Full Waveform Inversion Method Research Articles

Quantification of thickness loss in a liquid-loaded plate using ultrasonic guided wave tomography

Ultrasonic guided wave tomography (GWT) provides an attractive solution to map thickness changes from remote locations. It is based on the velocity-to-thickness mapping employing the dispersive characteristics of selected guided modes. This study extends the application of GWT on a liquid-loaded plate. It is a more challenging case than the application on a free plate, due to energy of the guided waves leaking into the liquid. In order to ensure the accuracy of thickness reconstruction, advanced forward models are developed to consider attenuation effects using complex velocities. The reconstruction of the thickness map is based on the frequency-domain full waveform inversion (FWI) method, and its accuracy is discussed using different frequencies and defect dimensions. Validation experiments are carried out on a water-loaded plate with an irregularly shaped defect using S0 guided waves, showing excellent performance of the reconstruction algorithm.

Quantitative Investigation on Grouting Quality of Immersed Tube Tunnel Foundation Base using Full Waveform Inversion Method

Abstract Full waveform inversion (FWI) method is used to reveal the internal structure of underground mediums in geotechnical engineering. It comprehensively utilizes the amplitude, travel time, and phase of a wave field. It also offers the potential to produce better resolution of the target medium and feasibility for the detection of buried low-velocity layers. A new FWI method for elastic waves in stratified mediums is presented, which adopts a quasi-linear method coupled with a random search algorithm. The strength of this approach is that the Jaccobian matrix is iteratively calculated instead of the Hession matrix, and the inversion work is helpful for getting out of the local minima within appropriate search scope. To verify our method, it is applied to numerical 2-D stratified models and the appropriate search step and range constraint for inversion are determined by parameter sensitivity analysis. With a series of waveform pretreatments, including filter process, waveform energy normalization, and waveforms mitigation based on correlation analysis, we extended it to use with 3-D stratified media models. Its feasibility and accuracy in recovering the unknown parameters of low-velocity layers are certified. Based on the results of the numerical cases, this FWI method can be used for detecting the grouting quality in immersed tube tunnels. The S-wave velocity profiles of low-velocity layers under the tunnel floor are obtained. Because the S-wave velocities of grouting layers will increase before and after grouting, the grouting quality is effectively evaluated by the FWI method and provides a practical reference for other similar projects.

Eruption mass estimation using infrasound waveform inversion and ash and gas measurements: Evaluation at Sakurajima Volcano, Japan

Eruption mass and mass flow rate are critical parameters for determining the aerial extent and hazard of volcanic emissions. Infrasound waveform inversion is a promising technique to quantify volcanic emissions. Although topography may substantially alter the infrasound waveform as it propagates, advances in wave propagation modeling and station coverage permit robust inversion of infrasound data from volcanic explosions. The inversion can estimate eruption mass flow rate and total eruption mass if the flow density is known. However, infrasound-based eruption flow rates and mass estimates have yet to be validated against independent measurements, and numerical modeling has only recently been applied to the inversion technique. Here we present a robust full-waveform acoustic inversion method, and use it to calculate eruption flow rates and masses from 49 explosions from Sakurajima Volcano, Japan. Six infrasound stations deployed from 12–20 February 2015 recorded the explosions. We compute numerical Green's functions using 3-D Finite Difference Time Domain modeling and a high-resolution digital elevation model. The inversion, assuming a simple acoustic monopole source, provides realistic eruption masses and excellent fit to the data for the majority of the explosions. The inversion results are compared to independent eruption masses derived from ground-based ash collection and volcanic gas measurements. Assuming realistic flow densities, our infrasound-derived eruption masses for ash-rich eruptions compare favorably to the ground-based estimates, with agreement ranging from within a factor of two to one order of magnitude. Uncertainties in the time-dependent flow density and acoustic propagation likely contribute to the mismatch between the methods. Our results suggest that realistic and accurate infrasound-based eruption mass and mass flow rate estimates can be computed using the method employed here. If accurate volcanic flow parameters are known, application of this technique could be broadly applied to enable near real-time calculation of eruption mass flow rates and total masses. These critical input parameters for volcanic eruption modeling and monitoring are not currently available.

