High-SNR Staining Algorithm for One-Way Wave Equation-Based Modelling and Imaging

Staining algorithms based on two-way wave equation migration methods have been applied to improve the signal-to-noise ratio (SNR) of poorly illuminated structures such as those in subsalt zones. In regular staining algorithms, when a source wavefield reaches the stained area that is associated with the target structures, a new wavefield called stained wavefield is excited, and this stained wavefield forward extrapolates synchronously with the real source wavefield. The forward-extrapolated stained and real source wavefields are cross-correlated with the backward-extrapolated receiver wavefield, and we obtain the stained and the real reverse time migration (RTM) images. The staining algorithms for RTM can suppress the noise of non-target regions and obtain high SNR images of the target structures. Whereas RTM methods are limited by the low computational efficiency and SNR, by contrast, one-way wave equation migration (OWEM) methods have the advantages of high efficiency and no interference from multiples. Thus, we developed a new staining method based on the generalised screen propagator (GSP) as a case of OWEM methods for subsalt imaging. Furthermore, a new stained wavefield called stained receiver wavefield is proposed here, forming two new staining strategies for seismic imaging, in which forward-propagated source and backward-propagated receiver wavefields can be conveniently selected to be stained at the stained area. Numerical experiments demonstrated that this staining GSP method is more effective in improving the SNR of subsalt structures compared to conventional GSP migration and RTM methods; moreover, these new staining strategies as applied to the OWEM methods can greatly improve the SNR of weakly illuminated structures in subsalt zones, in comparison with regular staining algorithms for one-way methods.     

A Stable Q Compensated Reverse Time Migration Method Based on Excitation Amplitude Imaging Condition

The stability and efficiency, especially the stability, are generally concerned issues in Q compensated reverse time migration (Q-RTM). The instability occurs because of the exponentially boosted high frequency ambient noise during the forward or backward seismic wavefield propagation. The regularization and low-pass filtering methods are two effective strategies to control the instability of the wave propagation in Q-RTM. However, the regularization parameters are determined experimentally, and the wavefield cannot be recovered accurately. The low-pass filtering method cannot balance the selection of cutoff frequency for varying Q values, and may damage the effective signals, especially when the signal-to-noise ratio (SNR) of the seismic data is low, the Q-RTM will be a highly unstable process. In order to achieve the purpose of stability, the selection of cutoff frequency will be small enough, which can cause great damage to the effective high frequency signals. In this paper, we present a stable Q-RTM algorithm based on the excitation amplitude imaging condition, which can compensate both the amplitude attenuation and phase dispersion. Unlike the existing Q-RTM algorithms enlarging the amplitude, the exponentially attenuated seismic wavefield will be used during both the forward and backward wavefield propagation of Q-RTM. Therefore, the new Q-RTM algorithm is relative stable, even for the low SNR seismic data. In order to show the accuracy and stability of our stable Q-RTM algorithm clearly, an example based on Graben model will be illustrated. Then, a realistic BP gas chimney model further demonstrates that the proposed method enjoys good stability and anti-noise performance compared with the traditional Q-RTM with amplitude amplification. Compare the Q-RTM images of these two models to the reference images obtained by the acoustic RTM with acoustic seismic data, the new Q-RTM results match the reference images quite well. The proposed method is also tested using a field seismic data, the result shows the effectiveness of our proposed method.     

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.     

Amplitude Compensation for One-Way Wave Propagators in Inhomogeneous Media and Its Application to Seismic Imaging

The WKBJ solution for the one-way wave equations in media with smoothly varying velocity variation with depth, c(z), is reformulated from the principle of energy flux conservation for acoustic media. The formulation is then extended to general heterogeneous media with local angle domain methods by introducing the concepts of Transparent Boundary Condition (TBC) and Transparent Propagator (TP). The influence of the WKBJ correction on image amplitudes in seismic imaging, such as depth migration in exploration seismology, is investigated in both smoothly varying c(z) and general heterogeneous media. We also compare the effect of the propagator amplitude compensation with the effect of the acquisition aperture correction on the image amplitude. Numerical results in a smoothly varying c(z) medium demonstrate that the WKBJ correction significantly improves the one-way wave propagator amplitudes, which, after compensation, agree very well with those from the full wave equation method. Images for a point scatterer in a smoothly varying c(z) medium show that the WKBJ correction has some improvement on the image amplitude, though it is not very significant. The results in a general heterogeneous medium (2D SEG/EAGE salt model) show similar phenomena. When the acquisition aperture correction is applied, the image improves significantly in both the smoothly varying c(z) medium and the 2D SEG/EAGE salt model. The comparisons indicate that although the WKBJ compensation for propagator amplitude may be important for forward modeling (especially for wide-angle waves), its effect on the image amplitude in seismic imaging is much less noticeable compared with the acquisition aperture correction for migration with limited acquisition aperture in general heterogeneous media.     

