In order to discuss the possibility of measuring seismic strain wave by borehole tensor strainmeters, the model of incident elastic P wave scattering by double-nested borehole is introduced to investigate frequency responses and bandwidth of borehole tensor strainmeter. The calculation of scattering waves around the two-ring borehole by wave function expansion gives diameter change of the borehole. It is shown that frequency responses of borehole strainmeter for different gauge combinations are mainly determined by mechanical parameters of rocks and the high frequency bandwidth means the measurability of P strain waves at acoustical frequency range quantitatively for borehole tensor strainmeters.

1 Introduction

In order to capture gentle tectonic strain caused by volcanic activity(Linde et al., 1993), fault failure process including slip transients, fault creep, earthquake nucleation, slow earthquake, and silent earthquake, and earthquake source characterization(Agnew and Wyatt, 2014; Barbour and Crowell, 2017), high sensitivity borehole tensor strainmeters, such as RZB strainmeter (OuYang et al., 2009), YRY strainmeter(Chi, 1993), and GTSM strainmeter(Gladwin, 1984; Gladwin and Hart, 1985), has been developed and installed in Plate Boundary Observatory (PBO)(Roeloffs, 2010) and China Borehole Strainmeter Network (Chi, 2009). The expansive grout cements the strainmeter to the borehole, which changes the strain that is in the rock to the diameter change of the stainless steel instrumental casing. These diameter changes measured by four gauges of different orientation gives the instrumental strains. The coupled parameters between the strain in the rock and instrumental strains must be in-situ calibrated, which is usually done by the comparison between instrumental strains and the calculated strain from theoretical earth tide(Hodgkinson et al., 2013; Langbein, 2010a, b). But theoretical earth tide is influenced by the deep structure of the Earth, the model of the ocean load both near and far from the coast, topographic and geologic effects, which will induces the evident error for the calibration(Langbein, 2010b). In order to increase the precision of in-situ calibration for borehole tensor strainmter, the combination of the measured paticle velocity from colocated borehore seisometer and local phase velocity yields the reference strain-wave signal for high-precision in-situ calibration of borehole tensor strainmeters(Agnew and Wyatt, 2014; Barbour and Agnew, 2012; Currenti et al., 2017; Ishii and Park, 2018; Qiu et al., 2015; Sacks et al., 1976). The dynamic couple relation between the reference strain wave from seismometer and measured instrumental strain wave from borehole tensor strainmeter must be provided for this attractive in-situ calibration for borehole tensor strainmeter, which has not been investigated yet.(Zhang et al., 2019)

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