The analysis and application of simplified two-parameter moveout equation for C-waves in VTI anisotropy media

Several parameters are needed to describe the converted-wave （C-wave） moveout in processing multi-component seismic data, because of asymmetric raypaths and anisotropy. As the number of parameters increases, the converted wave data processing and analysis becomes more complex. This paper develops a new moveout equation with two parameters for C-waves in vertical transverse isotropy （VTI） media. The two parameters are the C-wave stacking velocity （Vc2） and the squared velocity ratio （7v,i） between the horizontal P-wave velocity and C-wave stacking velocity. The new equation has fewer parameters, but retains the same applicability as previous ones. The applicability of the new equation and the accuracy of the parameter estimation are checked using model and real data. The form of the new equation is the same as that for layered isotropic media. The new equation can simplify the procedure for C-wave processing and parameter estimation in VTI media, and can be applied to real C-wave processing and interpretation. Accurate Vc2 and Yvti can be deduced from C-wave data alone using the double-scanning method, and the velocity ratio model is suitable for event matching between P- and C-wave data.     

基于虚拟偏移距方法的各向异性转换波保幅叠前时间偏移

In this paper, we use the method of pseudo-offset migration （POM） to complete converted wave pre-stack time migration with amplitude-preservation in an anisotropic medium. The method maps the original traces into common conversion scatter point （CCSP） gathers directly by POM, which simplifies the conventional processing procedure for converted waves. The POM gather fold and SNR are high, which is favorable for velocity analysis and especially suitable for seismic data with low SNR. We used equivalent anisotropic theory to compute anisotropic parameters. Based on the scattering wave traveltime equation in a VTI medium, the POM pseudo-offset migration in anisotropic media was deduced. By amplitude-preserving POM gather mapping, velocity analysis, stack processing, and so on, the anisotropic migration results were acquired. The forward modeling computation and actual data processing demonstrate the validity of converted wave pre-stack time migration with amplitude-preservation using the anisotropic POM method.     

Estimation of Thomsen＇s anisotropic parameters from walkaway VSP and applications

Estimation of Thomsen＇s anisotropic parameters is very important for accuratetime-to-depth conversion and depth migration data processing. Compared with othermethods, it is much easier and more reliable to estimate anisotropic parameters that arerequired for surface seismic depth imaging from vertical seismic profile （VSP） data, becausethe first arrivals of VSP data can be picked with much higher accuracy. In this study, wedeveloped a method for estimating Thomsen＇s P-wave anisotropic parameters in VTImedia using the first arrivals from walkaway VSP data. Model first-arrival travel times arecalculated on the basis of the near-offset normal moveout correction velocity in VTI mediaand ray tracing using Thomsen＇s P-wave velocity approximation. Then, the anisotropicparameters 0 and e are determined by minimizing the difference between the calculatedand observed travel times for the near and far offsets. Numerical forward modeling, usingthe proposed method indicates that errors between the estimated and measured anisotropicparameters are small. Using field data from an eight-azimuth walkaway VSP in TarimBasin, we estimated the parameters 0 and e and built an anisotropic depth-velocity modelfor prestack depth migration processing of surface 3D seismic data. The results showimprovement in imaging the carbonate reservoirs and minimizing the depth errors of thegeological targets.     

—维有耗散波动方程的奇性分析与小波

　Applying the usual technique of linearization to wave equations with strong singularity often produces artifacts, for those terms with strong singularities are omittedfor they are small in magnitude. Using the method of wavelets transform, the main terms in singularities are retained in simplification. So the result is more accurate in a point view of singularity analysis. We have applied the mathod to one-dimensional wave equations in inhomogeneous media, and got the same main terms in singularities as the accurate ones. In this paper, one-dimensional wave equations with dissipations in inhomogeneous media are considered. The method of wavelets analysis is improved,and the same main terms in singularities as the accurate solutions are obtained as well.So we conclude that applying wavelets analysis to singularity simplification is always effective, especially to high-frequency approximation and singularity analysis.     