Wave Propagation Simulation Using the CIP Method of Characteristic Equations

We apply the CIP (Cubic Interpolated Profile) scheme to the numerical simulation of the acoustic wave propagation based on characteristic equations.The CIP scheme is based on a concept that both the wavefield and its spatial derivative propagate along the same characteristic curves derived from a hyperbolic differential equation. We describe the derivation of the characteristic equations for the acoustic waves from the basic equations by means of the directional splitting and the diagonalization of the coefficient matrix, and establish geophysical boundary conditions. Since the CIP scheme calculates both the wavefield and its spatial derivatives, it is easy to realize the boundary conditions theoretically. We also show some numerical simulation examples and the CIP can simulate acoustic wave propagation with high stability and less numerical dispersion. The method of characteristics with the CIP scheme is a very powerful technique to deal with the wave propagation in complex geophysical problems.     

Linear Wavefield Optimization Using a Modified Source

Recorded seismic data are sensitive to the Earth's elastic properties, and thus, they carry information of such properties in their waveforms. The sensitivity of such waveforms to the properties is nonlinear causing all kinds of difficulties to the inversion of such properties. Inverting directly for the components forming the wave equation, which includes the wave equation operator (or its perturbation), and the wavefield, as independent parameters enhances the convexity of the inverse problem. The optimization in this case is provided by an objective function that maximizes the data fitting and the wave equation fidelity, simultaneously. To enhance the practicality and efficiency of the optimization, I recast the velocity perturbations as secondary sources in a modified source function, and invert for the wavefield and the modified source function, as independent parameters. The optimization in this case corresponds to a linear problem. The inverted functions can be used directly to extract the velocity perturbation. Unlike gradient methods, this optimization problem is free of the Born approximation limitations in the update, including single scattering and cross talk that may arise for example in the case of multi sources. These specific features are shown for a simple synthetic example, as well as the Marmousi model.     

Target-Oriented Inversion of Time-Lapse Seismic Waveform Data

Full waveform inversion of time-lapse seismic data can be used as a means of estimating the reservoir changes due to the production. Since the repeated computations for the monitor surveys lead to a large computational cost, time-lapse full waveform inversion is still considered to be a challenging task. To address this problem, we present an efficient target-oriented inversion scheme for time-lapse seismic data using an integral equation formulation with Gaussian beam based Green's function approach. The proposed time-lapse approach allows one to perform a local inversion within a small region of interest (e.g. a reservoir under production) for the monitor survey. We have verified that the T-matrix approach is indeed naturally target-oriented, which was mentioned by Jakobsen and Ursin [24] and allows one to reduce the computational cost of time-lapse inversion by focusing the inversion on the target-area only. This method is based on a new version of the distorted Born iterative T-matrix inverse scattering method. The Gaussian beam and T-matrix are used in this approach to perform the wavefield computation for the time-lapse inversion in the baseline model from the survey surface to the target region. We have provided target-oriented inversion results of the synthetic time-lapse waveform data, which shows that the proposed scheme reduces the computational cost significantly.     

