《CT理论与应用研究》杂志新刊标和地幔速度模型的说明

在《CT理论与应用研究》杂志1994－2001年本杂志“刊标”的基础上，在其上方增加象征三维体视学成像的三角形四面体的透视图：该刊标的右下侧为医学断面成像扫描仪（包括各种X－CT机与核磁共振MRI扫描仪等）：其左下侧为三维地幔速度模型和地球核的示意图，切出有两个地幔剖面，表示纵波速度二维变化的剖面。该速度剖面系根据赵大鹏教授的理论和计算方法，按照地球上的两个大圆弧做计算和绘制的彩色图，排在本期封4：第一大圆弧，从北极经西巴基斯坦（28°N，64°E）到马尔代夫群岛（3°N，73°E）；第二大圆弧，从马尔代夫群岛点（3°N，73°E）连接巴布新几内亚之南点（12°S，150°E），来计算两速度分布并作图的结果，其具体分布参见封4的两条彩色剖面和相应的地理位置图。由于赵教授这篇论文^[1]在中国国内只有很少数图书馆收藏，在Elsevier Science的EPSL网站上一般人只能查到摘要，本刊对于该地幔速度模型的制作方法和所用数据资料，该模型的优越性和特征进行了叙述，他所用的地震事件数目，多达7128个；用于层析反演成像的震相到时数多到近一百万条。该速度模型具有如下的特点：在所采用的速度结构中，包含用几个复杂形状的地质速度界面，如莫霍面，以及下沉板块的分界面，并给有三维的速度变化；提出一组三维网格，用以表示地下速度的三维结构。其中任何一点的速度变动，系由它周围8个节点上的速度变动经过线性内插来计算的。提出精确而快速地计算走时和射线路径的方法，即高效率的三维射线追踪技术，在射线追踪当中，计入了地震台的海拔高度，等等。这种层析成像方法，已在许多国家和各种大地构造环境中被引用。在网站上，他这篇文章在2001年被下载得最多。

当量和爆高(埋深)反演的声震分析方法

从声学模型、地震波模型和数据融合算法等3个方面系统介绍了当量和爆高(埋深)反演的声震分析方法最新成果:声学模型方面,介绍了半经验声学模型和全波形反演方法的进展,对已有声学模型进行了总结归纳,对比分析了各种模型的特点;地震波模型方面,基于地震波传播路径分为前驱地震波模型和声耦合地震波模型,分别对其进展和特点进行了介绍;数据融合算法方面,对已有的数据融合算法进行了总结归纳,对比分析了各种数据融合算法的特点和进展情况。最后,对声震分析方法进行了总结和展望。

Converted-wave Seismology in Anisotropic Media Revisited, Part I： Basic Theory

We have developed new basic theories for calculating the conversion point and the travel time of the P-SV converted wave (C-wave) in anisotropic, inhomogeneous media. This enables the use of conventional procedures such as semblance analysis, Dix-type model building and Kirchhoff summation, to implement anisotropic processing, and makes anisotropic processing affordable. Here we present these new developments in two parts: basic theory and application to velocity analysis and parameter estimation. This part deals with the basic theory, including both conversion-point calculation and moveout analysis.Existing equations for calculating the PS-wave (C-wave) conversion point in layered media with vertical transverse isotropy (VTI) are strictly limited to offsets about half the reflector depth (an offset-depth ratio, x/z, of 0.5), and those for calculating the C-wave traveltimes are limited to offsets equal to the reflector depth (x/z=1.0). In contrast, the new equations for calculating the conversion-point extend into offsets about three-times the reflector depth (x/z=3.0), those for calculating the C-wave traveltimes extend into offsets twice the reflector depth (x/z=2.0). With the improved accuracy, the equations can help in C-wave data processing and parameter estimation in anisotropic, inhomogeneous media.

Propagation and attenuation of P-waves in patchy saturated porous media

We establish a patchy saturation model and derive the seismic wave equations for patchy saturated porous media on the basis of Biot＇s equations and Johnson＇s bulk modulus. We solve the equations, obtain the attenuation coefficients, and analyze the characteristics of wave attenuation in the seismic frequency range. The results suggest that seismic waves show attenuation and dispersion in partially saturated rocks in the low frequency range. With frequency increasing, attenuation increases. The attenuation of P-waves of the second kind is more pronounced in agreement with Biot＇s theory. We also study the effect of porosity, saturation, and inner sphere radius on the attenuation of the P-waves of the first kind and find that attenuation increases with increasing frequency and porosity, and decreases with increasing frequency and degree of saturation. As for the inner sphere radius, wave attenuation is initially increasing with increasing frequency and inner sphere radius less than half the outer radius. Subsequently, wave attenuation decreases with increasing frequency and inner sphere radius is higher than half the outer sphere radius.

