Full-waveform Inversion Approach Research Articles

A single level set function approach for multiple material-phases applied to full-waveform inversion in the time domain

This paper presents a multiple material-phase level-set approach for acoustic full-waveform inversion in the time domain. By using a single level set (LS) function, several level values are used to define virtual boundaries between material phases with different (and known) wave propagation velocities. The aim of the proposed approach is to provide a suitable framework to identify multiple/nested inclusions or a finite number of almost homogeneous sedimentary layers with sharp interfaces between them. The use of a single LS function provides a significant reduction in the number of variables to be identified, when compared with the usual multi-material phase approaches defined by multiple functions, especially for problems with a high number of degrees of freedom. Numerical experiments show satisfactory results in identifying simultaneously different interfaces. Cases with and without inverse crime are evaluated, showing that the approach is reasonably robust in dealing with such a condition.

Ultra‐resolution surface‐consistent full waveform inversion

AbstractFull waveform inversion for land seismic data requires the development of specific strategies for modelling the complex response associated to the near surface. Seismic wave propagation is distorted by several effects, such as topographic relief, wavefield scattering, attenuation (often frequency‐dependent) and anisotropy. The modelling of such shallow complexities is often unmanageable by parametric inversions such that data preconditioning and surface‐related corrections are required before tackling the full waveform inversion velocity modelling problem. We developed a unified framework addressing both surface‐consistent corrections and full waveform inversion by using the transmitted portion of the wavefield. The problem of surface‐consistent decomposition is recast in terms of the transmitted wavefield leading to kinematic and dynamic corrections to account for sub‐resolution wave propagation distortions occurring in the near surface weathering layer. Seismic data are deconvolved from the effects of the near surface to better represent the deeper subsurface wavefield propagation. Signal‐to‐noise enhancement is obtained after the surface‐consistent transmission preconditioning by the generation of virtual super gathers reconstructed in the midpoint‐offset sorting domain. An original scheme of 1.5D Laplace–Fourier full waveform inversion, involving 3D radiation and 1D velocity inversion, is then applied for the velocity reconstruction where the amplitude information of the seismic data is fully preserved and utilized. The unified approach of surface‐consistent transmission preconditioning and velocity modelling is demonstrated on the Society of Exploration Geophysicists Advanced Modelling arid model dataset as well as on two complex field datasets containing near surface complexities typical of arid regions. The approach provides the solution of the near surface distortions by performing data preconditioning and velocity inversions in a unified scheme. The surface‐consistent full waveform inversion approach has been utilized for large land seismic projects and represents a robust tool for supporting land seismic imaging.

A novel seismic full waveform inversion approach for assessing the internal structure of a medieval sea dike

AbstractCoastal protection in the form of dike constructions has a long history at the German North Frisian coast dating back to the High Middle Ages. As the vast majority of the dikes built prior to the devastating storm surges of the Middle Ages have been irretrievably destroyed, mostly sparse remains and only a few well preserved of these medieval dikes are found along the German North Frisian coast and within the Wadden Sea. Not all details of their construction and dimensions are yet understood. In the present case study, we investigate the historical Schardeich on the island of Pellworm in the German North Sea in a noninvasive way using shear waves (SH‐waves). For the data interpretation, we applied a combination of seismic full waveform inversion and classical seismic reflection imaging to determine the interior structure of the dike and its underlying layers at the highest possible resolution. The results obtained on land are compared with dike remains found in the tidal flats. These remains show up in marine seismic sections as characteristic reflections, which probably represent a compaction layer caused by the load of the former dike. For ground truthing, we compare the seismic results with internal dike structures found in nearby excavations. The comparison highlights that FWI is a reliable tool for near‐surface archaeological prospecting. We find that SH‐wave FWI provides decimetre‐scale velocity and density models that allow, together with the seismic reflection section, to determine distinct construction phases of the dike. The investigated dike further shows a depression at base level of about 0.75 m, which is of the same order as observed for the dike base reflections in the tidal flats. Transferring these findings to the dike remains mapped in the tidal flats, we derive a height of the former dike from 2.2 to 4.4 m.

