Accurate simulations of pure-viscoacoustic wave propagation in tilted transversely isotropic media

Forward modeling of seismic wave propagation is crucial for the realization of reverse time migration(RTM) and full waveform inversion(FWI) in attenuating transversely isotropic media. To describe the attenuation and anisotropy properties of subsurface media, the pure-viscoacoustic anisotropic wave equations are established for wavefield simulations, because they can provide clear and stable wavefields. However, due to the use of several approximations in deriving the wave equation and the introduction of a fractional Laplacian approximation in solving the derived equation, the wavefields simulated by the previous pure-viscoacoustic tilted transversely isotropic(TTI) wave equations has low accuracy. To accurately simulate wavefields in media with velocity anisotropy and attenuation anisotropy, we first derive a new pure-viscoacoustic TTI wave equation from the exact complex-valued dispersion formula in viscoelastic vertical transversely isotropic(VTI) media. Then, we present the hybrid finite-difference and low-rank decomposition(HFDLRD) method to accurately solve our proposed pure-viscoacoustic TTI wave equation. Theoretical analysis and numerical examples suggest that our pure-viscoacoustic TTI wave equation has higher accuracy than previous pure-viscoacoustic TTI wave equations in describing q P-wave kinematic and attenuation characteristics. Additionally, the numerical experiment in a simple two-layer model shows that the HFDLRD technique outperforms the hybrid finite-difference and pseudo-spectral(HFDPS) method in terms of accuracy of wavefield modeling.

Overview of computation strategies on the dispersion analysis for explicit finite difference solution of acoustic wave equation

Finite-difference(FD)method is the most extensively employed numerical modeling technique.Nevertheless,when using the FD method to simulate the seismic wave propagation,the large spatial or temporal sampling interval can lead to dispersion errors and numerical instability.In the FD scheme,the key factor in determining both dispersion errors and stability is the selection of the FD weights.Thus,How to obtain appropriate FD weights to guarantee a stable numerical modeling process with minimum dispersion error is critical.The FD weights computation strategies can be classified into three types based on different computational ideologies,window function strategy,optimization strategy,and Taylor expansion strategy.In this paper,we provide a comprehensive overview of these three strategies by presenting their fundamental theories.We conduct a set of comparative analyses of their strengths and weaknesses through various analysis tests and numerical modelings.According to these comparisons,we provide two potential research directions of this field:Firstly,the development of a computational strategy for FD weights that enhances stability;Secondly,obtaining FD weights that exhibit a wide bandwidth while minimizing dispersion errors.

An amplitude-preserved adaptive focused beam seismic migration method

Gaussian beam migration （GBM） is an effec- tive and robust depth seismic imaging method, which overcomes the disadvantage of Kirchhoff migration in imaging multiple arrivals and has no steep-dip limitation of one-way wave equation migration. However, its imaging quality depends on the initial beam parameters, which can make the beam width increase and wave-front spread with the propagation of the central ray, resulting in poor migration accuracy at depth, especially for exploration areas with complex geological structures. To address this problem, we present an adaptive focused beam method for shot-domain prestack depth migration. Using the infor- mation of the input smooth velocity field, we first derive an adaptive focused parameter, which makes a seismic beam focused along the whole central ray to enhance the wave- field construction accuracy in both the shallow and deep regions. Then we introduce this parameter into the GBM, which not only improves imaging quality of deep reflectors but also makes the shallow small-scale geological struc- tures well-defined. As well, using the amplitude-preserved extrapolation operator and deconvolution imaging condi- tion, the concept of amplitude-preserved imaging has been included in our method. Typical numerical examples and the field data processing results demonstrate the validity and adaptability of our method.

2D Q-compensated multi-component elastic Gaussian beam migration

Elastic waves are affected by viscoelasticity during the propagation through the Earth,resulting in energy attenuation and phase distortion,in turn resulting in low seismic imaging accuracy.Therefore,viscoelasticity should be considered in seismic migration imaging.We propose a Q compensated multicomponent elastic Gaussian beam migration(Q-EGBM)method to(1)separate the elastic-wave data into longitudinal(P)and transverse(S)waves to perform PP-wave and PS-wave imaging;(2)recover the amplitude loss caused by attenuation;(3)correct phase distortions caused by dispersion;(4)improve the resolution of migration imaging.In this paper,to accomplish(2),(3),and(4),we derive complex-valued traveltimes in viscoelastic media.The results of numerical experiments using a simple five-layer model and a sophisticated BP gas model show that the method presented here has significant advantages in recovering energy decay and correcting phase distortion,as well as significantly improving imaging resolution.