The Precise Finite Difference Method for Seismic Modeling

D seismic modeling can be used to study the propagation of seismic wave exactly and it is also a tool of 3-D seismic data processing and interpretation. In this paper the arbitrary difference and precise integration are used to solve seismic wave equation, which means difference scheme for space domain and analytic integration for time domain. Both the principle and algorithm of this method are introduced in the paper. Based on the theory, the numerical examples prove that this hybrid method can lead to higher accuracy than the traditional finite difference method and the solution is very close to the exact one. Also the seismic modeling examples show the good performance of this method even in the case of complex surface conditions and complicated structures.

Study on Dynamic Response of the “Dualistic” Structure Rock Slope with Seismic Wave Theory

Currently, scant attention has been paid to the theoretical analysis on dynamic response mechanism of the ＂Dualistic＂ structure roek slope. The analysis presented here provides insight into the dynamic response of the ＂Dualistie＂ structure rock slope. By investigating the principle of energy distribution, it is shown that the effect of a joint plays a significant role in slope stability analysis. A dynamic reflection and transmission model （RTM） for the ＂Dualistic＂ structure rock slope and explicit dynamic equations are established to analyze the dynamic response of a slope, based on the theory of elastic mechanics and the principle of seismic wave propagation. The theoretical simulation solutions show that the dynamic response of the ＂Dualistic＂ structure rock slope （soft-hard） model is greater than that of the ＂Dualistic＂ strueture rock slope （hard-soft） model, especially in the slope crest. The magnifying effect of rigid foundation on the dynamic response is more obvious than that of soft foundation. With the amplitude increasing, the cracks could be found in the right slope （soft-hard） crest. The crest failure is firstly observed in the right slope （soft-hard） during the experimental process. The reliability of theoretical model is also investigated by experiment analysis. The conclusions derived in this paper could also be used in future evaluations of Multi-layer rock slopes.

Converted-wave Seismology in Anisotropic Media Revisited, Part II: Application to Parameter Estimation

In transversely isotropic media with a vertical symmetry axis （VTI）, the converted-wave （C-wave） moveout over intermediate-to-far offsets is determined by four parameters. These are the C-wave stacking velocity Vc2 , the vertical and effective velocity ratios γ0 and γeff, and the anisotropic parameter χeff. We refer to the four parameters as the C-wave stacking velocity model. The purpose of C-wave velocity analysis is to determine this stacking velocity model. The C-wave stacking velocity model Vc2, γ0, γeff, and χeff can be determined from P-and C-wave reflection moveout data. However, error propagation is a severe problem in C-wave reflection-moveout inversion. The current short-spread stacking velocity as deduced from hyperbolic moveout does not provide sufficient accuracy to yield meaningful inverted values for the anisotropic parameters. The non-hyperbolic moveout over intermediate-offsets （x/z from 1.0 to 1.5） is no longer negligible and can be quantified using a background γ. Non-hyperbolic analysis with a γ correction over the intermediate offsets can yield Vc2 with errors less than 1% for noise free data. The procedure is very robust, allowing initial guesses of γ with up to 20% errors. It is also applicable for vertically inhomogeneous anisotropic media. This improved accuracy makes it possible to estimate anisotropic parameters using 4C seismic data. Two practical work flows are presented for this purpose： the double-scanning flow and the single-scanning flow. Applications to synthetic and real data show that the two flows yield results with similar accuracy but the single-scanning flow is more efficient than the double-scanning flow.

Influence of Structure Plane Size on Seismic Response of Soil-Structure Interaction

The influence of the change of structure plane size on seismic response was studied for a soil-structure interaction system.Based on the finite element method,a soil-structure interaction calculation model was established to analyze the seismic response by changing the structure plane size and choosing different earthquake waves for different soil fields.The results show that when the natural periods of vibration for different structure plane sizes are close,under the same earthquake wave,the total displacement on the top layer of the structure and the foundation rotation displacement decrease with the increase of structure plane size,and the proportion of superstructure elastic selfdeformation displacement to the total displacement increases with the increase of structure plane size.While for different types of sites and seismic waves,under the horizontal and vertical seismic waves,the seismic responses of different plane sizes have a similar change rule.

Modeling seismic wave propagation in a coal-bearing porous medium by a staggered-grid finite difference method

A staggered-grid finite difference method is used to model seismic wave records in a coal bearing, porous medium. The variables analyzed include the order of the difference calculations, the use of a perfect match layer to provide absorbing boundary conditions, the source location, the stability conditions, and dispersion in the medium. The results show that the location of the first derivative of the dynamic variable with respect to space is coincident with the location of the first derivative of the kinematic varable with respect to time. Outgoing waves are effectively absorbed and reflection at the boundary is very weak when more than 20 perfect match layer cells are used. Blot theory considers the liquid phase to be homogeneous so the ratio of liquid to solid exposure of the seismic source depends upon the medium porosity. Numerical dispersion and generation of false frequencies is reduced by increasing the accuracy of the difference calculations and by reducing the grid size and time step. Temporal second order accuracy, a tenth order spatial accuracy, and a wavelength over more than ten grid points gave acceptable numerical results. Larger grid step sizes in the lateral direction and smaller grid sizes in the vertical direction allow control of dispersion when the medium is a low speed body. This provides a useful way to simulate seismic waves in a porous coal bearing medium.