The study and analysis of floating datum selection for rugged terrain

We analyze the characteristics of different floating datums for static corrections and discuss the methods for determining them. The effect of different floating datum corrections was studied using theoretical model experiments, resulting in the conclusion that the velocity obtained after the floating datum correction with the minimum static correction errors depends on the velocity of the layer below the low velocity layer （LVL） lower boundary and is not related to topographic relief and LVL structure. For the real data processing case, wave equation numerical model experiments were conducted which resulted in a new method for calculating objective functions based on the waveform and modifications to the calculation equation for minimum static correction errors to make the method suitable for real data static correction processing using inhomogeneous velocity models with lower velocity boundary relief. Real data processing results demonstrate the method＇s superiority.     

Analytic solution to the magnetotelluric response over anisotropic medium and its discussion

In the present paper,from the second order partial differential equations for solving the magnetotelluric(MT) fields of general anisotropic medium,we first obtained the second order partial differential equations for some anisotropic media with special conductivity(e.g.diagonal anisotropy,transverse anisotropy,azimuthal anisotropy,etc.) by simplifying the electrical conductivity tensor of anisotropic medium.And then we obtained the analytic solutions to MT fields for the case of transverse and azimuthal anisotropy through converting the conductivity parameter based on that of diagonal anisotropy.We further discussed the influence of the selection of integral limit and step length on precision in solving the analytic solutions for MT fields of isotropic medium.Finally,we presented the MT responses of two transverse and azimuthal anisotropic media as well as some applications of the analytic solutions to MT fields of anisotropic medium.     

弱各向异性介质中的P-SV波近似反射系数计算

We introduce the Thomsen anisotropic parameters into the approximate linear reflection coefficient equation for P-SV wave in weakly anisotropic HTI media. From this we get a new, more effective, and practical reflection coefficient equation. We performed forward modeling to AVO attributes, obtaining excellent results. The combined AVO attribute analysis of PP and PS reflection data can greatly reduce ambiguity, obtain better petrophysical parameters, and improve parameter accuracy.     

Study of elastic wave propagation in two-phase anisotropic media by numerical modeling of pseudospectral method

When there exists anisotropy in underground media, elastic parameters of the observed coordinate possibly do not coincide with that of the natural coordinate. According to the theory that the density of potential energy, dissipating energy is independent of the coordinate, the relationship of elastic parameters between two coordinates is derived for two-phase anisotropic media. Then, pseudospectral method to solve wave equations of two-phase anisotropic media is derived. At last, we use this method to simulate wave propagation in two-phase anisotropic media, four types of waves are observed in the snapshots, i.e., fast P wave and slow P wave, fast S wave and slow S wave. Shear wave splitting, SV wave cusps and elastic wave reflection and transmission are also observed.     

Exact traveltime computation in multi-layered transversely isotropic media with vertical symmetry axis

An approach to calculate the accurate ray paths and traveltimes in multi-layered VTI media (transversely isotropic media with a vertical symmetry axis) is proposed. The expressions of phase velocity, group velocity and Snell’s law used for computation are all explicit and exact. The calculation of ray paths and traveltimes for a given ele-mentary wave is equivalent to that of a transmission problem which is much easier to be treated with the formulae proposed. In the section of numerical examples, the proce...     

Experimental assessment and prediction of temporal scour depth around a spur dike

Spur dikes are river training structures that have been extensively used worldwide for towards enhancing flood control and the stability of embankments and riverbanks.However,scour around spur dikes can be a major problem affecting their stability and hydraulic performance.The precise computation of temporal scour depth at spur dikes is very important for the design of economical and safe spur dikes.This study focuses on experimentally assessing the temporal variation of scour depth around a vertical wall spur dike and identifying the parameters,which mostly influence spur dike performance for a channel bed surface comprised of sand-gravel mixtures.In the current study,the authors did physical experiments in a flume based study to obtain new data,aimed at deriving a new predictive model for spur dike scour and comparing its performance to others found in the literature.It was found that the dimensionless temporal scour depth variation increases with an increase in(i)the threshold velocity ratio,(ii)the densimetric Froude number of the bed surface sediment mixture,(iii)the flow shallowness(defined as the ratio of the approach flow depth,y,to the spur dike’s transverse length,l),and(iv)the flow depth-particle size ratio.It is also concluded that the temporal scour depth variation in the sediment mixture is influenced by the non-uniformity of sediment and decreases with an increase in the non-uniformity of the sediment mixture.A new mathematical model is derived for the estimation of temporal scour depths in sand-gravel sediment mixtures.The proposed equation has been calibrated and validated with the experimental data,demonstrating a good predictive capacity for the estimation of temporal scour depth evolution.     