On the use of neural networks for full waveform inversion

Neural networks have recently gained attention in the context of solving inverse problems. Physics-Informed Neural Networks (PINNs) are a prominent methodology for the task of solving both forward and inverse problems. In the paper at hand, full waveform inversion is the inverse problem under consideration. The performance of PINNs is compared against classical adjoint optimization. The comparison focuses on three key aspects: the forward-solver, the representation of the material, and the sensitivity computation for the gradient-based minimization. Starting from PINNs, each of these key aspects is investigated and adapted individually until the classical adjoint optimization emerges. It is shown that it is beneficial to use the neural network only for the discretization of the unknown spatially varying material field. Here the neural network produces reconstructions without oscillatory artifacts as typically encountered in classical full waveform inversion approaches. Due to this finding, a hybrid method is proposed. It exploits both the efficient gradient computation with the continuous adjoint method as well as the neural network ansatz for the unknown material field. This new hybrid method outperforms Physics-Informed Neural Networks and the classical adjoint optimization in two-dimensional and three-dimensional settings.

Frequency domain full waveform inversion with small‐scale laboratory measurements for reconnaissance in mechanized tunneling

AbstractIn mechanized tunneling, so‐called tunnel boring machines (TBMs) drill through the ground in an automatized manner. Therefore, the drilling process is very efficient but the maintenance costs are high. Seismic exploration seems appropriate to identify changing ground conditions in front of the TBM to reduce costs from damages of the TBM and from the corresponding dwell times. Today's seismic exploration techniques are using only a small amount of the information, which is contained in the seismic records from field observations, whereas full waveform inversion (FWI) tries to use the whole content. The potential of different FWI approaches for the application in mechanized tunneling has been investigated. An analysis of the performance of FWI not only employing synthetic examples but additionally measured waveforms is essential. Since seismic surveys at the construction side are not performed with FWI in mind, the data sets are usually not appropriate for testing the developed algorithms. Nevertheless, a validation of FWI approaches by measured waveforms is possible by using waveform recordings from a small‐scale experimental setup. A small‐scale super high strength grout specimen is constructed for validating an adjoint frequency domain FWI approach. Frequency domain models compute the seismic response of a system for an infinite time interval. The attenuation of the material as well as the attenuation effects at the free surfaces are hard to quantify over an infinite time interval. Therefore, the specimen is designed in a way that four of the six borders can be modeled as absorbing boundaries. For this purpose, the displacement recordings are truncated just before the waves that are reflected at the excluded borders arrive at the measurement points. This design in combination with a notch representing a rectangular tunnel makes the measurements more similar to data from a tunnel construction side. A rectangular hole is embedded in the specimen and acts as material discontinuity, which the FWI approach is aiming to detect.

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.

Elastic waveform inversion in the frequency domain for an application in mechanized tunneling

The excavation process in mechanized tunneling can be improved by reconnaissance of the geology ahead. A nondestructive exploration can be achieved in means of seismic imaging. A full waveform inversion approach, which works in the frequency domain, is investigated for the application in tunneling. The approach tries to minimize the difference of seismic records from field observations and from a discretized ground model by changing the ground properties. The final ground model might be a representation of the geology. The used elastic wave modeling approach is described as well as the application of convolutional perfectly matched layers. The proposed inversion scheme uses the discrete adjoint gradient method, a multi-scale approach as well as the L-BFGS method. Numerical parameters are identified as well as a validation of the forward wave modeling approach is performed in advance to the inversion of every example. Two-dimensional blind tests with two different ground scenarios and with three different source and receiver station configurations are performed and analyzed, where only the seismic records, the source functions and the ambient ground properties are provided. Finally, an inversion for a three-dimensional tunnel model is performed and analyzed for three different source and receiver station configurations.

