Spatial aliasing and 3C seismic sensors

Abstract

Temporal aliasing occurs when a waveform is sampled with less than two points per time period for a signal at a given frequency. This insufficiently sampled frequency will be incorrectly mapped into a lower (aliased) frequency. Analogous to this, spatial aliasing is said to occur when a propagating waveform is measured at spatial intervals larger than half the wavelength of any given signal in that waveform. Temporally aliased frequencies cannot be recovered with standard methods. On the other hand, we argue that “spatial aliasing” can be viewed as an expression of a nonuniqueness for estimating the direction of the propagation for signal at a given frequency, and that spatial aliasing may be overcome when 3C seismic sensors are used. Realizing this allows for using higher frequencies, and it therefore enables the generation of higher resolution images from the data. This is particularly useful for borehole-seismic data, which tend to contain higher frequencies than surface-seismic data, but does require that an array of 3C sensors is used or that an array of less expensive 1C sensors is supplemented by 3C sensors.