Deep seismic reflection processing in the complex demodulate domain: basic theory and application to residual static estimation

The fast Fourier transform enables us to transform time series data efficiently between the time, frequency, ‘complex trace’ and ‘complex demodulate’ domains. The complex demodulate domain is related to the complex trace domain via a time‐dependent phase rotation and optimal resampling. Data manipulation in any one domain has equivalents in the other domains, which may be more computationally efficient. Thus if we wish we can process seismic reflection data entirely in the complex demodulate (CD) domain. Working in the CD domain allows us to apply certain approximations which in turn allow us to carry out some involved operations very much more efficiently than in the time or frequency domains. We present some basic theory, some simple examples and an application to residual static estimation on crystalline bedrock. For this data a non‐linear stackpower optimization in the CD domain had run times significantly less than those of similar processing in the time domain, and produced essentially identical results. Using a more narrow frequency band degrades the results only slightly, and decreases run times by a factor of up to 20 compared to the time domain processing.