieved. Because viscoacoustic EWI is able to recover an accurate velocity model, the velocity update leakage to the [Formula: see text] model is largely reduced. We determine the effectiveness of this approach using synthetic data generated for the viscoacoustic Marmousi and Overthrust models. To further demonstrate the validity of our approach, we generate data in the time domain using a viscoelastic wave equation solver and obtain reasonable inversion results in the frequency domain using the viscoacoustic approximation.

SeisElastic2D: An open-source package for multiparameter full-waveform inversion in isotropic-, anisotropic- and visco-elastic media

Full-waveform inversion (FWI) has emerged as a powerful technique to obtain high-resolution subsurface elastic properties. However, several complicating features, including interparameter trade-offs, cycle-skipping, and high computational cost, motivate a careful assessment and validation of candidate versions of FWI prior to use. Field data application of elastic FWI remains a challenging task, and widely available tools for inversion and appraisal do not exist. SeisElastic2D is an open-source package for multiparameter FWI in isotropic-, anisotropic- and visco-elastic media consisting of a set of FORTRAN 90 routines and SHELL scripts. This package has a modular structure built upon several existing open-source packages including upgraded SPECFEM2D, seisDD, and Seismic Unix. Various model parameterizations for isotropic- and anisotropic-elastic FWI, designed to reduce interparameter trade-offs, are available, as are different misfit functions designed to mitigate cycle-skipping and source-structure trade-offs. New misfit functions, measuring amplitude variation and central-frequency shift, are provided to estimate attenuation models in visco-elastic FWI. This package can be installed and used on high-performance computing cluster and local workstation supporting massively parallel interface, in order to satisfy the high computational requirements of elastic FWI. These features of SeisElastic2D make it a powerful tool for elastic FWI to bridge the gap between academic studies and industrial applications.

Acoustic multi-parameter full waveform inversion based on the wavelet method

In this paper, the acoustic full waveform inversion based on the wavelet method is proposed. It allows to determine density and velocity parameters simultaneously in the time domain. The forward problem is solved based on the wavelet method. The numerical schemes for modelling are constructed in detail. The stability condition is derived for the first time. The inversion is an optimization process for minimizing the mismatch between the synthetic data and the observed data. The computational scheme for the gradient of the objective function is constructed based on the matrix analysis technique. The inversion is implemented from low frequency to high frequency successively. Furthermore, the inversion result of current low frequency is served as the initial guess of next high frequency. This hierarchic strategy includes the smaller wavelengths progressively and improves the inversion robustness. Numerical computations for the benchmark Marmousi model demonstrate that the method has good ability to reconstruct media parameters in complex structures.

3-D joint inversion of seismic waveform and airborne gravity gradiometry data

SUMMARYSeismic full waveform inversion (FWI) is a robust velocity model building technique for hydrocarbon exploration. However, the density reconstruction within the framework of multiparameter FWI leads to more degrees of freedom in the parametrization, and the sensitivity of the inversion change significantly from velocity to density, thereby increasing the ill-posedness of the inverse problem. Gravity gradiometry data inversion is an effective method for resolving density distribution. Combining gravity gradiometry data in FWI could alleviate the non-linearity of the inversion by contributing additional density information for the velocity model building. I develop a 3-D joint seismic waveform and gravity gradiometry inversion method for estimating the velocity and density distribution in the subsurface. The method alternatingly minimizes the waveform and gravity gradiometry misfit. The cross-gradient constraint is applied to enhance the structural similarity between the density and velocity models. The effectiveness of the joint inversion algorithm is demonstrated by a 3-D checkerboard model and 3-D SEAM model. Synthetic examples demonstrate that the joint inversion can improve the image quality in geologically complex areas. A case study from the South China Sea shows that the joint inversion improves the velocity and density solutions compared to a standalone seismic FWI. The joint inversion results are consistent with the pre-stack depth migration section and the shape of the salt body is well resolved.

