When imaging geologic structures below an overburden with laterally varying attenuation (Q) properties, it is important to account for the variable amplitude dimming, frequency loss, and phase distortion. Migration algorithms based on the viscoaoustic wave-equation have been developed to handle a 3-D Q model, but they require unmigrated input data and require significant run time. Fast 1- D Q-filtering techniques can be applied to compensate for Q effects and can be applied to migrated traces, but they don''t account for 3-D physical geometries. Here we present a pseudo migration approach that is applied to migrated seismic data. This approach utilizes the ray paths through the model and restores amplitude and phase according to the integration of the Q-effect along these ray paths. The computational efficiency of this algorithm is similar to that of 1-D filtering, yet it accounts for the 3-D geometries. The validity of our technology is illustrated by a 2.5-D synthetic data example.
3-D effects due to dipping geologic structures and nonzero source-receiver offsets must be handled appropriately to obtain valid imaging results. We first consider the simple zero-offset data case. In the case of zero-offset data and similar structural dips throughout the section, an apparent Q-model can be built for applying a 1-D Q-filter. This "Qmodel" will have an apparent thickening and lateral shift in position commensurate with the magnitude of the dip (Figure 1), so it will not have physical meaning except in cases of almost horizontal bedding. Moreover, if the structural dip is not constant throughout the section, it is impossible to build a Q-model for 1-D Q-filtering that accounts for all the Q-effects in the data- even in the simple zero-offset case (Figure 2).
We now consider the more meaningful case of data with varying source-receiver offsets. If there are similar structural dips throughout the section, a different apparent Q-model would need to be developed for each reflection angle bin (Figure 3). These "Q-models" would have apparent thickening/thinning, lateral shifts, and changes in value dependent on the magnitude of the dip, the reflection angle range, and the number of travel legs affected by the low-Q zones. Trying to verify that these multiple models are internally consistent and geologically reasonable would be extremely difficult, if not impossible. And again, if the structural dip is not constant throughout the section, it would be impossible to produce a Q-model for any reflection angle range that would allow 1-D Q-filtering to account for all the Q-effects in the data.
To account for these 3-D structural and acquisition effects of attenuation, Q-compensation techniques have been implemented within several conventional migration algorithms (e.g., Yu et al., 2002 and Liu et al., 2008). The best mitigation of attenuation effects results from applying prestack Q migration. In this case, the Q-model would be analogous to the velocity model and all effects due to travel path would be handled appropriately. However, there are many real-world instances where a full prestack migration project is impossible- either due to lack of time, resources, or access to the prestack data.