Full waveform inversion using oriented time‐domain imaging method for vertical transverse isotropic media

ABSTRACTFull waveform inversion for reflection events is limited by its linearised update requirements given by a process equivalent to migration. Unless the background velocity model is reasonably accurate, the resulting gradient can have an inaccurate update direction leading the inversion to converge what we refer to as local minima of the objective function. In our approach, we consider mild lateral variation in the model and, thus, use a gradient given by the oriented time‐domain imaging method. Specifically, we apply the oriented time‐domain imaging on the data residual to obtain the geometrical features of the velocity perturbation. After updating the model in the time domain, we convert the perturbation from the time domain to depth using the average velocity. Considering density is constant, we can expand the conventional 1D impedance inversion method to two‐dimensional or three‐dimensional velocity inversion within the process of full waveform inversion. This method is not only capable of inverting for velocity, but it is also capable of retrieving anisotropic parameters relying on linearised representations of the reflection response. To eliminate the crosstalk artifacts between different parameters, we utilise what we consider being an optimal parametrisation for this step. To do so, we extend the prestack time‐domain migration image in incident angle dimension to incorporate angular dependence needed by the multiparameter inversion. For simple models, this approach provides an efficient and stable way to do full waveform inversion or modified seismic inversion and makes the anisotropic inversion more practicable. The proposed method still needs kinematically accurate initial models since it only recovers the high‐wavenumber part as conventional full waveform inversion method does. Results on synthetic data of isotropic and anisotropic cases illustrate the benefits and limitations of this method.

Resolving the fine-scale velocity structure of continental hyperextension at the Deep Galicia Margin using full-waveform inversion

Continental hyperextension during magma-poor rifting at the Deep Galicia Margin is characterised by a complex pattern of faulting, thin continental fault blocks, and the serpentinisation, with local exhumation, of mantle peridotites along the S-reflector, interpreted as a detachment surface. In order to understand fully the evolution of these features, it is important to image seismically the structure and to model the velocity structure to the greatest resolution possible. Travel-time tomography models have revealed the long-wavelength velocity structure of this hyperextended domain, but are often insufficient to match accurately the short-wavelength structure observed in reflection seismic imaging. Here we demonstrate the application of two-dimensional (2D) time-domain acoustic full-waveform inversion to deep water seismic data collected at the Deep Galicia Margin, in order to attain a high resolution velocity model of continental hyperextension. We have used several quality assurance procedures to assess the velocity model, including comparison of the observed and modelled waveforms, checkerboard tests, testing of parameter and inversion strategy, and comparison with the migrated reflection image. Our final model exhibits an increase in the resolution of subsurface velocities, with particular improvement observed in the westernmost continental fault blocks, with a clear rotation of the velocity field to match steeply dipping reflectors. Across the S-reflector there is a sharpening in the velocity contrast, with lower velocities beneath S indicative of preferential mantle serpentinisation. This study supports the hypothesis that normal faulting acts to hydrate the upper mantle peridotite, observed as a systematic decrease in seismic velocities, consistent with increased serpentinisation. Our results confirm the feasibility of applying the full-waveform inversion method to sparse, deep water crustal datasets.

Joint acoustic full-waveform inversion of crosshole seismic and ground-penetrating radar data in the frequency domain

Integrating crosshole ground-penetrating radar (GPR) with seismic methods is an efficient way to reduce the uncertainty and ambiguity of data interpretation in shallow geophysical investigations. We have developed a new approach for joint full-waveform inversion (FWI) of crosshole seismic and GPR data in the frequency domain to improve the inversion results of both FWI methods. In a joint objective function, three geophysical parameters (P-wave velocity, permittivity, and conductivity) are effectively connected by three weighted cross-gradient terms that enforce the structural similarity between parameter models. Simulation of acoustic seismic and scalar electromagnetic problems is implemented using 2D finite-difference frequency-domain methods, and the inverse problems of seismic FWI and GPR FWI are solved using a matrix-free truncated Newton algorithm. The joint inversion procedure is performed in several hierarchical frequencies, and the three parameter models are sequentially inverted at each frequency. The joint FWI approach is illustrated using three numerical examples. The results indicate that the joint FWI approach can effectively enhance the structural similarity among the models, modify the structure of each model, and improve the accuracy of inversion results compared with those of individual FWI approaches. Moreover, joint inversion can reduce the trade-off between permittivity and conductivity in GPR FWI, leading to an improved conductivity model in which artifacts are significantly decreased.

