Full waveform inversion applied to hydroacoustic velocity mapping

When reliable a priori information is not available, it is difficult to correctly predict near-surface S-wave velocity models from Rayleigh waves through existing techniques, especially in the case of complex geology. To tackle this issue, we have developed a new method: two-grid genetic-algorithm Rayleigh-wave full-waveform inversion (FWI). Adopting a two-grid parameterization of the model, the genetic algorithm inverts for unknown velocities and densities at the nodes of a coarse grid, whereas the forward modeling is performed on a fine grid to avoid numerical dispersion. A bilinear interpolation brings the coarse-grid results into the fine-grid models. The coarse inversion grid allows for a significant reduction in the computing time required by the genetic algorithm to converge. With a coarser grid, there are fewer unknowns and less required computing time, at the expense of the model resolution. To further increase efficiency, our inversion code can perform the optimization using an offset-marching strategy and/or a frequency-marching strategy that can make use of different kinds of objective functions and allows for parallel computing. We illustrate the effect of our inversion method using three synthetic examples with rather complex near-surface models. Although no a priori information was used in all three tests, the long-wavelength structures of the reference models were fairly predicted, and satisfactory matches between “observed” and predicted data were achieved. The fair predictions of the reference models suggest that the final models estimated by our genetic-algorithm FWI, which we call macromodels, would be suitable inputs to gradient-based Rayleigh-wave FWI for further refinement. We also explored other issues related to the practical use of the method in different work and explored applications of the method to field data.

In investigation into the phenomenon of global warming, ocean acoustic tomography (OAT) has been used for analysis. In this analysis method, the most important factor is exact calculation of the sound speed in water, that is, the sound wave propagation time. However, so far, analysis of SOFAR propagations in the low-latitude sea area has been lacking. Such a sea area is very important for analysis of the El Nin o Current and others, although a special sound speed structure appears in the region of uniform sound speed formed around the SOFAR axis. For SOFAR propagation, we have compared time-domain results using two models, based on the measurement of far-range sound wave propagation in the sea east of Mindanao Island. The models chosen for the analysis are Stickler's normal mode method (SNM) and ray approximations. (The SNM time series is obtained via Fourier synthesis.) By this means we examined the characteristics of wave theory and ray theory in the low-latitude sea area.

An accurate earth model is key to any successful depth imaging effort. Full waveform inversion is an advanced velocity model building process which uses the full two way wave equation. Existing methods use a ray tracing approach to distribute velocity errors within the model. In this presentation, we will show examples of seismic data processed with the latest technology, including earth model building with full waveform inversion. Introduction The industry has moved to using two-way wave equation migrations(commonly known as reverse time migration), especially in areas of complex geology such as the salt bodies in the Gulf of Mexico and offshore Brazil. The velocity model, including velocity anisotropy, is key to any depth migration effort. The natural next step is to use the two-way wave equation for velocity model building. One of the most advanced tools for velocity model building using the two-way wave equation is Full Waveform Inversion(FWI). Full-waveform inversion uses computer intensive forward modeling of the seismic measurement combined with residual wavefield back propagation to iterate to a final velocity model, which can provide greater detail than tomographic ray tracing approaches. Velocity inversion using full waveform inversion has been used on a number of projects around the world including the GOM, Brazil and the North Sea.

Full waveform inversion (FWI) is an optimization procedure which minimizes the waveform difference between the observed and calculated seismic data. The method, through an iterative forward modeling and inversion based on the acoustic or elastic wave equation, has recently gained wide interest with specific application in exploration and producing. FWI is wellknown for its ability to obtain high resolution and accurate subsurface models in areas with complex geological structures related to the presence of salt bodies encountered in deep water exploration. However, conventional FWI algorithms require seismic data that contains low frequencies (<5Hz). Lack of low frequencies results in unreliable velocity models for seismic imaging. In this paper, we aim to relax the low-frequency requirement of FWI and propose a technique which employs principles from sparse deconvolution in order to recover the missing low frequencies. Through a series of synthetic examples, it is shown that our proposed methodology is able to preserve and utilize the traveltime information of the original data; hence, it allows convergence of the FWI. The major advantage of this method is that it is fully automatic, involving no residual moveout or traveltime difference analysis.

plex shallow subsurface. This workflow incorporates dispersion curve inversion, traveltime tomography and full waveform inversion into a single framework to optimize the advantages of each. An accurate near-surface velocity is derived using the dispersion curve inversion technique that overcomes limitations of traditional traveltime tomography. This velocity is then incorporated into layer-stripping full waveform or RMO inversion schemes by “freezing” the ultra-shallow part of the model in order to retrieve the deeper velocity structure. We illustrate the workflow on a test data set from Inner Mongolia, China, whose long-offsets and low-frequency content provide the necessary input for both the dispersion curve and full waveform inversion techniques. Using this data set, we demonstrate the efficacy of the integrated methodology in determining both the macro-velocity model and near-surface velocities in structurally complex geological setting.