Transition Operator Approach to Seismic Full-Waveform Inversion in Arbitrary Anisotropic Elastic Media

We generalize the existing distorted Born iterative T-matrix (DBIT) method to seismic full-waveform inversion (FWI) based on the scalar wave equation, so that it can be used for seismic FWI in arbitrary anisotropic elastic media with variable mass densities and elastic stiffness tensors. The elastodynamic wave equation for an arbitrary anisotropic heterogeneous medium is represented by an integral equation of the Lippmann-Schwinger type, with a 9-dimensional wave state (displacement-strain) vector. We solve this higher-dimensional Lippmann-Schwinger equation using a transition operator formalism used in quantum scattering theory. This allows for domain decomposition and novel variational estimates. The tensorial nonlinear inverse scattering problem is solved iteratively by using an expression for the Fréchet derivatives of the scattered wavefield with respect to elastic stiffness tensor fields in terms of modified Green's functions and wave state vectors that are updated after each iteration. Since the generalized DBIT method is consistent with the Gauss-Newton method, it incorporates approximate Hessian information that is essential for the reduction of multi-parameter cross-talk effects. The DBIT method is implemented efficiently using a variant of the Levenberg-Marquard method, with adaptive selection of the regularization parameter after each iteration. In a series of numerical experiments based on synthetic waveform data for transversely isotropic media with vertical symmetry axes, we obtained a very good match between the true and inverted models when using the traditional Voigt parameterization. This suggests that the effects of cross-talk can be sufficiently reduced by the incorporation of Hessian information and the use of suitable regularization methods. Since the generalized DBIT method for FWI in anisotropic elastic media is naturally target-oriented, it may be particularly suitable for applications to seismic reservoir characterization and monitoring. However, the theory and method presented here is general.     

Numerical Modeling of Anisotropic Elastic-Wave Sensitivity Propagation for Optimal Design of Time-Lapse Seismic Surveys

Reliable subsurface time-lapse seismic monitoring is crucial for many geophysical applications, such as enhanced geothermal system characterization, geologic carbon utilization and storage, and conventional and unconventional oil/gas reservoir characterization, etc. We develop an elastic-wave sensitivity propagation method for optimal design of cost-effective time-lapse seismic surveys considering the fact that most of subsurface geologic layers and fractured reservoirs are anisotropic instead of isotropic. For anisotropic media, we define monitoring criteria using qP- and qS-wave sensitivity energies after decomposing qP- and qS-wave components from the total elastic-wave sensitivity wavefield using a hybrid time- and frequency-domain approach. Geophones should therefore be placed at locations with significant qP- and qS-wave sensitivity energies for cost-effective time-lapse seismic monitoring in an anisotropic geology setting. Our numerical modeling results for a modified anisotropic Hess model demonstrate that, compared with the isotropic case, subsurface anisotropy changes the spatial distributions of elastic-wave sensitivity energies. Consequently, it is necessary to consider subsurface anisotropies when designing the spatial distribution of geophones for cost-effective time-lapse seismic monitoring. This finding suggests that it is essential to use our new anisotropic elastic-wave sensitivity modeling method for optimal design of time-lapse seismic surveys to reliably monitor the changes in subsurface reservoirs, fracture zones or target monitoring regions.     

A Nearly Analytical Discrete Method for Wave-Field Simulations in 2D Porous Media

The nearly analytic discrete method (NADM) is a perturbation method originally proposed by Yang et al. (2003) [26] for acoustic and elastic waves in elastic media. This method is based on a truncated Taylor series expansion and interpolation approximations and it can suppress effectively numerical dispersions caused by the discretizating the wave equations when too-coarse grids are used. In the present work, we apply the NADM to simulating acoustic and elastic wave propagations in 2D porous media. Our method enables wave propagation to be simulated in 2D porous isotropic and anisotropic media. Numerical experiments show that the error of the NADM for the porous case is less than those of the conventional finite-difference method (FDM) and the so-called Lax-Wendroff correction (LWC) schemes. The three-component seismic wave fields in the 2D porous isotropic medium are simulated and compared with those obtained by using the LWC method and exact solutions. Several characteristics of wave propagating in porous anisotropic media, computed by the NADM, are also reported in this study. Promising numerical results illustrate that the NADM provides a useful tool for large-scale porous problems and it can suppress effectively numerical dispersions.     

Heat Jet Approach for Atomic Simulations at Finite Temperature

In this paper, we propose a heat jet approach for atomic simulations at finite temperature. Thermal fluctuations are injected into an atomic subsystem from its boundaries, without modifying the governing equations for the interior domain. More precisely, we design a two way local boundary condition, and take the incoming part of a phonon representation for thermal fluctuation input. In this way, non-thermal wave propagation simulations are effectively performed at finite temperature. We further apply this approach to nonlinear chains with the Morse potential. Chains with model parameters fitted to carbon and gold are simulated at room temperature with fidelity.     

