The applicability of DMO/AMO in the presence of caustics

Reflection seismic data continuation is the computation of data at source and receiver locations that differ from those in the original data, using what data are available. Here, we develop a general theory of data continuation in the presence of caustics and illustrate it with two examples: dip moveout (DMO) and azimuth moveout (AMO). This theory does not require knowledge of the reflector positions. We construct the output data set from the input through the composition of three operators: an imaging operator, a modeling operator, and a restriction operator. This results in a single operator that maps directly from the input data to the desired output data. We use the calculus of Fourier integral operators to develop this theory in the presence of caustics. For both DMO and AMO, we compute impulse responses in a constant-velocity model and a more complicated model in which caustics are generated. This analysis reveals errors that can be introduced by assuming, for example, a model with a constant vertical velocity-gradient when the true model is laterally heterogeneous. Data continuation uses as input a subset (common-offset, common-angle) of the available data, which introduces artifacts in the continued data. One could suppress artifacts by stacking over a neighborhood of input data (using a small range of offsets, or angles, for example).