Example 1: A simple synthetic angle gather

We begin with synthetic data for the simple one-dimensional case described by Sava and Guitton (2003). Sava and Guitton (2003) use muting in the PRT domain to separate input data (Figure a) into a primary model (Figure c) and a multiple model (Figure b). We are able to use this multiple model for estimation of the noise PEF's, but find that the PRT-muted primary model does not produce satisfactory results as a model for signal PEF estimation. Because multiples and primaries overlap in some parts of the PRT domain (most importantly at near offsets), the primary model still contains some multiple energy, particularly in the deeper part of the record. We tested several model options for estimating the signal PEF: the raw PRT result; ${\bf Nd}$ (the convolution of the noise PEF's with the original data such that the signal is considered to be anything in the data that is not removed by the noise PEF's); and a windowed version of the PRT result. We know that the lower part of the record contains no primary energy so we create a signal model (Figure d) by windowing and zero-padding the PRT result. Using the windowed PRT result to estimate our signal PEF, we can remove nearly all of the multiple energy, leaving Figure f as our final estimated signal.

 

CIG_syn_nice
Figure 1 (a) Input data- a synthetic angle gather. (b) Multiple model estimated with PRT approach. (c) Primary model estimated from PRT approach. (d) Signal model used for PEF estimation. (e) Multiple model estimated with PEF approach. (f) Primary model estimated with PEF approach.

While this result is clearly better than the PRT result, it is hardly surprising given the simplicity of the situation and the choice of signal model. It does, however, illustrate the important point that with careful model choice we can cleanly separate primaries from multiples in the angle domain, and encourages us to consider more complicated cases. This example also illustrates an advantage of PEF's over the PRT approach. The multiple model from the PRT approach fails to capture some of the steeply dipping parts of the multiple energy at the larger angles (Figure b), while this energy is captured by the PEF approach (Figure e). Although this energy was not in the model used for noise PEF estimation, the same part of the signal PEF estimation model contains only random noise, so the signal/noise separation places that energy in the output noise model. The result is a more thorough separation of signal from noise.