Analytical solution for the influence of irregular shape loads on near borehole strain observations

Abstract

Borehole strain observations are widely used to research slow earthquakes, volcanic activity and seismic precursors. Due to the high resolution and sensitivity, borehole strain monitoring records not only tectonic signals, but also signals from environmental disturbances. Based on the analytical solution of the displacement caused by the punctate load model, this paper derives the equation of the peripheral strain field, which provides a theoretical basis for the quantitative calculation of the load effect of borehole strain observation, and proposes a method for calculating the strain effect of two-dimensional and three-dimensional irregularly shaped loads. The results show that, 1) For the two-dimensional irregular shape load model, we can calculate it by vector superposition after load scattering. 2) For the three-dimensional irregular shape load model, we can calculate by assigning different weights to the scattering points after load scattering using two-dimensional irregular shape load method. The convergence process during the vector superposition shows the correctness and feasibility of the method, and the study can provide a research basis for the quantitative analysis of the influence of peripheral load disturbance in borehole strain observation.