On the Accuracy of Seismic Wavefield Spatial Gradients

Rotation measurements have found applications in various fields of geophysics ranging from near-surface archaeological mapping to large scale upper mantle tomographic inversion. In the absence of a cost-effective sensor sensitive over the typical seismic frequency bandwidth, rotation measurement can be approximated by finite-differencing the response of the vertical particle velocity over a short distance. Accurate estimates of the horizontal gradient of the vertical wavefield can be obtained when perturbations associated with the measurement are minimised. These perturbations can be sensor related, for example geophone sensitivity and natural frequency, and/or deployment related such as tilt and coupling errors. We developed a “sensitivity” chart ranking these perturbations according to impact. We recommend the use of geophones with low variance in sensitivity, deployed as vertical as possible (less than 5 degrees tilt error) at highly accurate position (error in the order of centimetres). Moreover, the distance between the two receivers should be about 1/8 of the minimum wavelength in order to reduce the error due to finite-differencing.