Full-waveform inversion (FWI) has become the centerpiece of velocity model building (VMB) in seismic data processing in recent years. It has proven capable of significantly improving the velocity model and, thus, the migration image for different acquisition types and geologic settings, including complex environments such as salt. With the advent of FWI imaging, the scope of FWI applications has extended further from VMB into the imaging landscape. However, current FWI applications in the industry prevalently employ the acoustic approximation. One common problem of acoustic FWI (A-FWI) is the apparent salt halos at the salt-sediment interface in the resulting FWI velocity and FWI image, the presence of which hinders direct interpretation and imaging focusing around salt bodies. With synthetic and field data examples, we demonstrate that this salt halo is caused mainly by the large mismatch between the elastic recorded data and the acoustic modeled data, particularly at middle to long offsets. To overcome limitations imposed by acoustic assumptions, we developed an elastic FWI (E-FWI) algorithm that combines an elastic modeling engine with the time-lag cost function, which we call elastic time-lag FWI (E-TLFWI). With a more accurate modeling engine, E-TLFWI significantly reduces the salt halo observed in its acoustic counterpart. However, we also observe that the images migrated using the A-FWI and E-FWI velocity models remain similar overall, with some slight improvements around and beneath salt boundaries, particularly near steep salt flanks, as a result of the reduced salt halo. By contrast, FWI images derived from E-TLFWI show considerable benefits over those from acoustic time-lag FWI, such as improved event focusing, better structural continuity, and higher signal-to-noise ratio. The sharpened salt boundaries and enhanced quality of the FWI images reveal the significant value of E-FWI and provide the justification for its greatly increased cost.

In shallow water acoustic tomography, broadband mid-frequency acoustic waves (1 to 5 kHz) follow multiple ray-like paths to travel through the ocean. Travel-time (TT) variations associated to these raypaths are classically used to estimate sound speed perturbations of the water column using the ray theory. In this shallow water environment, source and receiver arrays, combined with adapted array processing, provide the measurement of directions-of-arrival (DOA) and directions-of-departure (DOD) of each acoustic path as new additional observables to perform ocean acoustic tomography. To this aim, the double-beamforming technique is used to extract the TT, DOA, and DOD variations from the array-to-array acoustic records. Besides, based on the first order Born approximation, we introduce the time-angle sensitivity kernels to link sound speed perturbations to the three observable variations. This forward problem is then inversed by the maximum a posteriori method using both the extracted-observable variations and the proposed sensitivity kernels. Inversion results obtained on numerical data, simulated with a parabolic equation code, are presented. The inversion algorithm is performed with the three observables separately, namely TT, DOA, and DOD. The three observables are then used jointly in the inversion process. The results are discussed in the context on ocean acoustic tomography.

Viscous attenuation can have a strong impact on seismic wave propagation, but it is rarely taken into account in full waveform inversion (FWI). When viscoelasticity is considered in time domain FWI, the displacement formulation of the wave equation is usually used instead of the popular velocity–stress formulation. However, inversion schemes rely on the adjoint equations, which are quite different for the velocity–stress formulation than for the displacement formulation. In this paper, we apply the adjoint state method to the isotropic viscoelastic wave equation in the velocity–stress formulation based on the generalized standard linear solid rheology. By applying linear transformations to the wave equation before deriving the adjoint state equations, we obtain two symmetric sets of partial differential equations for the forward and adjoint variables. The resulting sets of equations only differ by a sign change and can be solved by the same numerical implementation. We also investigate the crosstalk between parameter classes (velocity and attenuation) of the viscoelastic equation. More specifically, we show that the attenuation levels can be used to recover the quality factors of P and S waves, but that they are very sensitive to velocity errors. Finally, we present a synthetic example of viscoelastic FWI in the context of monitoring CO₂ geological sequestration. We show that FWI based on our formulation can indeed recover P- and S-wave velocities and their attenuation levels when attenuation is high enough. Both changes in velocity and attenuation levels recovered with FWI can be used to track the CO₂ plume during and after injection. Further studies are required to evaluate the performance of viscoelastic FWI on real data.

