Hyp-curvelet Frame And Multiple Waves Recognition,Separation And Elimination

By this time, wavelets analysis is most efficaciously at dealing with point sigularities. Unfortunately, the variables of the tensor multiplicative wavelet function are separable, and wavelets analysis is often fail when it is used to represent the higher sigularities. The seismic observed data are usually regarded as the convolution of higher dimensional seismic wavelet and reflectance of layer interface. But the variables of the higher dimensional seismic wavelet are independent and not separable. Therefore, in the higher dimension, we must think about the character of the observed data / function, and choose the wavelet which has mathematical construction corresponding to the character of observed data /function.This thesis has introduced a new multiscale analysis method which faces to the higher sigularities. In the higher dimension, there are a great variety of sigularities along different curve, curved surface, hypersurface besides point sigularities. If these sigularities are along simple functional arrangement, we can construct curvelet which is based on the simple function.The thesis has constructed a multiscale transform which can efficaciously representsigularities along hyperbola (hyperboloid)--hyp-curvelet transform. When the edge of thehyperbola is expanded, the coefficients are sparse, the most power of the sigularties along the hyperbola are gathered in a few coefficients. So in the hyp-curvelet multiscale space, if the data which are less than the threshold are cut, the random noise and the unhyperbola noise can be suppressed.The digital hyp-curvelet transform and reconstruction have been implemented. Considering the character of the seismic signal and the sample rate of the gather, the author discretes the hyp-curvelet function and obtains the hyp-curvelet frame. When the hyperbolic edges are projected into the multiscale spaces which are spanned by the hyp-curvelet frame, the information of the frame coefficients is redundant, so the large projected values are enough for the inverse approaching of the hyperbolic edges.On CMP and CSP gathers, the reflection time-distance curve of plane interfacial which is covered with symmetrical medium can be approximated as hyperbola. In the multiscale spaces which are spanned by the hyp-curvelet, the gathering degree and the location of the projected power of the different hyperbola edges are different. So the intercept time and the rms velocity can be more exactly estimated, the primary waves and the multiple waves can berecognized. Alter removing the data less than the threshold in the multiscale space, we can gain the corresponding result by the inverse approached hyp-curvelet transform ?with the orthogonal projection of the hyp-curvelel frame, the inverse result only includes primarys, so the multiples have been eliminated, even near-offset multiples?...