A Gauss–Newton full-waveform inversion in PML-truncated domains using scalar probing waves

This study considers the characterization of subsurface shear wave velocity profiles in semi-infinite media using scalar waves. Using surficial responses caused by probing waves, a reconstruction of the material profile is sought using a Gauss–Newton full-waveform inversion method in a two-dimensional domain truncated by perfectly matched layer (PML) wave-absorbing boundaries. The PML is introduced to limit the semi-infinite extent of the half-space and to prevent reflections from the truncated boundaries. A hybrid unsplit-field PML is formulated in the inversion framework to enable more efficient wave simulations than with a fully mixed PML. The full-waveform inversion method is based on a constrained optimization framework that is implemented using Karush–Kuhn–Tucker (KKT) optimality conditions to minimize the objective functional augmented by PML-endowed wave equations via Lagrange multipliers. The KKT conditions consist of state, adjoint, and control problems, and are solved iteratively to update the shear wave velocity profile of the PML-truncated domain. Numerical examples show that the developed Gauss–Newton inversion method is accurate enough and more efficient than another inversion method. The algorithm's performance is demonstrated by the numerical examples including the case of noisy measurement responses and the case of reduced number of sources and receivers.

Reflection full-waveform inversion using a modified phase misfit function

Reflection full-waveform inversion (RFWI) updates the low- and highwavenumber components, and yields more accurate initial models compared with conventional full-waveform inversion (FWI). However, there is strong nonlinearity in conventional RFWI because of the lack of low-frequency data and the complexity of the amplitude. The separation of phase and amplitude information makes RFWI more linear. Traditional phase-calculation methods face severe phase wrapping. To solve this problem, we propose a modified phase-calculation method that uses the phase-envelope data to obtain the pseudo phase information. Then, we establish a pseudophase-information-based objective function for RFWI, with the corresponding source and gradient terms. Numerical tests verify that the proposed calculation method using the phase-envelope data guarantees the stability and accuracy of the phase information and the convergence of the objective function. The application on a portion of the Sigsbee2A model and comparison with inversion results of the improved RFWI and conventional FWI methods verify that the pseudophase-based RFWI produces a highly accurate and efficient velocity model. Moreover, the proposed method is robust to noise and high frequency.

A direct inverse method for subsurface properties: The conceptual and practical benefit and added value in comparison with all current indirect methods, for example, amplitude-variation-with-offset and full-waveform inversion

Direct inverse methods solve the problem of interest; in addition, they communicate whether the problem of interest is the problem that we (the seismic industry) need to be interested in. When a direct solution does not result in an improved drill success rate, we know that the problem we have chosen to solve is not the right problem — because the solution is direct and cannot be the issue. On the other hand, with an indirect method, if the result is not an improved drill success rate, then the issue can be either the chosen problem, or the particular choice within the plethora of indirect solution methods, or both. The inverse scattering series (ISS) is the only direct inversion method for a multidimensional subsurface. Solving a forward problem in an inverse sense is not equivalent to a direct inverse solution. All current methods for parameter estimation, e.g., amplitude-variation-with-offset and full-waveform inversion, are solving a forward problem in an inverse sense and are indirect inversion methods. The direct ISS method for determining earth material properties defines the precise data required and the algorithms that directly output earth mechanical properties. For an elastic model of the subsurface, the required data are a matrix of multicomponent data, and a complete set of shot records, with only primaries. With indirect methods, any data can be matched: one trace, one or several shot records, one component, multicomponent, with primaries only or primaries and multiples. Added to that are the innumerable choices of cost functions, generalized inverses, and local and global search engines. Direct and indirect parameter inversion are compared. The direct ISS method has more rapid convergence and a broader region of convergence. The difference in effectiveness increases as subsurface circumstances become more realistic and complex, in particular with band-limited noisy data.