Theoretical Error Analysis of the Accuracy of Focal Depth Determination of Near Earthquakes

Focal depth is one of the most difficult seismic parameters to determine accurately in seismology. The focal depths estimated by various methods are uncertain to a considerable degree, which affects the understanding of the source process. The influence of various factors on focal depth is non-linear. The influence of epicentral distance, arrival time residual and velocity model （crust model） on focal depth is analyzed based on travel time formula of near earthquakes in this paper. When wave propagation velocity is constant, the error of focal depth increases with the increase of epicentral distance or the distance to station and the travel time residual. When the travel time residual is constant, the error of focal depth increases with the increase of the epicentral distance and the velocity of seismic wave. The study also shows that the location error perhaps becomes bigger for shallower earthquakes when the velocity is known and the travel time residual is constant. The horizontal error caused by location accuracy increases with the increase of the epieentrai distance, the travel time residual and the velocity of seismic waves, thus the error of focal depth will increase with these factors. On the other hand, the errors of focal depth will lead to change of the origin time, therefore resultant outcomes will all change.

Near-surface model reconstruction using pseudo well-surface simultaneous travel time tomographic inversion

The static correction of a near-surface model may be improved by using travel time tomographic inversion.We discuss unfavorable factors in the inversion of surface seismic waves that have been analyzed by the first break.These factors show that sources and geophones arranged on the surface,or close to the surface,give a first break that only includes the direct wave and the up going wave from the down going to up going transition.These up going waves have weak directivity when they arrive at a geophone and so the rays passing through the grids have small directional differences and a narrow azimuth.Drawing lessons from the advantages of Vertical Seismic Profiling(VSP) acquisition mode we describe a pseudo well-surface simultaneous travel time tomographic inversion of a near-surface model.The well depth should be increased in the surface seismic study to produce a pure up going wave,to enhance the verticality of the rays and to increase the azimuth and shorten path length of the rays.Simulations of the effect of well depth on a pseudo well-surface simultaneous travel time tomographic inversion model are reported.The results show that the static corrections are improved significantly when the well depth extends below the weathered or sub-weathered layers.The root mean square error of the statics is 1.14 or 0.93 ms for these two situations,respectively.

Seismic to Reservoir Simulation by Cooperative Inversion

Cooperative inversion for petroleum reservoir characterization produces an Earth model that fits all available geological, geophysical and reservoir production data to within acceptable error criteria. The mathematical formulation for the inversion requires an appropriate modeling description of both seismic wave propagation and reservoir fluid flow. The inversion requires the minimization of an objective function which is the weighted sum of model misfits for both geophysical and production data. While the complete automation of cooperative inversion may be unrealistic or intractable, geophysical data can provide useful information for enhancing heavy oil production. A methodology is given to demonstrate possible cooperative inversion application in heavy oil reservoirs.

Seismic wave scattering inversion for fluid factor of heterogeneous media

Elastic wave inverse scattering theory plays an important role in parameters estimation of heterogeneous media.Combining inverse scattering theory,perturbation theory and stationary phase approximation,we derive the P-wave seismic scattering coefficient equation in terms of fluid factor,shear modulus and density of background homogeneous media and perturbation media.With this equation as forward solver,a pre-stack seismic Bayesian inversion method is proposed to estimate the fluid factor of heterogeneous media.In this method,Cauchy distribution is utilized to the ratios of fluid factors,shear moduli and densities of perturbation media and background homogeneous media,respectively.Gaussian distribution is utilized to the likelihood function.The introduction of constraints from initial smooth models enhances the stability of the estimation of model parameters.Model test and real data example demonstrate that the proposed method is able to estimate the fluid factor of heterogeneous media from pre-stack seismic data directly and reasonably.

Identification of the nonlinear properties of rubber-bearings in base-isolated buildings with limited seismic response data

Seismic behaviors of base-isolated structures are highly affected by the nonlinear characteristics of the isolated systems. Most of the currently available methods for the identification of nonlinear properties of isolator require either the measurements of all structural responses or the assumptions of the proper mathematic models for the rubber-bearings. In this paper, two algorithms are proposed to identify the nonlinear properties of rubber-bearings in base-isolated buildings using only partial measurements of structural dynamic responses. The first algorithm is applicable to the case that proper mathematical models are available for the base isolators. It is based on the extended Kalman filter for the parametric identification of nonlinear models of rubber-bearing isolators and buildings. For the general case where it is difficult to establish a proper mathematical model to describe the nonlinear behavior of a rubber-bearing isolator, another algorithm is proposed to identify the model-tYee nonlinear property of rubber-bearing isolated system. Nonlinear effect of rubber-bearing is treated as ＇fictitious loading＇ on the linear building under severe earthquake. The algorithm is based on the sequential Kalman estimator for the structural responses and the least-squares estimation of the ＇fictitious loading＇ to identify the nonlinear force of rubber-bearing isolator. Simulation results demonstrate that the proposed two algorithms are capable of identifying the nonlinear properties of rubber-bearing isolated systems with good accuracy.