钻孔应变观测数据的分形特征研究

形变观测数据是地震监测预报和地球科学研究重要数据源，其中环境干扰排除、地震震例等异常数据的检测是形变观测数据推广应用的关键内容。本文针对形变观测数据中的钻孔应变观测数据，通过计算绘制功率谱图，研究其Hurst指数与盒维数分形特征，实现对观测数据中地震事件等异常数据的检测。实验结果表明钻孔应变观测数据符合1/f分布，其具有长时间记忆的分形特征，Hurst指数与分形盒维数变化都凸显出了地震等异常数据。随着信噪比的下降，钻孔应变观测数据的Hurst指数呈现下降的趋势，其盒维数呈现增加的趋势，进一步证实了Hurst指数与分形盒维数之和为2的关系，而它们的变化较大，表明具有较弱的抗噪能力。本文的研究结果可为地震研究提供理论基础。

Study on Fractal Geometry in Borehole Strain Observation Data

The deformation observation data is crucial in earthquake monitoring and forecasting and earth science. The detection of outlier data, such environmental interference and earthquake, is very important to apply those data to other field. In this paper, we study the Hurst exponent and the fractal box-dimension of the borehole strain data to detect the outlier data. The experiments indicate that the power spectrum of the borehole strain data resemble the 1/f distribution, which means the fractal geometry of the borehole strain data. Its Hurst exponent identify the characteristics of long time memory. The outlier data, such as earthquake, can be detected by Hurst exponent and fractal box-dimension. With the decrease of signal-to-noise ratio(SNR), the Hurst exponent is an decreasing trend, and the fractal box-dimension is an increasing trend, which further confirming the relationship between the Hurst exponent and the fractal box-dimension. However, these indexes change greatly, which indicates that they have poor anti-noise ability. Our results can provide the theoretical basis for seismic research.