A fast space-time-domain Gaussian beam migration approach using the dominant frequency approximation

The Gaussian beam migration(GBM) is a steady imaging approach, which has high accuracy and efficiency. Its implementation mainly includes the traditional frequency domain and the recent popular space-time domain. Firstly, we use the upward ray tracing strategy to get the backward wavefields. Then,we use the dominant frequency of the seismic data to simplify the imaginary traveltime calculation of the wavefields, which can cut down the Fourier transform number compared with the traditional GBM in the space-time domain. In addition, we choose an optimized parameter for the take-off angle increment of the up-going and down-going rays. These optimizations help us get an efficient space-time-domain acoustic GBM approach. Typical four examples show that the proposed method can significantly improve the computational efficiency up to one or even two orders of magnitude in different models with different model parameters and produce good imaging results with comparable accuracy and resolution with the traditional GBM in the space-time domain.

Simultaneous determination of chlorogenic acid and baicalin in heat-clearing and detoxicating oral liquid by NIRS

The calibration model for simultaneous deter-mination of chlorogenic acid and baicalin in heat-clearing and detoxicating oral liquid was built by partial least squares and near infrared spectroscopy, and the method of spectral pre-treatment was discussed. Building model from calibration set obtained good results, and vali-dated by prediction. According to heat-clearing and detoxicating oral liquid from 30 batches of 6 factories, the correlation coefficient of chloro-genic acid and baicalin model are 0.9993 and 0.9923, The root mean square error of cross validation (RMSECV) are 0.467 and 0.480, and the standard Error of prediction (SEP) of chloro- genic acid and baicalin are 0.356 and 0.370 re-spectively. The correlation coefficients in pre-diction set are 0.9997 and 0.9969, prediction results are accurate and reliable. This method can be applied in rapid analysis of heat- clearing and detoxicating oral liquid, and it is fit for on-line detection and has a wide application prospect.

Extracting angle-domain common-image gathers in VTI media using ansiotropic-Helmholtz P/S wave-mode decomposition

Common-image gathers are extensively used in amplitude versus angle(AVA)and migration velocity analysis(MVA).The current state of methods for anisotropic angle gathers extraction use slant-stack,local Fourier transform or low-rank approximation,which requires much computation.Based on an anisotropic-Helmholtz P/S wave-mode decomposition method,we propose a novel and efficient approach to produce angle-domain common-image gathers(ADCIGs)in the elastic reverse time migration(ERTM)of VTI media.To start with,we derive an anisotropic-Helmholtz decomposition operator from the Christoffel equation in VTI media,and use this operator to derive the decomposed formulations for anisotropic P/S waves.Second,we employ the first-order Taylor expansion to calculate the normalized term of decomposed formulations and obtain the anisotropic-Helmholtz decomposition method,which generates the separated P/S wavefields with correct amplitudes and phases.Third,we develop a novel way that uses the anisotropic-Helmholtz decomposition operator to define the polari-zation angles for anisotropic P/S waves and substitute these angles to decomposing formulations.The polarization angles are then calculated directly from the separated vector P-and S-wavefields and converted to the phase angles.The ADCIGs are thusly produced by applying the phase angles to VTI ERTM.In addition,we develop a concise approximate expression of residual moveout(RMO)for PP-reflections of flat reflectors in VTI media,which avoids the complex transformations between the group angles and the phase angles.The approximate RMO curves show a good agreement with the exact solution and can be used as a tool to assess the migration velocity errors.As demonstrated by two selected examples,our ADCIGs not only produce the correct kinematic responses with regards to different velocity pertubatation,but also generate the reliable amplitude responses versus different angle.The final stacking images of ADCIGs data exhibit the identical imaging effect as that of VTI ERTM.

A computational method for wide-azimuth 3D dip-angle gathers using Gaussian beam migration

The dip-angle-domain common-image gather(DDCIG)is a key tool to separate the diffraction and reflection imaging results.Reflectors with different spatial geometries produce different responses in DDCIGs.Compared with Kirchhoff migration,Gaussian beam migration(GBM)is more effective and robust to overcome the multipathing problem.As a ray-based method,it has explicit angle information naturally during the propagation.We have developed a 3D DDCIG computational method using GBM,which obtain both the imaging result and angle-domain gathers with only one pass of calculation.The angle-gather computation is based on geometrical optics,and multiple angle conversions are implemented under the rules of space geometry,which helps to avoid rounding errors and improve accuracy.Additionally,the multi-azimuth joint presentation strategy is proposed to describe the characteristic of omnidirectional dip angles using a finite number of gathers.After using a 2D model to illustrate application advantages of DDCIG,we apply the proposed method to two 3D models to test its feasibility and accuracy.A field data example further demonstrates the adaptability of our method to seismic imaging for a land survey.