A Rayleigh Wave Globally Optimal Full Waveform Inversion Framework Based on GPU Parallel Computing

Conventional gradient-based full waveform inversion (FWI) is a local optimization, which is highly dependent on the initial model and prone to trapping in local minima. Globally optimal FWI that can overcome this limitation is particularly attractive, but is currently limited by the huge amount of calculation. In this paper, we propose a globally optimal FWI framework based on GPU parallel computing, which greatly improves the efficiency, and is expected to make globally optimal FWI more widely used. In this framework, we simplify and recombine the model parameters, and optimize the model iteratively. Each iteration contains hundreds of individuals, each individual is independent of the other, and each individual contains forward modeling and cost function calculation. The framework is suitable for a variety of globally optimal algorithms, and we test the framework with particle swarm optimization algorithm for example. Both the synthetic and field examples achieve good results, indicating the effectiveness of the framework. .

Time Domain Full Waveform Inversion Based on Gradient Preconditioning with an Angle-Dependent Weighting Factor

There are lots of low wavenumber noises in the gradients of time domain full waveform inversion(FWI),which can seriously reduce the accuracy and convergence speed of FWI.Thus,we introduce an angle-dependent weighting factor to precondition the gradients so as to suppress the low wavenumber noises when the multi-scale FWI is implemented in the high frequency.Model experiments show that the FWI based on the gradient preconditioning with an angle-dependent weighting factor has faster convergence speed and higher inversion accuracy than the conventional FWI.The tests on real marine seismic data show that this method can adapt to the FWI of field data,and provide high-precision velocity models for the actual data processing.

Three-dimensional frequency-domain full waveform inversion based on the nearly-analytic discrete method

The nearly analytic discrete(NAD)method is a kind of finite difference method with advantages of high accuracy and stability.Previous studies have investigated the NAD method for simulating wave propagation in the time-domain.This study applies the NAD method to solving three-dimensional(3D)acoustic wave equations in the frequency-domain.This forward modeling approach is then used as the“engine”for implementing 3D frequency-domain full waveform inversion(FWI).In the numerical modeling experiments,synthetic examples are first given to show the superiority of the NAD method in forward modeling compared with traditional finite difference methods.Synthetic 3D frequency-domain FWI experiments are then carried out to examine the effectiveness of the proposed methods.The inversion results show that the NAD method is more suitable than traditional methods,in terms of computational cost and stability,for 3D frequency-domain FWI,and represents an effective approach for inversion of subsurface model structures.

Evaluation of Multi-Scale Full Waveform Inversion with Marine Vertical Cable Data

Seismic illumination plays an important role in subsurface imaging. A better image can be expected either through optimizing acquisition geometry or introducing more advanced seismic mi- gration and/or tomographic inversion methods involving illumination compensation. Vertical cable survey is a potential replacement of traditional marine seismic survey for its flexibility and data quality. Conventional vertical cable data processing requires separation of primaries and multiples before migration. We proposed to use multi-scale full waveform inversion （FWI） to improve illumination coverage of vertical cable survey. A deep water velocity model is built to test the capability of multi-scale FWI in detecting low velocity anomalies below seabed. Synthetic results show that multi-scale FWI is an effective model building tool in deep-water exploration. Geometry optimization through target ori- ented illumination analysis and multi-scale FWI may help to mitigate the risks of vertical cable survey. The combination of multi-scale FWI, low-frequency data and multi-vertical-cable acquisition system may provide both high resolution and high fidelity subsurface models.

Quantitative ultrasound brain imaging with multiscale deconvolutional waveform inversion

High-resolution images of human brain are critical for monitoring the neurological conditions in a portable and safe manner.Sound speed mapping of brain tissues provides unique information for such a purpose.In addition,it is particularly important for building digital human acoustic models,which form a reference for future ultrasound research.Conventional ultrasound modalities can hardly image the human brain at high spatial resolution inside the skull due to the strong impedance contrast between hard tissue and soft tissue.We carry out numerical experiments to demonstrate that the time-domain waveform inversion technique,originating from the geophysics community,is promising to deliver quantitative images of human brains within the skull at a sub-millimeter level by using ultra-sound signals.The successful implementation of such an approach to brain imaging requires the following items:signals of sub-megahertz frequencies transmitting across the inside of skull,an accurate numerical wave equation solver simulating the wave propagation,and well-designed inversion schemes to reconstruct the physical parameters of targeted model based on the optimization theory.Here we propose an innovative modality of multiscale deconvolutional waveform inversion that improves ultrasound imaging resolution,by evaluating the similarity between synthetic data and observed data through using limited length Wiener filter.We implement the proposed approach to iteratively update the parametric models of the human brain.The quantitative imaging method paves the way for building the accurate acoustic brain model to diagnose associated diseases,in a potentially more portable,more dynamic and safer way than magnetic resonance imaging and x-ray computed tomography.

