APPLICATION OF LEVIN TRANSFORM FOR INCREASING THE ACCURACY AND CONVERGENCY OF THE TAYLOR EXPANSION FOR TRAVELTIME EQUATION IN AN ANISOTROPY-VERTICAL TRANSVERSE ISOTROPY MEDIUM AT THE FAR-OFFSET OF SEISMIC DATA

• Main Author: Purba, Humbang
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/63679
• Institution: Institut Teknologi Bandung

Long-offsets seismic is necessary for the improvement of subsurface imaging quality for deep targets and reservoir characterization. However, when a medium has anisotropic behavior, there will be a hockey stick phenomenon, regarded as a disturbance that interferes strongly in the seismic recording at the fat offsets. This phenomenon has implications for the increase of the residual moveout so that it should be eliminated with the consequence of reducing seismic image quality and also losing much information dealing with reservoir. The traveltime equation has an important role in long-offset seismic data processing, in particular, to reduce or eliminate such phenomenon, which is caused by the anisotropy factor itself. Previous researchers have used the Taylor expansion for traveltime equation in seismic processing but it has a drawback in convergency when using higher-order so that it becomes inaccurate over a wide range of offset. Recently, many researchers have started to employ some nonlinear transformations for increasing the convergence acceleration, but the accuracy is still limited when the offset-depth ratio (ODR) > 4. Whereas for subsurface mapping in deeper targets, an even larger ODR is required. This research transforms the Taylor expansion series for traveltime into a new traveltime equation in the form of a numerator and denominator by using the Levin Transform method. This aims to improve and increase its convergence to achieve better accuracy at the far offsets, especially at ODR > 4. The more convergent the traveltime equation, the more accurate the approximation of the calculated traveltime value to the real data will be. Having better accuracy will suppress the increase of the residual moveout The phases of the method test are started from formulating a new traveltime equation resulting from Levin's transformation. Then, performing a single-layer synthetic test and extensive search for the best choice of Levin parameter for the fastest convergence acceleration at the interval 0 ? ODR ? 6. The best Levin parameters are obtained when involving much larger high-order terms and usingiv the first sum Taylor series. The best accuracy is indicated by the best fitting between the traveltime calculation and the exact model so that the relative error of traveltime is much smaller than in previous studies. Furthermore, in a multi-layered synthetic test, a vertical transversely isotropic (VTI) model is used in semblance analysis to obtain velocity and anisotropy (?) parameters in both effective (or rootmean-square) and interval analysis. Then, normal moveout (NMO) correction and residual moveout calculation are carried out using these parameters. The proposed method yields more accurate velocity and ? parameter than compared methods in both effective and interval. The NMO residual is calculated in the frequency domain to achieve high accuracy as well. The proposed method also shows great superiority to reduce the residual NMO to most several approximations. Applying to the real seismic data, the velocity and ? parameters resulting from velocity analysis are used for the NMO correction. The proposed method provides much small residual moveout, especially at the far offsets, in which the hockey stick effect appears. The stacking trace process also demonstrates the best-stacked result qualitatively and quantitatively. This can be shown by spike features of the wavelet trace, small residual NMO value, and a broader frequency spectrum than the existing methods. This will have many implications to imaging quality and also to the lithology identification and reservoir properties analysis.