Multiparameter Full-Waveform Inversion of 3-D On-Ground GPR With a Modified Total Variation Regularization Scheme

Ground-penetrating radar (GPR) full-waveform inversion (FWI) is an emerging near-surface high-resolution imaging technology that has been widely used in GPR 2-D imaging to better quantitatively evaluate the permittivity and conductivity of the subsurface. However, the 2-D imaging method limits the applicability and accuracy of FWI for the 3-D object cases. In this letter, we develop a 3-D FWI algorithm involving permittivity and conductivity for GPR in the frequency domain. The method employs the edge-based finite element method to solve the forward problem and the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method to solve the inverse problem, which avoids the calculation of the Hessian matrix. In particular, by using the parameter scaling and scaling factor, it is convenient to carry out the simultaneous inversion of permittivity and conductivity with high efficiency. In addition, a modified total variation regularization scheme is utilized for ensuring the stability of the inversion, as well as identifying the abnormal body boundary more effectively. As a demonstration, a synthetic 3-D model experiment is presented to test the proposed algorithm. The results show that the proposed inversion strategy can accurately reconstruct the permittivity structure together with the conductivity distribution from the 3-D on-ground GPR data.

Elastic full-waveform inversion with probabilistic petrophysical model constraints

Full-waveform inversion (FWI) based on the minimization of data residuals may not enhance our understanding of the subsurface and can at times lead to misleading subsurface models. Additionally, unconstrained multiparameter FWI may also lead to models that do not represent realistic lithology for independently derived parameters. We have developed a method for elastic FWI that explicitly imposes petrophysical restrictions to guide models toward realistic and feasible lithology, that is, to subsurface models consistent with the seismic data and with the underlying petrophysics. We exploit petrophysical information, such as that provided by well logs, to constrain the inversion and to avoid implausible models. We achieve this goal by confining the inverted models to a feasible region defined by a probability density function instead of imposing lithologic facies as a function of position. Inside this feasible petrophysical regime, the inverted models do not need to obey a specific trend, that is, we do not link the parameters with explicit and potentially inaccurate petrophysical relations. Instead, we define a petrophysical basin of attraction that confines models to a feasible region validated by regional lithologic and petrophysical information. We find through elastic models that incorporating probabilistic petrophysical constraints into the inversion objective function leads to models that are superior to models obtained either without constraints or with approximate analytic constraints. In addition, we discover that these constraints can help in mitigating common issues affecting elastic FWI, such as the artifacts produced by interparameter crosstalk and limited acquisition coverage.

2D multi-parameter waveform inversion of land reflection seismic data obtained from the particle-motion response from the vertical geophone

Onshore seismic exploration analyzes seismic wave propagation in elastic media, which includes the conversion between P- and S-waves. The development of multi-wave and multi-component seismic exploration methods provides data that enable onshore elastic wave full-waveform inversion. However, most data sets of onshore exploration are single component obtained from the particle-motion response from the vertical geophone. When the aiming area has a low-velocity zone, the ray path of reflected wave that propagates to the detector is nearly perpendicular to the ground surface, so that we call it P-wave data. In this paper, we focus on multi-parameter waveform inversion using P-wave reflection seismic data. Although only P-wave data are received, it still contains the converted P-wave information, and the converted P-wave energy gradually increases as the offset increases. As seismic acquisition technology, observation systems and science develop, the folds and acquisition offset increase significantly, and the seismic data contain important converted P-wave information. In this paper, the first-order elastic velocity–stress equation is decomposed to obtain the scalar-P-wave equation from which the S-wave velocity is included firstly. Then we present the theoretical framework for onshore multi-parameter full-waveform inversion using P-wave data. In order to explore the inversion potential of the P-wave data (extracting the S-wave velocity from the converted P-wave information) and accuracy and stability of the P- and S-wave velocity inverted by our method, we carry out numerical tests via different inversion strategies, by using the P-wave data regarded as containing converted P-wave information, and get successful results.