A Bipolar-Bisection Piecewise Encoding Scheme for Multi-Source Reverse Time Migration

Conventional shot-record reverse time migration (RTM) suffers from a high computational burden when dealing with massive data. The computational cost of RTM can be reduced by shot-encoding techniques, and plane-wave encoding is a commonly used and effective shot-encoding scheme. However, plane-wave encoding requires long time padding to avoid information loss, which decreases the efficiency of the time-domain wavefield extrapolator, and the time padding becomes longer with the increasing distance between multiple sources. The piecewise plane-wave encoding scheme cuts multiple sources into several segments prior to implementing plane-wave encoding, hence reduces the time padding, but brings new crosstalk due to the mutual interference between shots in different source segments. We suppress the crosstalk artifacts by a new bipolar-bisection amplitude encoding method, in which half of the encoding array of each migration is different from that of any other migrations to reduce the number of crosstalk terms with as few migrations as possible. We embed the bipolar-bisection method into piecewise plane-wave encoding. Compared with plane-wave encoding, the proposed scheme requires considerably shorter time padding and thus works more efficiently and can generate a qualified imaging result. The feasibility of the proposed method is tested on the 2D SEG/EAGE salt model and the Marmousi model.     

温敏型液态氟碳纳米粒声致相变及体外超声显像

目的制备一种脂质包裹液态氟碳(PFP)的新型温敏型纳米粒(HSNP),观察其于加热和低强度聚焦超声(LIFU)辐照下的相变情况,体外检测其超声显影效果。方法采用薄膜分散法制备包裹PFP的HSNP。检测其物理性质;光镜下观察HSNP加热下的相变情况;制备内含HSNP高分子聚丙烯酰胺凝胶模型,同时建立含磷酸盐缓冲液(PBS)和脂质悬液的凝胶模型作为对照,观察LIFU辐照后凝胶模型的超声显影效果。结果成功制备包裹PFP的HSNP,其外观呈乳白色混悬液,镜下微球大小均一,形态规则,平均粒径(507.9±101.7)nm,平均电位(-5.87±4.41)mV。HSNP于45℃时开始转变为微气泡,随温度升高气泡随之增多增大。LIFU辐照前,基波和谐波下含PBS和脂质悬液凝胶模型呈无回声,含HSNP凝胶模型基波和谐波呈无回声为主伴散在点状高回声,LIFU辐照后,含PBS和脂质悬液凝胶模型基波下呈散在点状高回声,谐波下未见明显改变,含HSNP凝胶模型基波下呈密集点状强回声,谐波下呈细密点线状高回声;辐照后含HSNP凝胶模型平均超声灰度值(161.13±2.74)明显高于含PBS(24.09±2.38)和脂质悬液(25.03±2.50)凝胶模型(P均0.05)。结论本研究制备包裹PFP的HSNP为新型超声造影剂,可声致相变,体外可实现增强超声显影。     

Q Inversion and Comparison of Influential Factors among Three Methods: CFS,SR, and AA

The goals of this study were to examine factors influencing Q inversion and to provide references for practical application. Three different methods for inverting Q values with VSP data were explored, including centroid frequency shift (CFS), spectral ratio (SR), and amplitude attenuation (AA). Comparison between the CFS and the other two methods was conducted on frequency band widths and low attenuation, wavefield components, interface interference, and thin layers. Results from several sets of VSP modeling data indicated that the CFS method is more stable and accurate for dealing with thin and high Q layers. Frequency band width, especially the presence of high frequencies, influences the inversion effect of all three methods. The wider the band, the better the results. Q inversion from downgoing wavefield was very similar to that of the upgoing wavefield. The CFS method had fewer outliers or skip values from the full wavefield than the other two methods. Moreover, the applications to Q inversion for the set of field VSP data demonstrated that the Q curves from the CFS method coincided with the geological interpretations better than the Q curves of the other methods. Meanwhile, inverse Q filtering shifted the frequency component from 25 Hz to 35 Hz. The results demonstrated that the Q curve is more sensitive to geological horizons than velocity.     

Contrast-enhanced colour Doppler ultrasonography in suspected breast cancer recurrence.