Waveform inversion via reduced order modeling

We introduce a novel approach to waveform inversion based on a data-driven reduced order model (ROM) of the wave operator. The presentation is for the acoustic wave equation, but the approach can be extended to elastic or electromagnetic waves. The data are time resolved measurements of the pressure wave gathered by an acquisition system that probes the unknown medium with pulses and measures the generated waves. We propose to solve the inverse problem of velocity estimation by minimizing the square misfit between the ROM computed from the recorded data and the ROM computed from the modeled data, at the current guess of the velocity. We give a step by step computation of the ROM, which depends nonlinearly on the data and yet can be obtained from them in a noniterative fashion, using efficient methods from linear algebra. We also explain how to make the ROM robust to data inaccuracy. The ROM computation requires the full array response matrix gathered with colocated sources and receivers. However, we find that the computation can deal with an approximation of this matrix, obtained from towed-streamer data using interpolation and reciprocity on-the-fly. Although the full-waveform inversion approach of nonlinear least-squares data fitting is challenging without low-frequency information, due to multiple minima of the data fit objective function, we find that the ROM misfit objective function has better behavior, even for a poor initial guess. We also find by explicit computation of the objective functions in a simple setting that the ROM misfit objective function has convexity properties, whereas the least-squares data fit objective function displays multiple local minima.

Toward high-fidelity imaging: Dynamic matching FWI and its applications

Full-waveform inversion (FWI) is firmly established within our industry as a powerful velocity model building tool. FWI carries significant theoretical advantages over conventional velocity model building methods such as refraction and reflection tomography. Specifically, by solving a nonlinear inverse problem through the wave equation, FWI is able to recover a broadband velocity model containing both high and low spatial wavenumbers, thus extending the approximation of residual moveout correction inherent in traditional velocity model building approaches. Moreover, FWI is capable of inverting information from the entire wavefield (i.e., early arrivals, reflections, refractions, and multiple energy) rather than from a subset as in conventional approaches (i.e., first break and primary reflections), thereby availing itself of more information to better constrain its model estimate. However, these theoretical benefits cannot be realized easily in practice because various complexities of real seismic data often conspire to violate algorithmic assumptions, leading to unsatisfactory results. Dynamic matching FWI (DMFWI) is a newly developed algorithm that solves an inversion problem that maximizes the cross correlation of two dynamically matched data sets — one recorded and the other synthetic. Dynamic matching of the two data sets de-emphasizes the amplitude impact, which allows the algorithm to focus on minimizing their kinematic differences rather than amplitude in the data-fitting process. The multichannel correlation makes the algorithm robust for data with low signal-to-noise ratio. Applications of DMFWI across different types of acquisition and geologic settings demonstrate that this novel FWI approach can resolve complex velocity errors and provide high-quality migrated images that exhibit a high degree of geologic plausibility. Additionally, reflectivity images can be obtained in a straightforward manner as natural byproducts through computation of the directional derivative of the inverted FWI velocity models.

Kohn–Vogelius criterion applied to inversion problems in acoustic wave propagation in time domain

This article deals with the problem of identifying inclusions in a homogeneous acoustic medium using the full-waveform inversion (FWI) approach. The aim is to evaluate an alternative to the standard way of calculating the objective function, introducing the Kohn–Vogelius criterion for this purpose. While in the standard approach the objective function is calculated as a measure of the difference between the simulated acoustic pressure and the corresponding value experimentally acquired at a finite number of receivers, in the Kohn–Vogelius procedure the experimental signal is used as an inhomogeneous boundary condition for an auxiliary problem. Thus, the objective function is calculated as a measure of the difference between the original and auxiliary propagation problems. It is then expected that both being solved by the same discretized model, improvements in identification can be achieved when compared to the standard procedure. The sensitivity is obtained through conventional operations of the adjoint method. The spatial discretization was performed using finite elements and the temporal discretization by the Newmark method. The acoustic propagation velocity distribution is controlled through a level set approach that allows for a sharp interface between two media with previously known propagation velocities. Numerical results showed that both, standard and Kohn–Vogelius-based objective functions provided comparable results when the inverse crime was included. However, in a series of examples where the inverse crime was avoided, the objective function based on the Kohn–Vogelius criterion introduced relevant improvements in the quality of the inversion. Despite these encouraging improvements, the Kohn–Vogelius procedure still presents approximately twice the computational cost compared to the Standard case. Therefore, further investigations will be necessary to consider this procedure as an efficient alternative to the problem under study.

