
{"publication_number": "US-6963804-B2", "abstract": "a method of processing data of seismic traces for geophysical interpretation of the earth &# 39 ; s subsurface includes the steps of determining a modified hilbert transform of an input trace of data values to detect rapid and slow changes in the input trace with reduced sensitivity to noise and providing results of modified hilbert transform to enable identification of any detected rapid or slow changes . the modified hilbert transform is advantageously a windowed fourier transform , wherein the input trace is represented as x , where t indicates time , a window function is represented by win , a first function is defined as g = x \u00b7 win , x is the fourier transform of g , hi represents a sum over imaginary portions of x , hr represents a sum over real portions of x , and the modified hilbert transform is h = hr + i \u00b7 hi . in its most general form , for any integer n greater than 1 , hr = \u03c3\u03c9real 