ABSTRACT

We address the question of whether or not there always is a “bandwidth benefit” in non-uniform spatial sampling of geophysical data. Answering this question is, for example, important in the context of random sampling of seismic data, as it recently has been shown that there can be such a benefit under certain assumptions on the spectral structure of the data. Assume that a fixed number of sensors are placed either uniformly (i.e., on a regular grid) or non-uniformly (either randomly distributed or following any suitable non-uniform sampling scheme). The bandwidth supported by uniform sampling is that of the Nyquist wavenumbers corresponding to the sampling distances on the regular grid. The bandwidth supported by the non-uniform sampling we propose here refers to the maximum bandwidth of data that could be reconstructed by a linear operator at arbitrary sampling locations within the survey area without unacceptably high reconstruction error. Without making further assumptions on the spectral structure of the data, i.e., especially without assuming sparseness of the data spectrum, we will argue that we see no such bandwidth benefit in non-uniform sampling in the examples we have investigated.

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