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《Chinese Journal of Geophysics》 1987-06
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YANG WEN-CAI JIAO FU-GUANG(Beijing Computer Center, The Ministry of Geology and Mineral Resources)  
This paper introduces a new procedure for P-wave 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 zero-offset 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 source-receiver 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 i-th layer,Vj = RMS velocity data at time tj,△T1 = T1 - T1-1, 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 section-block between adjacent velocity-analysis 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 sectio-block. For instance, an 2-D 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 2-D scalar wave equation can be written as:wherevi(x) = continuous effective velocity for the i-th interface, can be calculated via c(x' , z), P(x, z) = pseudo-source 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 source-term 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.
【Fund】: 国家自然科学基金会;; 地震学联合基金
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