转换波四参数速度分析方法在k71地区的应用

3-D converted-wave data were acquired using digital MEMS （micro-electromechanical system） three component （3C） sensors in the alternating sand and shale sequence in the overburden of the Shengli Ken-71 area. This gives rise to serious non-hyperbolic moveout effects in the converted-wave data due to both the asymmetrical ray path and anisotropic effects. Conventional velocity analysis and moveout correction based on isotropic methods do not flatten reflections events. Here, we use a four-parameter theory to evaluate these effects and process the data. These four parameters include the PS converted wave stacking velocity （Vc2）, the vertical velocity ratio （Y0）, the effective velocity ratio （Yeff）, and the anisotropy parameter （xoff）, The method utilizes the moveout information at different offsets to estimate the different parameters and ensures that the events are properly aligned for stacking, As a result, this four-parameter theory leads to an improvement in imaging quality and correlation between the P-waves and converted-waves.     

Multimineral optimization processing method based on elemental capture spectroscopy logging

Calculating the mineral composition is a critical task in log interpretation. Elementalcapture spectroscopy （ECS） log provides the weight percentages of twelve common elements,which lays the foundation for the accurate calculation of mineral compositions. Previousprocessing methods calculated the formation composition via the conversion relation betweenthe formation chemistry and minerals. Thus, their applicability is limited and the methodprecision is relatively low. In this study, we present a multimineral optimization processingmethod based on the ECS log. We derived the ECS response equations for calculating theformation composition, then, determined the logging response values for the elements ofcommon minerals using core data and theoretical calculations. Finally, a software modulewas developed. The results of the new method are consistent with core data and the meanabsolute error is less than 10%.     

Characteristics analysis on high density spatial sampling seismic data

China＇s continental deposition basins are characterized by complex geological structures and various reservoir lithologies. Therefore, high precision exploration methods are needed. High density spatial sampling is a new technology to increase the accuracy of seismic exploration. We briefly discuss point source and receiver technology, analyze the high density spatial sampling in situ method, introduce the symmetric sampling principles presented by Gijs J. O. Vermeer, and discuss high density spatial sampling technology from the point of view of wave field continuity. We emphasize the analysis of the high density spatial sampling characteristics, including the high density first break advantages for investigation of near surface structure, improving static correction precision, the use of dense receiver spacing at short offsets to increase the effective coverage at shallow depth, and the accuracy of reflection imaging. Coherent noise is not aliased and the noise analysis precision and suppression increases as a result. High density spatial sampling enhances wave field continuity and the accuracy of various mathematical transforms, which benefits wave field separation. Finally, we point out that the difficult part of high density spatial sampling technology is the data processing. More research needs to be done on the methods of analyzing and processing huge amounts of seismic data.     

Theory and application of equivalent transformation relationships between plane wave and spherical wave

Based on the governing equations and the equivalent models,we propose an equivalent transformation relationships between a plane wave in a one-dimensional medium and a spherical wave in globular geometry with radially inhomogeneous properties.These equivalent relationships can help us to obtain the analytical solutions of the elastodynamic issues in an inhomogeneous medium.The physical essence of the presented equivalent transformations is the equivalent relationships between the geometry and the material properties.It indicates that the spherical wave problem in globular geometry can be transformed into the plane wave problem in the bar with variable property fields,and its inverse transformation is valid as well.Four different examples of wave motion problems in the inhomogeneous media are solved based on the presented equivalent relationships.We obtain two basic analytical solution forms in Examples Ⅰ and Ⅱ,investigate the reflection behavior of inhomogeneous half-space in Example Ⅲ,and exhibit a special inhomogeneity in Example Ⅳ,which can keep the traveling spherical wave in constant amplitude.This study implies that our idea makes solving the associated problem easier.     