Ocean Acoustic Tomography (OAT) is an efficient and economical marine acoustic observation technique. Targeted observation is an appealing procedure to reduce the uncertainty of ocean environment prediction through additional observation. This study aimed to assess the validity of OAT as an observation method for targeted observation. OAT based on Niche Genetic Algorithm was employed to extract sound speed and temperature profiles from acoustic transmission time, utilizing data from the 2019 Yellow Sea experiment. The inversion results were compared with measurement data, which are found to be accurate and reliable. To further evaluate OAT as targeted observation method, the vertical bias structure of OAT was added on synchronous measurement data in the sensitive area of targeted observation to simulate OAT observation in sensitive area. This simulated data was then incorporated into a 3D-Var assimilation system to improve the short-term prediction of the target region. Comparing the predictions derived with the measurement data at the verification time, it shows that the simulated OAT observation improved the quality of target region prediction, indicating that OAT can be an effective observation method for targeted observation. An Observing System Simulation Experiment was conducted to assess the impact of OAT characteristics on prediction improvement. The results show that both adding observation nodes and extending the observation duration have positive effects, while extending the observation duration performs better.

Full Waveform Inversion (FWI) is a seismic imaging technique that utilizes the entire content of seismic trace. This method aims to minimizes differences between real and synthetic seismograms. FWI consists of three main steps: forward modelling to simulate synthetic seismograms, adjoint simulation to calculate the gradient misfit, and optimization to obtain an appropriate model perturbation. FWI is an extremely non-linear inversion technique and computationally intensive since it involves many model parameters. In the context of geophysics, finding parameter models that describe the structure of the earth’s subsurface is the main goal. Geophysical measurements in the field only obtain data that is influenced by the parameter model, in this case seismic recording data, therefore mathematical techniques are studied and applied to determine the correct parameter model from the data obtained, also known as the inversion process. In this study, main research area is on optimization step which include mathematical approach to find perturbation model effectively. The Newton method can be used in the optimization step of FWI. However, its implementation is not promising due to high computational cost in calculating Hessian matrix. To reduce computation cost, an identity matrix is chosen to replace the Hessian matrix, as it usually done in the steepest descent method. Since FWI has a high level of non-linearity, steepest descent method requires many iterations to minimize the objective function. Therefore, this study uses a conjugate gradient method to make the data misfit minimized more quickly. Apart from that, the Line search technique is used to find an appropriate step-length at each iteration on both methods. The FWI workflow is applied to the synthetic acoustic velocity model. We conduct FWI using steepest descent and conjugate gradient methods. The results show that the conjugate gradient method requires fewer iterations than the steepest descent method to minimize the objective function. FWI model result using conjugate gradient method is closer with the true model compared to steepest descent method, showed on misfit result and model image. By comparing these methods we can see that conjugate gradient method can be chosen for application on FWI optimization step for better result on seismic imaging. On the industry scale, better results provide less uncertainty on the model parameters that useful for energy exploration or engineering.

Accurate knowledge of the spatial and temporal evolution of the three-dimensional ocean sound speed profile (SSP) is crucial for underwater source localization. Ocean acoustic tomography (OAT) methods aim at reconstructing SSPs variations based on acoustic measurements between multiple source-receiver pairs (e.g., eigenrays arrival times). This study investigates the estimation of range-dependent SSPs using a classical model-based OAT method (i.e., ray-based ocean acoustic tomography), for various configurations of source and receiver configurations using autonomous platforms in a highly-dynamic upper ocean environment. A regional oceanographic simulation of the De Soto Canyon circulation in the Gulf of Mexico is used to construct 3D sound speed variations spanning a month long which exhibits significant sub-mesoscale variability. Two main aspects affecting OAT performance in the presence of high 3D SSPs variability are investigated: (1) The influence of the input acoustic data (i.e., source-receivers configuration and platform motion, arrival-times accuracy...) and (2) the actual implementation of the OAT scheme (i.e., selection of complexity reduction basis, linearized forward model assumptions as well as the use of iterative solvers) on SSPs estimations errors. Practical implications for the design of OAT experiments in the dynamic upper ocean will be discussed. [Work supported by the Office of Naval Research.]

