Regularization of non-uniformly sampled seismic data

Surface seismic data is almost always non-uniformly sampled in space. Even if the underlying survey design is based on uniform sampling, it will be near to impossible to plant the sensors, and actuate the sources, at the required locations uniformly distributed in space. More recently deliberate non-uniform sampling has been suggested to acquire data with less sensors (and/or sources). In a more abstract setting the following two questions need to be addressed hence; what is the minimum number of sensors required, and how does one distribute them optimally? The answer to these questions of course depends on what type of data analysis is proposed for the acquired data. Role models for most data analysis steps, at least for seismic data, are spatial spectral analysis and regularization, i.e. the interpolation of the data unto a uniform grid. These two tasks are closely related; if the data is acquired such that a spectral analysis is possible the data regularization is possible as well in a form of Fourier synthesis of the data. However, in certain circumstances data regularization does not require an explicit spectral analysis step. My talk will hence consist of two parts: in the first part I will address the task of data regularization without explicit spectral analysis, followed by the task of regularization with explicit spectral analysis.