The advent of sparse 3-D acquisition often means that acquisition geometry influences the amplitudes of seismic reflections. The first step in the attenuation of this acquisition ÒfootprintÓ is understanding its origin. This article provides elementary insights.The most notable aspect of Figure 1, amplitudes along a slightly dipping horizon, is the periodic change in the amplitude. This periodic modulation reflects the surface acquisition geometry.In order to gain insight into the origin of the acquisition footprint, we did some simple modeling based on Figure 1. In Figure 2, the acquisition geometry for our model, horizontal blue lines are receiver lines, and diagonal red lines are source lines. Our model subsurface is a single reflector with no dip whose zero-offset round-trip traveltime is 1900-ms. We used a boxcar wavelet to idealize the actual wavelet. Figure 3, a time slice at 1900 ms after NMO correction followed by stack, has laterally constant amplitude because (1) the model did not contain any amplitude versus offset behavior; (2) NMO correction was applied with the correct velocity; and (3) an Òaverage-weightingÓ approach was used to stack the data. With a slight exception due to NMO stretch, all traces in all bins are identical after NMO correction. In Òaverage-weightingÓ stack, the stacked amplitudes were determined by the summation of individual trace amplitudes divided by the total number of traces for each respective bin (i.e., 1/N stacking). Thus, the stacked traces have identical bin-to-bin amplitudes. Figure 4 illustrates the ramification of altering a parameter in the stack program. In Figure 4 the fold-of-stack weighting term is the square root of the total number of traces in the stacked bin. As the fold of stack changes from bin to bin, so too does the total stacked amplitude. At seismic times deeper than the far-offset mute time, this amplitude variation is independent of seismic trace time and does not reflect the particular collection of offsets that comprise any bin, but only the variation of total fold from one bin to the next. Deeper than the far-offset mute time, different time slices will reveal the same relative amplitude pattern. Because of the time-independent nature of this phenomenon, a simple poststack amplitude scaling could address the lateral amplitude variation. The left and right portions of Figure 4 show the effect of regions of the edges of the survey introducing a decreased fold of stack. Figure 5 illustrates the amplitudes at the same 1900 ms time slice but after application of an NMO velocity that is 1.05 times the correct NMO velocity. The lateral variation in amplitude is not due to the total fold-of-stack variations because this, and all later examples, uses the average-weighting amplitude correction in the stack process. Instead, this pattern arises because the error in the NMO correction velocity introduced an offset-dependent amplitude. The amplitude on the near-offset traces at 1900 ms is unchanged because our 5% velocity error does not alter near-offset trace...

Optimal selection of locations for sensors in a seismic survey has been a long-standing issue for geophysicists. If they could sample the earth at two points per wavelength or better in all dimensions according to Nyquist sampling theory, design would not be an issue. The reality of limited access and funding requires geophysicists to make do with orders of magnitude fewer sampling points than Nyquist theory would dictate. Compressive sensing (CS) provides a new theory for nonuniform sampling that allows the use of significantly fewer sensors than current practice in seismic exploration would require. CS concepts can be applied to seismic survey design.

The goal of simultaneous shooting is to acquire better seismic data more quickly at lower total cost. Effective source deblending techniques provide us with one of the tools for accomplishing this goal. The use of compressive sensing theory gives us another tool by helping to increase the effective spatial bandwidth of our acquired data. Seismic surveys designed to collect both optimally sampled and blended data can reduce acquisition costs and significantly improve image quality. In this paper, we consider a joint deblending and reconstruction problem using the framework of a synthesis-based basis pursuit denoising model. The combination of a "deblending" operator together with a "restriction" operator leads to a joint inversion in which the data are both deblended and reconstructed at regular sampling intervals. Our inversion model can be further constrained by down-weighting the evanescent portion of the wavefield. We illustrate our method using both synthetic and real data examples simulating continuous-time recording under ocean bottom node (OBN) settings.

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