Seismic waveform tomography with shot-encoding using a restarted L-BFGS algorithm.

In seismic waveform tomography, or full-waveform inversion (FWI), one effective strategy used to reduce the computational cost is shot-encoding, which encodes all shots randomly and sums them into one super shot to significantly reduce the number of wavefield simulations in the inversion. However, this process will induce instability in the iterative inversion regardless of whether it uses a robust limited-memory BFGS (L-BFGS) algorithm. The restarted L-BFGS algorithm proposed here is both stable and efficient. This breakthrough ensures, for the first time, the applicability of advanced FWI methods to three-dimensional seismic field data. In a standard L-BFGS algorithm, if the shot-encoding remains unchanged, it will generate a crosstalk effect between different shots. This crosstalk effect can only be suppressed by employing sufficient randomness in the shot-encoding. Therefore, the implementation of the L-BFGS algorithm is restarted at every segment. Each segment consists of a number of iterations; the first few iterations use an invariant encoding, while the remainder use random re-coding. This restarted L-BFGS algorithm balances the computational efficiency of shot-encoding, the convergence stability of the L-BFGS algorithm, and the inversion quality characteristic of random encoding in FWI.

Quantitative imaging for civil engineering by joint full waveform inversion of surface-based GPR and shallow seismic reflection data

Full waveform inversion (FWI) of ground penetrating radar (GPR) and seismic data is a promising imaging tool for the detailed characterization of latent cavities and tunnels. In this study, surface-based GPR FWI and seismic FWI are combined to quantitatively image the geometry and geophysical attributes of the subsurface. These two FWI methods are integrated into a joint procedure and linked by cross-gradient functions which can provide structural constraints between the parameters. The elastic and electromagnetic properties of the medium (P-wave velocity, permittivity, and conductivity) are linked and simultaneously inverted in the joint FWI approach. This joint FWI approach is tested using three numerical examples. In the first two examples, target objects with various shapes are contained in both homogeneous and inhomogeneous media. In the third example, two sediment-filled cavities and a fractured area are analyzed in the calcarenite layers. The results show that the joint FWI approach can integrate the common structure of models and correct the model structures that are inaccurately reconstructed in the individual FWI methods, providing a comprehensive structural interpretation of the study areas.

Acoustic Waveform Inversion for Ocean Turbulence

AbstractThe seismic oceanography method is based on extracting and stacking the low-frequency acoustic energy scattered by the ocean heterogeneity. However, a good understanding on how this acoustic wavefield is affected by physical processes in the ocean is still lacking. In this work an acoustic waveform modeling and inversion method is developed and applied to both synthetic and real data. In the synthetic example, the temperature field is simulated as a homogeneous Gaussian isotropic random field with the Kolmogorov–Obukhov spectrum superimposed on a background stratified ocean structure. The presented full waveform inversion method is based on the ray-Born approximation. The synthetic seismograms computed using the ray-Born scattering method closely match the seismograms produced with a more computationally expensive finite-difference method. The efficient solution to the inverse problem is provided by the multiscale nonlinear inversion approach that is specifically stable with respect to noise. Full waveform inversion tests are performed using both the stationary and time-dependent sound speed models. These tests show that the method provides a reliable reconstruction of both the spatial sound speed variation and the theoretical spectrum due to fully developed turbulence. Finally, the inversion approach is applied to real seismic reflection data to determine the heterogeneous sound speed structure at the west Barents Sea continental margin in the northeast Atlantic. The obtained model illustrates in more detail the processes of diapycnal mixing near the continental slope.