In conventional marine seismic surveys, due to the time-delayed reflections from the sea surface on both source and receiver sides, ghosts present in recorded seismograms and lead to both phase and spectrum distortions (especially near certain frequency notches). To achieve a high-quality broad-band image/velocity model with conventional reverse time migration (RTM)/full waveform inversion (FWI) that adopts a synthetic zero-phase source wavelet and absorbing surface condition during wavefield modelling, marine seismic data have to be pre-processed to remove ghost effects. However, seismic deghosting is not a trivial task. Instead of employing an external deghosting process, we propose a strategy to compensate for ghost effects during FWI and RTM, which consists of two parts: first, to address phase distortions due to ghost effects by means of obtaining an accurate source wavelet estimation and adopting an appropriate surface boundary condition in both forward and backward wave propagation to appropriately generate ghosts; secondly, to build a compensation operator in the adjoint state computation to mitigate spectrum distortions caused by dominant ghost effects. To demonstrate the success and robustness of the proposed strategy, we present both synthetic experiments and field examples, which suggest that this strategy can lead to successful applications of FWI/RTM directly on marine seismic data without an extra deghosting process.

Full waveform inversion (FWI) is a seismic imaging method suitable for wide aperture / azimuth acquisitions thanks to its ability to account for waves propagating over a broad range of incidence angles. Wide aperture / azimuth acquisitions makes, however, the imaging quite sensitive to anisotropy because of the intrinsic difference between vertical and horizontal velocities in vertical transversely isotropic (VTI) media. In this study, we present a numerical procedure to define the best parametrization for acoustic VTI FWI. High-resolution velocity model for either the vertical, the horizontal or the normal move out (NMO) velocity can be developed by monoparameter FWI, when the considered wave speed is combined with the Thomsen’s parameters δ and e in the parametrization, and when available smooth background models of δ and e are kept fixed during FWI. An alternative is to jointly reconstruct two wavespeeds (for example, the vertical and the horizontal velocities) using a model parametrization that combines these two wavespeeds and δ . However, the spatial resolution of the two resulting velocity models is more limited that of the velocity model obtained with the first mentioned parametrization.

We introduce an inversion approach to simultaneously invert for both velocity and reflectivity. The core of the inversion workflow is a novel wave-equation that provides the full acoustic wavefield, which is parameterized in terms of velocity and vector reflectivity. A key aspect is the separation of the low- and high-wavenumber components of the gradient based on inverse scattering theory, enabling the sensitivity kernels to update the velocity and the vector reflectivity, respectively. The estimation problem is essentially a multi-parameter inversion where the crosstalk trade-offs between the two parameters are minimized with scale separation. Our adjoint state-based inversion is equivalent to performing Full Waveform Inversion (FWI) and Least-Squares Reverse Time Migration (LS-RTM) using the full acoustic wavefield within the same framework. The final inverted reflectivity is an accurate estimate of the true earth reflectivity, compensated for acquisition and poor illumination effects, and with reduced image crosstalk from multiples. The new approach reduces the turnaround time of imaging projects by combining velocity model building (FWI) and imaging (LS-RTM) into a single inversion process with minimum data preprocessing from an inaccurate initial model. We demonstrate the benefits of our scheme using synthetic and field data examples.

Time-domain full waveform inversion (FWI) in the acoustic regime comprises a parameter identification problem for the acoustic wave equation: Pressure waves are initiated by sources, get scattered by the earth’s inner structure, and their reflected parts are picked up by receivers located on the surface. From these reflected wave fields the two parameters, density and sound speed, have to be reconstructed. Mathematically, FWI reduces to the solution of a nonlinear and ill-posed operator equation involving the parameter-to-solution map of the wave equation. Newton-like iterative regularization schemes are well suited and well analyzed to tackle this inverse problem. Their convergence results are often based on an assumption about the nonlinear map known as tangential cone condition. In this paper we verify this assumption for a semi-discrete version of FWI where the searched-for parameters are restricted to a finite dimensional space. As a byproduct we establish that the semi-discrete seismic inverse problem is Lipschitz stable, in particular, it is conditionally well-posed.