Imaging near-surface S-wave velocity and attenuation models by full-waveform inversion with distributed acoustic sensing-recorded surface waves

Distributed acoustic sensing (DAS) technology is, increasingly, the seismic acquisition mode of choice for its high spatial sampling rate, low cost, and nonintrusive deployability. It is being widely evaluated as an enabler of seismic monitoring for [Formula: see text] sequestration in building subsurface time-lapse images and in characterizing near-surface environments. To advance this evaluation, field seismic surveys with optical fibers have been conducted at the Containment and Monitoring Institute’s Field Research Station (CaMI.FRS) in Newell County, Alberta, Canada. In comparison to the standard geophones, optical fibers deployed in surface trenches at CaMI.FRS have recorded high-quality surface waves, rich in low frequencies and exhibiting limited spatial aliasing. These benefits have motivated us to apply the full-waveform inversion (FWI) approach to image the S-wave velocity ([Formula: see text]) and attenuation (quality factor [Formula: see text]) models at shallow site using the surface waves recorded by optical fibers. Compared to the conventional surface-wave dispersion approach, FWI can intrinsically incorporate fundamental and high-order modes and produce [Formula: see text] model with high spatial resolution that resolves horizontal variations. The low-frequency components below 10 Hz measured in the DAS recordings are helpful to overcome the cycle-skipping problem of FWI. Following the adjoint-state method, [Formula: see text] sensitivity kernel can be calculated efficiently with memory strain variables. The [Formula: see text] model is iteratively estimated with a new misfit function measuring root-mean-square amplitude differences, which helps to reduce the trade-off artifacts. The synthetic data obtained from the inverted models are consistent with the observed data in amplitude and phase. The inversion results provide valuable information to characterize the near-surface environments at CaMI.FRS and are expected to support seismic imaging in deeper [Formula: see text] injection zones.

Calibration of a Stationary Multichannel GPR Monitoring System Using Internal Reflection Measurements

Advanced and extensive processing of ground-penetrating radar (GPR) data, for example, needed for full-waveform inversion approaches, requires a reliable temporal calibration of the system. Usually, the calibration of GPR systems is performed with a known medium between the transmitting and receiving antennas. Thereby, the observed time difference between the expected and measured signal arrival times, termed as time-zero, can be accounted for as a system-specific time delay. For measurement configurations where the antennas are permanently positioned around an object for monitoring purposes, time-consuming additional measurements where parts of the system need to be deinstalled would be required. This is not feasible for the proposed system. Therefore, novel calibration methods for such stationary monitoring systems are required to capture the temporal drift of time-zero. In this article, we present a novel calibration approach that uses internal signal reflections in the measurement system to derive the system-specific time delay without the necessity of knowing the medium between the antennas. We demonstrate that parasitic reflection and coupling signals can be used for accurate in situ calibrations. The presented approach is capable of identifying and correcting for the differences in hardware fabrication, while also correcting the temporal changes in time-zero during experiments. The presented approach is able to reduce the error in time-zero to below 25 ps, enabling high-resolution soil research. The presented approach is characterized by requiring no additional calibration setups or measurements since all the necessary data can be acquired during the original soil measurement.

Inspection and Imaging of Tree Trunk Defects Using GPR Multifrequency Full-Waveform Dual-Parameter Inversion

Ground-penetrating radar (GPR) has been regarded as a potentially efficient way of evaluating the growth status of trees and preventing deterioration associated with trunk defects. However, the majority of current GPR data inversions focused on imaging the macroscale location of defects. As the first attempt to seek a preferable quantitative inversion methodology for specifying tree protection and remedies, this paper proposes a full-waveform inversion approach involving dual-parameter attributes applied to common-offset GPR data from a commercial antenna. Specifically, the synchronous inversion of both dielectric constant and conductivity improves the identification accuracy of certain defect types. In particular, both a multi-frequency strategy and total-variation regularization are seamlessly introduced to assure inversion stability by overcoming local minima and cycle skipping. Through an irregular trunk model test, the effectiveness of the optimized inversion is initially verified by presenting the precise features of the crack, hollow, and decay with the dual parameter inversion results. In addition, several other synthetic trunk models and in-site trunk model tests further demonstrate the robustness and practicability of the proposed algorithm, which can offer more specific and comprehensive guidance for the formulation of tree protection and restoration measures.