Traveltime-based reflection full-waveform inversion for elastic medium

The main difficulty of full waveform inversion (FWI) based on local optimization methods is that it tends to trap in local minima or cycle-skipping associated with inaccurate initial models and waveform misfit functions, especially for elastic media. To address this issue, we first discuss the relationship between reverse time migration (RTM) and traditional reflection FWI (RFWI). Then, we present an elastic RFWI (ERFWI) methodology. However, for ERFWI, high nonlinearity still exists in data residuals related misfit function, when true amplitude migration is not adopted. To further mitigate the cycle skipping and avoid the requirements of true amplitude migration, we develop a traveltime-based ERFWI method to update the low-wavenumber components of P- and S-velocity models. The traveltime-based ERFWI only eliminates traveltime residuals along the wave-path of sensitivity kernels to extract the long-wavelength background of the middle and deep parts. Once the traveltime of reflected waves is described correctly, the inversion result using the traveltime-based ERFWI method could be used as a velocity model for prestack depth migration (PSDM) or as an initial model for the conventional FWI to obtain high-resolution velocity model. The final results by combining traveltime-based ERFWI and conventional FWI illustrate that the combined method can obtain an improved result, compared with regular FWI methods.

Geophysics Bright Spots

In the March-April 2017 issue of Geophysics, we see an improved structure-tensor-based coherence technique to detect and map seismic faults and channels. We learn about a new viscoelastic reverse time migration algorithm with attenuation compensation. We also learn about a new sparse dictionary method for full-waveform inversion (FWI). In rock physics, we see a new approach to amplitude variation with offset and azimuth (AVOA) analysis that helps determine fracture fluid properties, as well as a new study of acoustic measurements in well-mated fracture environments.

Challenges and solutions for performing 3D time-domain elastic full-waveform inversion

The full-waveform inversion (FWI) method relies on an effective numerical solution of the wave equation. The wave equation must be solved numerous times during an inversion run. In the past, to be able to use FWI in practice, it was necessary to assume that the earth's subsurface was a 2D acoustic medium. Recent increases in computational power have made it possible to include more real-world physics in the FWI method, such that the computational subsurface can mimic the real-world subsurface as closely as possible. Going from 2D to 3D is challenging, primarily due to the numerical methods involved in solving the wave equation. Including elastic effects is not straightforward due to the increase in possible models that can explain the data, more complicated wave phenomena involved in the wave propagation, as well as trade-off between the subsurface elastic parameters during the inversion. We discuss some of the challenges and solution strategies for using the FWI method in the time domain using a 3D elastic computational domain.

A novel full waveform inversion method based on a time-shift nonlinear operator

A novel full waveform inversion method based on a time-shift nonlinear operator

Limited-view ultrasonic guided wave tomography using an adaptive regularization method

Ultrasonic guided waves are useful to assess the integrity of a structure from a remote location. Recently, tomography techniques have been developed to quantitatively estimate the thickness map of plate-like structures based on the dispersion characteristics of guided waves. In many applications only limited locations are available to place transducers. The missing viewing angles lead to artifacts which can degrade the image quality. To address this problem, this paper applies the regularization method to synthesize the missing components. The regularization technique is performed by an adaptive threshold approach to the limited view reconstruction. The effectiveness of this method combined with the full waveform inversion method is demonstrated by using numerical simulations as well as experiments on an irregularly shaped defect and two flat-bottom defects. The results indicate that the additional components obtained from the regularization method can significantly reduce the artifacts, leading to better reconstruction accuracy.

