Theoretical Frequency Response Analysis Of Component Borehole Strain Observation

As a crustal strain observation instrument,high-sensitivity tensor borehole strainmeters can effectively compensate for the measuremental bands of GPS and seismographs,which mainly include RZB tensor borehole strainmeter,YRY tensor borehole strainmeter,and Gladwin tensor borehole strainmeter.These tensor borehole strainmeters have been widely used in the PBO and the Chinese borehole strainmeters network,and effectively advanced the relevant investigation on volcanic dynamics,geodynamics,and seismogenesis process.The theoretical model of high-sensitivity tensor borehole strainmeters observation is stress concentration around a circular hole subjected to far field strain fields,which is suitable for quasi-static strain fields changes.However,there is still no systematic research on the feasibility of quantitative seismic-strain-wave measurement by high-sensitivity tensor borehole strainmeters.In fact,tensor borehole strainmeters observations are equivalent to low-pass filters,including a borehole system(corresponding to the theoretical frequency response)and an internal diameter measurement sensor system(corresponding to the instrument frequency response).The ultimate bandwidth of tensor borehole strainmeters observation depends on the minimum bandwidth of the theoretical frequency response and the instrument,s frequency response.The bandwidth of the instrument's frequency response can be controlled by the sensor design,while the theoretical frequency response not.In order to explore the feasibility of quantitative observation of seismic strain wave by tensor borehole strainmeters,this thesis introduces the model of elastic wave scattering by borehole system and different combination of inner diameter changes to analyze the theoretical frequency response of tensor borehole strainmeters observation.When the incident wave is incident on the borehole,the diameter change of the borehole is determined by the total wavefield generated by the superposition of the incident wavefield and the scattered wavefield,which can be calculated by the theory of elastic wave scattering by borehole.Similar to the static case,different combinations of inner diameter changes are proposed to reflect the areal strain and the maximum shear strain of the incident wave.This thesis investigates theoretical frequency responses of tensor borehole strainmeters for the empty hole model,one layer model(inner stainless instrument casing),and two layer model(including the stainless instrument casing and expansive grout layer)for the incident P or SV wave perpendicular to the borehole axis,respectively.Secondly,,this thesis gives the theoretical frequency response of tensor borehole strainmeters for the empty hole model,one layer model(inner stainless instrument casing),and two layer model(including the stainless instrument casing and expansive grout layer)when the incident P or SV wave is obliquely incident to the borehole axis,respectively.From the aboved analysis,this thesis gives the following innovative understanding,1.The combinations of inner diameter changes FV4,FVZ,and TV could reflect the areal strain,and TS and FS the maximum shear strain of the incident wave.2.The bandwidth of theoretical frequency response is much greater than that of instrumental frequency response,which indicates that the bandwidth of tensor borehole strainmeters can be expanded by increasing the frequency response bandwidth of the instrument.3.The expansive grout and stainless instrument casing layers have a certain influence on the amplitude of theoretical frequency response.Therefore,the calibration coefficient of strain wave observation for the tensor borehole stranmetersmust be realized by the in-situ calibration method.4.The polarization angle and oblique angle of the incident elastic wave have a great influence on the amplitude of the theoretical frequency response,which means that the polarization angle and oblique angle of the incident elastic wave should be accurately determined in practical borehole tensor strainmeter obesevation,especially for dynamic in-situ calibration.