Shaping the Wavelet
Wang, Yuchun E.*1; Huo, Shoudong 1
(1) Saudi Aramco, Dhahran, Saudi Arabia.
Wavelets have been widely used in seismic data processing and interpretation for different purposes such as deconvolution, well ties and acoustic inversion, and data compression. Wavelet extraction methods roughly fall into two categories: statistical methods that use seismic data only, and deterministic (or semi-deterministic) methods in which well log data is utilized. We propose a new deterministic technique that may be more stable and offers better results than the traditional wavelet extraction methods currently being used.
Based on a simple convolutional model, a seismic trace is the convolution of a wavelet with the earth’s reflectivity. Performing convolution in the frequency domain, the seismic spectrum becomes the product of the wavelet and the reflectivity. If we have the reflectivity from the well logs and the seismic data, theoretically the wavelet spectrum can be obtained by complex division or its equivalent. The difficulty arises as the reflectivity spectrum falls below the noise level and approaches zero at certain frequencies. To overcome this inherent instability of division by zero, a small positive number is typically added (white noise) to the denominators. Our new stabilization method uses “shaping regularization” to overcome the problem of division by zero. The method works if the following two assumptions are valid: most of the reflectivity spectrum is reliable, and the wavelet spectrum is smooth in both amplitude and phase.
Our wavelet extraction experiment is described in the following steps: (1) input of edited sonic and density logs; (2) computation of the borehole impedance; (3) conversion from depth to time using a check shot survey; (4) application of edge-preserving smoothing to the impedance; (5) computation of the reflectivity and seismic frequency spectra; (6) application of the shape regularization to obtain the wavelet spectrum; and (7) conversion of the wavelet back to the time domain. We tested the new wavelet extraction using (a) a single trace closest to the well location and (b) an average of the 121 closest traces to the well. In both cases, the “shaped” wavelets are sharper than the wavelet extracted using algorithms that relied on the traditional “white noise” stabilization technique. Initial results show that the “shaping wavelet” method is a promising technique and worthy of further research.
AAPG Search and Discovery Article #90141©2012, GEO-2012, 10th Middle East Geosciences Conference and Exhibition, 4-7 March 2012, Manama, Bahrain