In addition we have the problem of spatial aliasing. Because of improving technology, we can expect a substantial reduction in aliasing on the geophone axis, but aliasing on the shot axis will remain. There are only twenty-four hours in a day, and we must wait ten seconds between shots for the echoes to die down. So, given a certain area to survey and a certain number of months to survey it in, we end out with a certain number of shotpoints per square kilometer. With marine data, the spacing in the line of the path of the ship presents no problems compared to the problems presented by data spacing off the line.
Migration provides a mapping from a data space to a model space.
When data is missing, the transformation matrix gets broken into two parts. One part operates on the known data values, and the other part operates on the missing values. This book mostly ignores the missing part. Noisy data can be defined as data that doesn't fit our model. If the missing data were replaced by zeroes, for example, the data would be regarded as complete, but noisy.