Instrumental response of borehole tensor strainmeters for oblique-incident seismic waves

Abstract

Abstract It has been proven qualitatively that borehole tensor strainmeters (BTSM) could measure three surface-wave-induced strain components in the horizontal-normal plane. But strain waves are usually incident obliquely to borehole axis to induce not only horizontalnormal strain components but also the three other strain components in the plane of vertical normal, which are usually assumed to zero in conventional model of BTSM installed near the earth surface. Therefore quantitative kinematical-parameter measurement of strain waves of wave normal oblique to borehole axis by BTSM is still a challenging problem. In this paper, a scattering model of oblique-incidence seismic waves by an empty borehole is introduced to investigate instrumental responses of BTSM. Besides for the four gauges in conventional BTSM, three other gauges considering the influences of strain components in the plane of vertical normal are also introduced to build dynamic calibration matrix between instrumental and incident strains. It shows that within the effective bandwidth of BTSM, zero-frequency-gain for dynamic calibration matrix could be adopted approximately to build quantitative relation between instrumental strain waves of BTSM and oblique-incidence seismic strain waves. It is shown that the recommended gauge combinations could promise quantitative measurement of kinematic parameters of the incident strain P or S wave if high-resolution insitu calibration of BTSM has been conducted, which is important to the development of early warning system by borehole strainmeters.