Layer-Stripping Full Waveform Inversion with Damped Seismic Reflection Data

Full waveform inversion（FWI） directly minimizes errors between synthetic and observed data.For the surface acquisition geometry,reflections generated from deep reflectors are sensitive to overburden structure,so it is reasonable to update the macro velocity model in a top-to-bottom manner.For models dominated by horizontally layered structures,combination of offset/time weighting and constant update depth control（CUDC） is sufficient for layer-stripping FWI.CUDC requires ray tracing to determine reflection traveltimes at a constant depth.As model complexity increases,the multi-path effects will have to be considered.We developed a new layer-stripping FWI method utilizing damped seismic reflection data,which does not need CUDC and ray tracing.Numerical examples show that effective update depth（EUD） can be controlled by damping constants even in complex regions and the inversion result is more accurate than conventional methods.

Full Waveform Inversion Method for Horizontally Inhomogeneous Stratified Media

Full waveform inversion method is an approach to grasp the physical property parameters of un- derground media in geotechnical nondestructive detection and testing field. Using finite-diference time domain(FDTD) method for elastic wave equations, the full-wave field in horizontally inhomogeneous stratified media for elastic wave logging was calculated. A numerical 2D model with three layers was computed for elastic wave propagation in horizontally inhomogeneous media. The full waveform inversion method was verified to be feasible for evaluating elastic parameters in lateral inhomogeneous stratified media and showed well accuracy and conver- gence. It was shown that the time cost of inversion had certain dependence on the choice of starting initial model. Furthermore, this method was used in the detection of nonuniform grouting in the construction of immersed tube tunnel. The distribution of nonuniform grouting was clearly evaluated by the S-wave velocity profile of grouted mortar base below the tunnel floor.

Convolution-based multi-scale envelope inversion

Envelope inversion(El)is an efficient tool to mitigate the nonlinearity of conventional full waveform inversion(FWI)by utilizing the ultralow-frequency component in the seismic data.However,the performance of envelope inversion depends on the frequency component and initial model to some extent.To improve the convergence ability and avoid the local minima issue,we propose a convolution-based envelope inversion method to update the low-wavenumber component of the velocity model.Besides,the multi-scale inversion strategy(MCEI)is also incorporated to improve the inversion accuracy while guaranteeing the global convergence.The success of this method relies on modifying the original envelope data to expand the overlap region between observed and modeled envelope data,which in turn expands the global minimum basin of misfit function.The accurate low-wavenumber component of the velocity model provided by MCEI can be used as the migration model or an initial model for conventional FWI.The numerical tests on simple layer model and complex BP 2004 model verify that the proposed method is more robust than El even when the initial model is coarse and the frequency component of data is high.

Elastic direct envelope inversion based on wave mode decomposition for multi-parameter reconstruction of strong-scattering media

The parameter reconstruction of strong-scattering media is a challenge for conventional full waveform inversion(FWI).Direct envelope inversion(DEI)is an effective method for large-scale and strongscattering structures imaging without the need of low-frequency seismic data.However,the current DEI methods are all based on the acoustic approximation.Whereas,in real cases,seismic records are the combined effects of the subsurface multi-parameters.Therefore,the study of DEI in elastic media is necessary for the accurate inversion of strong-scattering structures,such as salt domes.In this paper,we propose an elastic direct envelope inversion(EDEI)method based on wave mode decomposition.We define the objective function of EDEI using multi-component seismic data and derive its gradient formulation.To reduce the coupling effects of multi-parameters,we introduce the wave mode decomposition method into the gradient calculation of EDEI.The update of Vp is primarily the contributions of decomposed P-waves.Two approaches on Vs gradient calculation are proposed,i.e.using the petrophysical relation and wave mode decomposition method.Finally,we test the proposed method on a layered salt model and the SEG/EAGE salt model.The results show that the proposed EDEI method can reconstruct reliable large-scale Vp and Vs models of strong-scattering salt structures.The successive elastic FWI can obtain high-precision inversion results of the strong-scattering salt model.The proposed method also has a good anti-noise performance in the moderate noise level.

