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In this context, the present study aims at comparing an MREbased method combined with a wave equation inversion algorithm to rotational rheometry.


Linearization IllPosedness for 2.5D Wave Equation Inversion Model


The imagingtechnique is derived from s method for waveequation inversion.




 This paper introduces a new procedure for Pwave velocity imaging from reflection seismic data based on integrated inversion techniques. After deconvolution, stacking and migration, interpretors may distinguish the events between primary reflections and other events on a seismic section. Therefore, it is possible to obtain traveltime data and a statistical estimate of the wavelet W(t) from both CSP gathers and zerooffset sections by using an interactive workstation. If the dips of formations in the studied... This paper introduces a new procedure for Pwave velocity imaging from reflection seismic data based on integrated inversion techniques. After deconvolution, stacking and migration, interpretors may distinguish the events between primary reflections and other events on a seismic section. Therefore, it is possible to obtain traveltime data and a statistical estimate of the wavelet W(t) from both CSP gathers and zerooffset sections by using an interactive workstation. If the dips of formations in the studied area are gentle, then the traveltime data T(x, t) can be picked up from common sourcereceiver seismic traces on a stacked seismic section.The traveltime data are insufficient for velocity imaging because there exist infinite solutions which can fit the data. We use both the traveltime and RMS velocity data to construct a joint inversion procedure. The first step in this procedure is to redo velocity analysis which keeps consistence between picked primary reflections and RMS velocity data V(x', t), where x' represents the position of the velocity analysis traces. In order to guarantee the. vertical resolution of velocity imaging, the spacing of the velocity analysis should be less than 21 CDP traces, and depending on the thickness of target layers; the time intervel in the analysis should be less than 21 ms.The second step is joint inversion of traveltime data and RMS velocities for velocity analysis traces, producing intervel velocity and layer thickness via generalized inversion techniques. The equations in the joint inversion procedure can be represented as follows:*=1 wherec1 = interval velocity of the ith layer,Vj = RMS velocity data at time tj,△T1 = T1  T11, the diffirence of traveltimes between adjacent reflectors,δVi = errors in the RMS velocity data.After this equation is solved by employing a generlized inversion technique, the thickness of each layer can be calculated easily. This joint inversion method has been tested by synthetic models, having vertical resolution of 60 m and interval velocity variance about ± 100 m/s. In the areas lacking wells, the inversion results, acting like acoustic logging data, provide satisfactory constraints for quality control of velocity imaging.The third step in the imaging procedure estimates the velocity variations in each sectionblock between adjacent velocityanalysis traces via inversion of traveltime T(x, t) and the resulted interval velocity data c(x', z) on the block boundaries. Various techniques in computed tomography and wave equation inversion may be used for velocity reconstruction in a sectioblock. For instance, an 2D scalar wave equation may be reduced to the eikonal equation via. WKJB approximation, then discrete reconstruction algorithms, e. g. ART or SIRT in computed tomography, may be applied. By employing the "Exploding reflector" model, the 2D scalar wave equation can be written as:wherevi(x) = continuous effective velocity for the ith interface, can be calculated via c(x' , z), P(x, z) = pseudosource term representing velocity discontinuities on reflectors, W(t) = source signiture obtained from wavelet processing.In order to determine the velocity discontinuity P(x, z) which is actually a singular function of the velocity function c(x, z), we need singularity inversion techniques to solve the sourceterm inverse problems of partial differential equations. Finally, a discretized image of c(x, z) can be obtained from P(x, z) and vi(x).The above mentioned procedure of velocity imaging has been tested by a few drilling wells in a sedimentary basin in western China. The results (see enclosed color photos) shows a positive relation between velocity images and variation of lithology, giving distinguished indications of obscure traps for locating oil and gas deposits.  本文介绍了根据反射地震数据进行波速成象的一种方法,其基础为多种反演技术的综合。由于要求的波速图象C(x,z)具有间断性,除利用走时数据T(x,t)外,在地层比较水平的情况下,还利用了均方根速度V(x,t)和统计子波W(t)的数据来成象。计算机层析成象过程分为三步:首先重做速度分析,取得与初次反射走时一致的均方根速度数据;然后用反射走时与均方根速度联合反演对应分析道的层速度和界面深度;最后由联合反演结果和反射面走时求波速图象函数的数字化版。文中还给出了波速成象方法在我国西北某沉积盆地上的应用及验证结果。  Wave velocity inversion is essentially a wave equation inversion method. Most of the inversion methods we see at present have the aid of solution of integral equation. The research work in this field is only at its initial stage. A new wave equation inversion method that is based on the complementary function is put forward in this paper. This new method includes the following steps: (1) the wave equation, whose wave velocity is taken as parameter, is transformed into oneorder... Wave velocity inversion is essentially a wave equation inversion method. Most of the inversion methods we see at present have the aid of solution of integral equation. The research work in this field is only at its initial stage. A new wave equation inversion method that is based on the complementary function is put forward in this paper. This new method includes the following steps: (1) the wave equation, whose wave velocity is taken as parameter, is transformed into oneorder differential equation system by making Fourier transform and variable transform; (2) variation of the nonlinear parameter equation system in frequencywavenumber domain is made to obtain linear equations; (3) using complementary function method, iterative computations are made to obtain the optimum estimate of velocity parameter. This method is quite simple, and the trial computation using theoretical model can bring fairly satisfactory result.  波速反演实际上是一种波动方程反演方法。目前所见的大部分反演方法都借助于积分方程求解。这方面的研究工作还处于探索阶段。本文以余函数为基础,给出一种新的波动方程反演方法。其基本思想是从波动方程出发,将其中波速视为参数,通过对方程进行傅里叶变换及变数变换,把波动方程化作一阶微分方程组,并对频率一波数域中非线性参数的方程实行变分,从而使方程线性化,然后利用余函数方法进行逐次迭代运算,求得速度参数的最佳估计值。此法运算过程比较简单,用理论模型试算,可得到较为满意的结果。  The author puts forward the layerbylayer inversion method for onedimensional wave problem,which is based on the gradient regula rization(GR)method for wave equation inversion.According to wave character,a large problem can be divided into several subproblems solved respectively so that onedimensional wave inversion problem can be solved on a personal computer.The essential principle and algo rithm are expounded,and some numerical examples given.Compared with nonlayered inversion method,this... The author puts forward the layerbylayer inversion method for onedimensional wave problem,which is based on the gradient regula rization(GR)method for wave equation inversion.According to wave character,a large problem can be divided into several subproblems solved respectively so that onedimensional wave inversion problem can be solved on a personal computer.The essential principle and algo rithm are expounded,and some numerical examples given.Compared with nonlayered inversion method,this method offers equal accuracy, but takes much less computer time.The author also lists some troubles incurred due to layerbylayer calculation,and recommends some measures to cope with the troubles.  本文在求解波动方程反问题的 GR(梯度正则化法)方法基础上提出一种一维波动问题的分层反演方法。该方法利用地震波的传播特点,将大型问题化为若干小型问题来求解,使得一维波动反问题可以在微机上求解。文中阐明了一维分层反演的基本原理和算法,给出了相应的数值算例,与不分层反演所得结果的对比表明,两者的精度一样,但用机时间大大缩减。文中还讨论了由于分层计算而带来的一些问题,并提出了有效的解决方法。   << 更多相关文摘 
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