Application of the Linearity Method to Processing and Analyzing of Precursory Data

In this paper,the spatial linearity method is applied to synthetical processing of precursory data from different stations and different disciplines.The new characteristic value(a)obtained can describe the whole precursory field.The authors present the formulas for calculating spatial linearity.Furthermore,the spatial linearity method is applied to processing of geoelectrical resistivity and groundwater level data from 1970 to 1994 in North China.The results show that the new characteristic value(a)could detect the anomaly 1 year before moderately strong earthquakes.     

Re-Look to Conventional Techniques for Trapping Efficiency Estimation of a Reservoir

All reservoirs are subjected to sediment inflow and deposition up to a certain extent leading to reduction in their capacity. Thus, the important practical problem related to the life of reservoir is the estimation of sedimentation quantity in the reservoirs. Large number of methods and models are available for estimation of reservoir sedimentation process. However, each model differs greatly in terms of their complexity, inputs and other requirements. In the simplest way, the fraction of sediment deposit in the reservoir can be determined through the knowledge of its trap efficiency. Trap efficiency （Te） is the proportion of the incoming sediment that is deposited or trapped in a reservoir. Most of the Te estimation methods define a relationship of the T, of the reservoir to their capacity and annual inflow, generally through curves. In this study, the empirical relationships given by Brune and Brown were used and compared for estimating the trap efficiency of Gobindsagar Reservoir （Bhakra Dam） on Satluj River in Bilaspur district of Himachal Pradesh, in the Himalayan region of India. A new set of regression equations has been developed for Brune＇s method and compared with Brown and other available Brune＇s equations. It has been found that Brune＇s equations developed in the present study estimated better than the other Brune＇s equations reported in literature. Later, in the present study it was found that Brown＇s approach was over estimating the T,. Hence it was again modified for Gobindsagar reservoir. It was also identified that sediments coming to this particular reservoir were mainly of coarse nature.     

Transient analysis of 1D inhomogeneous media by dynamic inhomogeneous finite element method

The dynamic inhomogeneous finite element method is studied for use in the transient analysis of one dimensional inhomogeneous media. The general formula of the inhomogeneous consistent mass matrix is established based on the shape function. In order to research the advantages of this method, it is compared with the general finite element method. A linear bar element is chosen for the discretization tests of material parameters with two fictitious distributions. And, a numerical example is solved to observe the differences in the results between these two methods. Some characteristics of the dynamic inhomogeneous finite element method that demonstrate its advantages are obtained through comparison with the general finite element method. It is found that the method can be used to solve elastic wave motion problems with a large element scale and a large number of iteration steps.     

完全匹配层在数值模拟孔隙介质声波传播中的应用

The nonsplitting perfectly matched layer （NPML） absorbing boundary condition （ABC） was first provided by Wang and Tang （2003） for the finite-difference simulation of elastic wave propagation in solids. In this paper, the method is developed to extend the NPML to simulating elastic wave propagation in poroelastic media. Biot＇s equations are discretized and approximated to a staggered-grid by applying a fourth-order accurate central difference in space and a second-order accurate central difference in time. A cylindrical twolayer seismic model and a borehole model are chosen to validate the effectiveness of the NPML. The results show that the numerical solutions agree well with the solutions of the discrete wavenumber （DW） method.     

A New Theory of Love Waves in Multi-layered Media with Irregular Interfaces

In this article, we have derived a new and more general formulation of Love waves in arbitrarily irregular multi-layered media by using the global generalized reflection/transmission (abbreviated to R/T thereafter) matrices method developed earlier by Chen [17~20]. From the basic principle that the modal solutions are the non-trivial solutions of the free elastodynamic equation under appropriate boundary conditions, we naturally derived the characteristic frequencies and the corresponding distorted modes of Love wave in irregular multi-layered media. Moreover, we have derived the corresponding excitation formulation of Love waves in such laterally heterogeneous media by using the general solution of elastodynamic equation [17~20]. Similar to the result for laterally homogeneous layered structure, the Love waves radiated from a point source in irregular multi-layered media can be expressed as a superposition of distorted modes. Since the structure model used here is quite arbitrary, it can be used for so