FULL WAVEFORM INVERSION OF THE SECOND‐ORDER TIME INTEGRAL WAVEFIELD

AbstractWe proposed a new full waveform inversion (FWI) method, namely full waveform inversion of the second‐order time integral wavefield, by enhancing low‐frequency components of seismic data with a second‐order time integration of seismic wavefield, which can efficiently reduce the initial model dependence of FWI. According to the propagation equation of scattering wavefield in scattering theory, we derived a propagation equation for the scattering wavefield with second‐order time integral, and used the leading order Born approximation for the linearization of the propagation equation. Based on the propagation equation for the scattering wavefield with second‐order time integral, using the scattering wavefield to invert for the distribution of scattering sources in subsurface, and using wavefield modeling to construct the incident wavefield, and according to the linear relationship between the scattering wavefield and the incident wavefield and velocity perturbation in the linear propagation equation for the scattering wavefield with second‐order time integral, we applied a formula similar to the imaging formula of migration to obtain the estimation of velocity perturbation, and established an iterative inversion method for the full waveform inversion of second‐order integral wavefield. Applying the inversion result of full waveform inversion of second‐order integral wavefield as the initial velocity model for the conventional FWI can efficiently reduce the initial model dependence of FWI. Numerical tests using synthetic data of the Marmousi model demonstrated the validity and feasibility of the proposed method. The final results of the new method can deliver much improved results than the conventional FWI. Furthermore, to test the independence from the seismic frequency‐band, we use a low‐cut source wavelet (cut from 4Hz below) to generate the synthetic data. The inversion results by our new method show no appreciable difference from the full‐band source results.

Multiparameter estimation with acoustic vertical transverse isotropic full-waveform inversion of surface seismic data

Obtaining accurate depth-migrated images demands an anisotropic representation of the earth. As a prominent tool for building high-resolution earth models, full-waveform inversion (FWI) therefore must not only account for anisotropy during wavefield simulation but also reconstruct the anisotropy fields. We have developed an inversion strategy to perform acoustic multiparameter FWI of surface seismic data in transversely isotropic media with a vertical axis of symmetry (VTI). During the early era of FWI practice, most studies only invert for the most dominant parameter, that is, the vertical velocity, and the rest of the model parameters are either ignored or kept constant. Recently, more and more emphases focus on inverting for more parameters, such as for the vertical velocity and the anisotropy fields; these are referred to as multiparameter inversion. Due to the dominant influence of the vertical velocity on the kinematics of surface seismic data, we have developed a hierarchical approach to invert for the vertical velocity first, but we kept the anisotropy fields unchanged and only switched to joint inversion of the vertical velocity and the anisotropy fields when the inversion for the vertical velocity approaches convergence. In addition, we have illustrated the necessity of incorporating the diving and reflection energy during inversion to mitigate the nonuniqueness of the solutions caused by the coupling between the vertical velocity and the anisotropy fields. We also demonstrate the success of our method for VTI FWI using synthetic and real data examples based on marine surface seismic acquisition. Our results show that incorporation of multiparameter anisotropy inversion produced better focused migration images.

Stress Distribution Near the Seismic Gap Between Wenchuan and Lushan Earthquakes

The Wenchuan M S 8.0 earthquake and Lushan M S 7.0 earthquake unilaterally fractured northeastward and southwestward, respectively, along the Longmenshan fault belt. The aftershock areas of the two earthquakes were separated by a gap with a length of nearly 60 km. We have determined the focal mechanisms of 471 earthquakes with magnitude M ≥ 3 from Jan 2008 to July 2014 near the seismic gap using a full waveform inversion method. Normal, thrust and strike-slip focal mechanisms can be found in northern segment. But in a significant contrast, focal mechanisms of the earthquakes in the southern segment are dominated by thrust faulting. Based on the determined source parameters, we further apply a damped linear inversion method to derive the regional stress field. The southern segment is characterized by an obvious thrust faulting stress regime with a nearly horizontal maximum compression that orients in SE–NW direction. The stress environment in the northern segment is a lot more complicated. The maximum compressional stresses appear to rotate around the ‘‘asperity’’ near west of the Dujiangyan city. Stress field also shows strong variation with time and depth. Before 2009, the seismic activities are more concentrated on the Pengxian–Guanxian fault and Yingxiu–Beichuan fault with dominant strike-slip faulting and normal faulting, while after 2009, the seismic activities are dominated by thrust faulting from north to south, while the activities are more concentrated on the Wenchuan–Maoxian fault in northern segment and Pengxian–Guanxian fault in southern segment. The maximum compressional stresses vary in different depths from north to south, thus may imply the decoupled movement in shallow and in depth.