Application of a global–local full‐waveform inversion of Rayleigh wave to estimate the near‐surface shear wave velocity model

AbstractWe present a global–local full‐waveform inversion (FWI) of surface waves to estimate a high‐resolution shear wave velocity model of the near‐surface at the site of Grenoble (France). The seismic data we use have been acquired in the framework of the InterPACIFIC project. A first attempt is made by employing the multichannel analysis of surface waves (MASW) to invert the fundamental modes of Rayleigh waves. This inversion is solved through a global optimization driven by the neighbourhood algorithm. However, the limiting 1D assumption, together with the severely ill‐posedness of the MASW inversion motivate us to exploit all the information content of the recorded Rayleigh waves (i.e., travel‐times and amplitudes) by implementing a global–local FWI approach. We first perform a global FWI in which a genetic algorithm (GA) is used to minimize the L2 norm difference between observed and simulated seismic waveforms up to 30 Hz. This inversion employs a two‐grid scheme in which the subsurface is described by a fine grid input to the forward modelling, whereas the unknowns are defined on a coarse grid. A bilinear interpolation brings the coarse‐grid model into the fine grid. To accelerate the convergence, two strategies are considered; offset marching and frequency marching. Then, the long‐wavelength velocity profile provided by the GA inversion is used as the starting point for a local FWI for further refinement of the predicted model. In this case, we employ a frequency‐marching strategy up to a maximum frequency of 60 Hz. Both the global and local approaches use a finite difference code for the forward computation. Despite the limited a priori information infused into the inversion framework, the presented global–local FWI scheme provides reliable results as demonstrated by the good match between recorded and predicted seismograms and by the agreement of the estimated velocity with both nearby borehole data and stratigraphic information on the study site. Our global–local strategy also achieves better data fitting and improved matching with the available borehole data with respect to the velocity profile estimated when the local FWI is started from the MASW predictions.

Spyro: a Firedrake-based wave propagation and full-waveform-inversion finite-element solver

Abstract. In this article, we introduce spyro, a software stack to solve wave propagation in heterogeneous domains and perform full waveform inversion (FWI) employing the finite-element framework from Firedrake, a high-level Python package for the automated solution of partial differential equations using the finite-element method. The capability of the software is demonstrated by using a continuous Galerkin approach to perform FWI for seismic velocity model building, considering realistic geophysics examples. A time domain FWI approach that uses meshes composed of variably sized triangular elements to discretize the domain is detailed. To resolve both the forward and adjoint-state equations and to calculate a mesh-independent gradient associated with the FWI process, a fully explicit, variable higher-order (up to degree k=5 in 2D and k=3 in 3D) mass-lumping method is used. We show that, by adapting the triangular elements to the expected peak source frequency and properties of the wave field (e.g., local P-wave speed) and by leveraging higher-order basis functions, the number of degrees of freedom necessary to discretize the domain can be reduced. Results from wave simulations and FWIs in both 2D and 3D highlight our developments and demonstrate the benefits and challenges with using triangular meshes adapted to the material properties.

Probabilistic Full-Waveform Inversion Considering the Discontinuities of the Material Properties of a Layered Half-Space

The goal of full-waveform inversion (FWI) is to extract quantitative information pertaining to the material and geometrical properties from measured wave fields with their full contents considered. As an inverse problem, FWI itself is associated with ill-posedness, which means instability and nonuniqueness of the solution, because the fields are measured only at some locations. Owing to these unfavorable conditions, several regularization techniques have been utilized for stable estimations, but it is difficult when using a regularization technique to select a regularization factor, which has no physical meaning. In this paper, the FWI approach is applied to estimate the material properties of a layered half-space. The thin-layered method, an efficient analysis method for wave propagation in a layered medium, is employed for this purpose. It is formulated in the maximum a posteriori (MAP) form, and Tikhonov regularization is expressed as a prior distribution, whose standard deviation replaces the role of the regularization factor to ensure an intuitive meaning. Additionally, a technique to remove outliers is newly introduced for the regularization technique; it captures discontinuities accurately in the material properties of a layered half-space. Through this additional technique, the limitation of the smoothness effect in existing regularization techniques is alleviated. The proposed MAP approach including the regularization-based prior and outlier-removal technique is applied to several numerical examples to estimate the profiles of the shear velocities of a layered half-space. The numerical investigations conducted here confirm the validity of the proposed approach with satisfactory accuracy.

