Analytical solution of the influence of irregularly shaped loads in the near field on crustal deformation monitoring

Crustal movement and deformation monitoring are important methods for reflecting changes in crustal stress. Crustal deformation data can be used to accurately describe the movement and deformation characteristics of active blocks and their boundary zones, providing effective data constraints for earthquake prediction and scientific research. Crustal deformation monitoring mainly includes crustal movement monitoring (such as Global Navigation Satellite System (GNSS) observations), surface strain monitoring (such as borehole strain observations), and surface tilt monitoring (such as vertical pendulum tilt observations). The high-precision and high temporal resolution data generated are widely used in the study of slow earthquakes, volcanic activity, and earthquake precursors. Given the close relationship between geophysical instruments and observation environments, crustal deformation monitoring instruments can not only record structural signals, but also interference signals caused by changes in surrounding loads. This article is based on the analysis displacement solution caused by the point load model, and derives formulas for calculating the surrounding tilt field and strain field, providing a theoretical basis for the quantitative calculation of the influence of surrounding loads in crustal deformation monitoring. In addition, this article also proposes a method for calculating the strain effects of two-dimensional and three-dimensional irregular shaped loads. Finally, based on the four component borehole strain observation data from Guza borehole strainmeter and the observation data of the surrounding river water level, the applicability of this analytical solution in quantitatively calculating the degree of influence of irregular load models in the surrounding area was verified under the conditions of setting the surrounding medium parameters (elastic modulus and Poisson's ratio). The results indicate that: (a) for the two-dimensional irregular shaped load model problem, vector superposition calculation can be performed after load scattering; (b) For the problem of three-dimensional irregular shaped load models, different weights can be assigned to scattering points after load scattering, and the two-dimensional irregular shaped load method can be used for calculation. The convergence process during vector superposition proves the correctness and feasibility of this method. This study provides a research foundation for the quantitative analysis of the influence of surrounding load interference in crustal deformation monitoring; (c) There is a high possibility that the data disturbance information of the four component drilling strain observation data at Guzan Station in summer is affected by the disturbance of the water level data of nearby rivers. This research work can quantitatively explain the degree of influence of load type interference factors on high-precision geophysical observation data, providing a quantitative interpretation scheme for the extraction of earthquake precursor anomalies.

Fund support: Ningxia Natrual Science Foundation Project (2024AAC03436); National Natural Science Foundation of China (41704062); National Key Research and Development Program of China (2021YFC3000705-06).

Figure 1 Example of the influence of irregularly shaped loads in the near field. In the figure: (a) represents the positional relationship between the Guzan borehole strainmeter and the Dadu River; (b) Representing the comparison of the changes in actual observed data with the results of irregular load model calculations.