Restoration of Seismic Amplitude Using a Frequency-Dependent Gain Function
Weihong Zhu* and Khalid O. Al-Rufaii
It is well known that the Earth absorbs acoustic energy and that high frequencies lose their energy faster than lower frequencies. The loss of seismic energy can be attributed to several factors such as absorption, geometrical spreading, and scattering of energy at an interface due to reflection, refraction, conversion, and transmission. Deconvolution and (Q) attentuation-compensation operations are usually performed in order to restore as much of the attenuated high-frequency energy as is justified by the signal-to-noise ratio. The conventional approach for amplitude recovery is to compute and apply a time-dependant gain function. Here, we extend the conventional exponential gain function to account for the inelastic attenuation effect as well. We introduced a frequency factor into the computation and application of the exponential gain function to account for the inelastic attenuation. This process was performed in the frequency domain. There were three steps involved in the computation. First, a 1-D forward Gabor transform was applied (small windows fast Fourier transform). Next, frequency-gain curves and inelastic attenuation were computed and applied for each Gabor slice. Finally, the data was transformed back to the time domain. It is worth mentioning here that the geometrical spreading, which causes the loss of seismic amplitude can be recovered either before or after the 1-D Gabor transform with no visible difference as was indicated by our extensive testing. Moreover, the two processes of the seismic-energy restoration are reversible. This further enhances the robustness of our methodology. We demonstrate the accuracy and effectiveness of our proposed approach using both synthetic and real data examples.
AAPG Search and Discovery Article #90077©2008 GEO 2008 Middle East Conference and Exhibition, Manama, Bahrain