Characterizing near-surface structures at the Ostia archaeological site based on instantaneous-phase coherency inversion

Traditional least-squares full-waveform inversion (FWI) suffers from severe local minima problems in the case of the presence of strongly dispersive surface waves. In addition, recorded wavefields are often characterized by amplitude errors due to varying source coupling and incorrect 3D-to-2D geometric-spreading correction. Thus, least-squares FWI is considered less suitable for near-surface applications. We introduce an amplitude-unbiased coherency measure as a misfit function that can be incorporated into FWI. Such coherency has been used previously in phase-weighted stacking to enhance weak but coherent signals. The benefit of this amplitude-unbiased misfit function is that it can extract information uniformly for all seismic signals (surface waves, reflections, and scattered waves). Using the adjoint-state method, we show how to calculate the gradient of this new misfit function. We validate the robustness of the new approach using checkerboard tests and synthetic data contaminated by random noise. We then apply the new FWI approach to a field data set acquired at an archaeological site located in Ostia, Italy. The goal of this survey is to map the unexcavated archaeological remains with high resolution. We identify a known tumulus in the FWI results. The instantaneous-phase coherency FWI results also establish that the shallow subsurface under the survey lines is quite heterogeneous. The instantaneous-phase coherency FWI of near-surface data can be a promising tool to image shallow small-scale objects buried under shallow soil covers, as found at archaeological sites.

Love wave full-waveform inversion for archaeogeophysics: From synthesis tests to a field case

High precision detection of the shallow-surface structure is of great significance to geotechnical engineering and archaeological geophysical research. Surface wave Full waveform inversion (FWI) is attracting more and more attention in shallow seismic exploration. The FWI of Love waves is more straightforward and has a higher precision and resolution compared with Rayleigh waves. In the classic gradient-based FWI algorithm, the gradient amplitude does not scale with increasing depth due to the coupling effect and double scattering; thus, the inversion image cannot represent the significant small-scale characteristic structures in archaeogeophysics. To overcome the above limitations, a pre-conditioned FWI approach was presented, and a complete elastic Love waves FWI workflow was developed for archaeogeophysics. The superior performance of the developed method was verified through synthesis tests and a field experiment. The synthetic tests on a tomb model show that the pre-conditioned approach has a better parameter reconstruction capability, can characterize small-scale anomalies, improves the convergence rate, and has a strong anti-noise ability. In the field experiment, the pre-conditioned approach-based Love waves FWI workflow was adopted to invert the recorded Love waves datasets gathered in Xianyang City, China. The target of the survey was to determine the location and approximate size of a buried ancient tomb to provide reliable guidance for further excavation. The obtained FWI image revealed an underground profile with a depth of 9.5 m, and a low-velocity anomaly with a height of about 1.6 m and a length of about 4.7 m was delineated, which we identified as the tomb. The subsequent excavation confirmed this conclusion. The above results show that the complete Love wave FWI workflow developed has the ability to perform accurate imaging under the condition of few shots.

Data-adaptive global full-waveform inversion

SUMMARYWe present a novel approach to global-scale full-waveform inversion (FWI) that can reduce computational cost by over an order of magnitude, compared to previously published methods, without sacrificing physical and mathematical rigour. This is based on data-adaptation, and thereby application-oriented specialization, on two complementary levels. On the simulation level, we exploit the approximate azimuthal symmetry of seismic wavefields by implementing wavefield-adapted meshes and discrete adjoints, thereby lowering numerical simulation cost. On the measurement level, we use a quasi-stochastic approach where variable mini-batches of data are used during an iterative misfit minimization in order to promote a parsimonious exploitation of data. In addition to the methodological developments, we present an inversion of long-period (100–200 s) seismic waveforms from 1179 earthquakes for 3-D whole-mantle structure. The computational cost of the 72 iterations in the inversion approximately equals one third of a single iteration using an FWI approach with widely used cubed-sphere-based meshes and non-stochastic gradient optimization. The resulting LOng-Wavelength earth model (LOWE) constitutes the first global FWI constructed entirely from a spherically symmetric initial mantle structure. While mostly serving as a showcase for the method, LOWE contains a wealth of regional-scale structures that compare well to earlier tomographic images. Being conservatively smooth and based on minimal assumptions, it may therefore serve as starting model for future inversions at shorter period or smaller scales.