Theoretical Frequency Response and Corresponding Bandwidth of an Empty Borehole for The Measurement of Strain Waves in Borehole Tensor Strainmeters

摘要

Borehole tensor strainmeters such as the RZB tensor strainmeter, YRY tensor strainmeter, and Gladwin tensor strainmeter are highly sensitive to ground deformation over periods of minutes to months, bridging the gap in the sensitivity and frequency between Global Positioning System and seismic measurements. To discuss the possibility of quantitatively measuring seismic strain waves by borehole tensor strainmeters, a model of the scattering of plane elastic P and S waves by an empty borehole is introduced to investigate the theoretical frequency response and corresponding bandwidth of an empty borehole for borehole tensor strainmeters. The calculation of scattering waves around the empty borehole gives the changes in the diameter of the borehole. Different gauge combinations are introduced to reflect the areal strain and the maximum shear strain of the incident waves. The theoretical frequency responses for different gauge combinations are determined by the nondimensional wavenumber of the incident wave, the Poisson's ratio of the surrounding rock, and the difference between the azimuth angle of the first gauge and the incident angle of the incident wave. Theoretical-frequency-response analysis of different gauge combinations for an empty borehole confirms that different gauge combinations serve as low-pass filters. The 1% bandwidth of the gauge combinations shows that borehole tensor strainmeters could quantitatively measure seismic strain waves in the acoustic frequency range if the instrumental effective bandwidth of the gauge is sufficiently large, which will advance high-frequency seismology and benefit in situ calibration of borehole tensor strainmeters.