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Surface Consistency is a common term used in the Seismic Data Processing profession.
Terms like Surface Consistent Statics, Surface Consistent Decon, Surface Consistent Amplitudes are commonly used when discussing processing sequences.
Surface Consistent means that a single operator is used for all traces that have the same surface point in common. For example, Surface Consistent amplitudes computes and applies a single amplitude correction to all samples on all traces that come from the same shot. Similarly it will compute and apply a single amplitude correction to all samples on all traces that were recorded by the same receiver.
SC (Surface Consistent) Decon will compute one operator to be applied to all traces from the same shot by averaging (or weighted averaging) of the information from all of the traces from the same shot or all of the traces from the same receiver.
SC (Surface Consistent) Statics will compute one "static" or time correction to be applied to all traces that come from the same shot and a separate correction for all traces that come from the same receiver. Each trace comes from one shot and one receiver and will have separate shot and receiver statics (or time corrections) that are added together and applied as a single time shift.
Surface Consistent operators can be more stable when compared with single trace operators that can vary significantly from one trace to the next. Surface Consistent operators take into account region trends and regional variations that can be more smoothly varying.
Variations in amplitude, time, phase and frequency can be caused by differences in source or receiver coupling, or added energy from a local noise source, or near surface energy attenuation differences.
"Coupling" is the technical term that simply means how well the source and receiver are in direct contact with firm ground. A local noise source may be something like a generator on the ground near a shot or receiver location. The near surface can have very detrimental effects on energy amplitudes, for example sand or other unconsolidated local material near or under a shot or receiver can significantly change the character of the recorded energy at that location compared to a neighboring position that is a hard ground surface.
From a computational perspective, SC (or Surface Consistent) processes require more resources and time as you generally need to pass over the data twice. The first pass is used to accumulate the statistics from which the operators are designed. The second pass is the application step where the SC operator is applied. Single trace versions of the same processes can design and apply the operator on the single trace in memory as the trace is passed down the processing workflow.