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 incorrectly be 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 non-uniqueness for estimating the direction of the propagation for signal at a given frequency, and that spatial aliasing may be overcome when three-component seismic sensors are used. Realizing this allows for using higher frequencies, and 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 three-component sensors is used, or that an array of less expensive single-component sensors is supplement by three-component sensors.

Approaches to decomposing acoustic data

“…Off‐axis elemental waveforms with the same slowness along the axis of the array may well be different and be travelling in different directions in three‐dimensional space. To distinguish them, one would need to use multi‐component sensors that allow measuring the direction of particle motion (Haldorsen, 2021). However, multi‐component sensors are not conventionally used.…”

Imaging complex three‐dimensional structures, applying three‐component vector migration to synthetic vertical seismic profiling data

“…The denser spatial sampling for the DAS array is important for single‐component measurements – more so than for multi‐component measurements. Because of the constraints from the polarization measurements of 3C sensors, the sensor interval can be larger for 3C sensor array (Haldorsen, 2021) than for one‐component (1C) arrays. Supplementing the densely sampled DAS array with sparsely distributed 3C sensors, either optical or electrical, may be an option worth considering.…”