BACKGROUND: Postoperative scarring and radiotherapy changes in the conservatively treated breast often mimic breast cancer recurrence, resulting in many unnecessary biopsies. Local breast cancer recurrence may be detected more accurately with contrast-enhanced colour Doppler imaging. METHODS: Fifty-eight women with suspected local breast cancer recurrence were evaluated prospectively by means of conventional and contrast-enhanced colour Doppler imaging before surgical biopsy. RESULTS: Sensitivity for the detection of breast cancer recurrence using contrast enhancement was 94 per cent (specificity 67 per cent). Contrast enhancement significantly increased overall diagnostic accuracy, from 80 to 90 per cent (P < 0. 04). CONCLUSION: Contrast-enhanced colour Doppler imaging is a highly accurate method for detecting local breast cancer recurrence. Its adoption may substantially reduce biopsy rates.     

A Preconditioned 3-D Multi-Region Fast Multipole Solver for Seismic Wave Propagation in Complex Geometries

The analysis of seismic wave propagation and amplification in complex geological structures requires efficient numerical methods. In this article, following up on recent studies devoted to the formulation, implementation and evaluation of 3D single- and multi-region elastodynamic fast multipole boundary element methods (FM-BEMs), a simple preconditioning strategy is proposed. Its efficiency is demonstrated on both the single- and multi-region versions using benchmark examples (scattering of plane waves by canyons and basins). Finally, the preconditioned FM-BEM is applied to the scattering of plane seismic waves in an actual configuration (alpine basin of Grenoble, France), for which the high velocity contrast is seen to significantly affect the overall efficiency of the multi-region FM-BEM.     

Preface

Ru-Shan Wu is a special scientist who has made tremendous contributions in many fields of geophysics that he has worked on and has had strong impact on several generations of scientists throughout the world. He is appreciated for his contributions to science and for his generous, outgoing and happy personality that make him a role model for those who follow in his footsteps. Ru-Shan has sustained high-quality scientific output over the course of his long career. His work is widely recognized for its value and creativity. He has keen insight into the underlying physics of wave propagation and he continues to successfully transform that insight into fundamental advances in our understanding of wave propagation and imaging.     

Numerical Methods for Two-Fluid Dispersive Fast MHD Phenomena

The finite volume wave propagation method and the finite element RungeKutta discontinuous Galerkin (RKDG) method are studied for applications to balance laws describing plasma fluids. The plasma fluid equations explored are dispersive and not dissipative. The physical dispersion introduced through the source terms leads to the wide variety of plasma waves. The dispersive nature of the plasma fluid equations explored separates the work in this paper from previous publications. The linearized Euler equations with dispersive source terms are used as a model equation system to compare the wave propagation and RKDG methods. The numerical methods are then studied for applications of the full two-fluid plasma equations. The two-fluid equations describe the self-consistent evolution of electron and ion fluids in the presence of electromagnetic fields. It is found that the wave propagation method, when run at a CFL number of 1, is more accurate for equation systems that do not have disparate characteristic speeds. However, if the oscillation frequency is large compared to the frequency of information propagation, source splitting in the wave propagation method may cause phase errors. The Runge-Kutta discontinuous Galerkin method provides more accurate results for problems near steady-state as well as problems with disparate characteristic speeds when using higher spatial orders.     

Forward Scattering and Volterra Renormalization for Acoustic Wavefield Propagation in Vertically Varying Media

We extend the full wavefield modeling with forward scattering theory and Volterra Renormalization to a vertically varying two-parameter (velocity and density) acoustic medium. The forward scattering series, derived by applying Born-Neumann iterative procedure to the Lippmann-Schwinger equation (LSE), is a well known tool for modeling and imaging. However, it has limited convergence properties depending on the strength of contrast between the actual and reference medium or the angle of incidence of a plane wave component. Here, we introduce the Volterra renormalization technique to the LSE. The renormalized LSE and related Neumann series are absolutely convergent for any strength of perturbation and any incidence angle. The renormalized LSE can further be separated into two sub-Volterra type integral equations, which are then solved non-iteratively. We apply the approach to velocity-only, density-only, and both velocity and density perturbations. We demonstrate that this Volterra Renormalization modeling is a promising and efficient method. In addition, it can also provide insight for developing a scattering theory-based direct inversion method.