Imaging disturbance zones ahead of a tunnel by elastic full-waveform inversion:Adjoint gradient based inversion vs.parameter space reduction using a level-set method

We present and compare twoflexible and effective methodologies to predict disturbance zones ahead of underground tunnels by using elastic full-waveform inversion.One methodology uses a linearized,iterative approach based on misfit gradients computed with the adjoint method while the other uses iterative,gradient-free unscented Kalmanfiltering in conjunction with a level-set representation.Whereas the former does not involve a priori assumptions on the distribution of elastic properties ahead of the tunnel,the latter intro-duces a massive reduction in the number of explicit model parameters to be inverted for by focusing on the geometric form of potential disturbances and their average elastic properties.Both imaging methodologies are validated through successful reconstructions of simple disturbances.As an application,we consider an elastic multiple disturbance scenario.By using identical synthetic time-domain seismo-grams as test data,we obtain satisfactory,albeit different,reconstruction results from the two inversion methodologies.The computa-tional costs of both approaches are of the same order of magnitude,with the gradient-based approach showing a slight advantage.The model parameter space reduction approach compensates for this by additionally providing a posteriori estimates of model parameter uncertainty.

Acoustic waveform inversion in frequency domain:Application to a tunnel environment

Waveform inversion is an approach used to find an optimal model for the velocity field of a ground structure such that the dynamic response is close enough to the given seismic data.First,a suitable numerical approach is employed to establish a realistic forward computer model.The forward problem is solved in the frequency domain using higher-order finite elements.The velocity field is inverted over a specific number of discrete frequencies,thereby reducing the computational cost of the forward calculation and the nonlinearity of the inverse problem.The results are presented for different frequency sets and with different source and receiver locations for a twodimensional model.The influence of attenuation effects is also investigated.The results of two blind tests are presented where only the seismic records of an unknown synthetic model with an inhomogeneous material parameter distribution are provided to mimic a more realistic case.Finally,the result of the inversion in a three-dimensional space is illustrated.

Concepts in the Direct Waveform Inversion(DWI)Using Explicit Time-Space Causality

The Direct Waveform Inversion(DWI)is a recently proposed waveform inversion idea that has the potential to simultaneously address several existing challenges in many full waveform inversion(FWI)schemes.A key ingredient in DWI is the explicit use of the time-space causality property of the wavefield in the inversion which allows us to convert the global nonlinear optimization problem in FWI,without information loss,into local linear inversions that can be readily solved.DWI is a recursive scheme which sequentially inverts for the subsurface model in a shallow-to-deep fashion.Therefore,there is no need for a global initial velocity model to implement DWI.DWI is unconditionally convergent when the reflection traveltime from the boundary of inverted model is beyond the finite recording time in seismic data.In order for DWI to work,DWI must use the full seismic wavefield including interbed and free surface multiples and it combines seismic migration and velocity model inversion into one process.We illustrate the concepts in DWI using 1D and 2D models.

Multi-Frequency Contrast Source Inversion for Reflection Seismic Data

In the contrast source inversion(CSI)method,the contrast sources(equiva-lent scattering sources)and the contrast(parameter perturbation)are iteratively recon-structed by an alternating optimization scheme.Traditionally integral equation CSI method is formulated for transmission tomography using analytic Green’s function in homogeneous background.To extend the method to the case of reflection seismology,in this paper,we use WKBJ method to compute the Green’s function of depth dependent background media and the solving method of equations to initialize the contrast source of different frequencies,resulting in an efficient method to invert multi-frequency reflection seismic data–multi-frequency contrast source inversion method(MFCSI).Numerical results for the Marmousi model show that MFCSI method can obtain good results even when low frequency data are missing,in which case the conventional FWI fails.