Application of fractal interpolation method to geo-electric field interference data process
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摘要: 当地电场和地电阻率同场地观测时，地电场观测会受到地电阻率观测的供电干扰，这类干扰时间短、干扰形态和出现时间固定，影响了地电场观测数据的正常变化形态，给数据分析和地震科学研究造成困难。为解决这一干扰问题，本文在比较分形插值方法与传统插值方法优劣的基础上，采用分形插值方法对受干扰的地电场观测数据进行重建，以提高信号重建的精度。结果表明，采用该方法重建的数据是对原数据很好的近似，可有效地恢复观测数据信息，保持观测数据原有的变化趋势。Abstract: Geo-electric field and geo-electrical resistivity observation is one of the most important ways of earthquake monitoring. In recent years, geoelectric field observation has been subjected to more and more interference caused by subways, high-voltage direct current transmission, and electrical facilities, etc. Among all these interferences, there is a special type of known interference in the earthquake geo-electric field observation, which is so-called “interference from current” caused by the electric current in measuring geo-electrical resistivity if the geo-electric field and geo-electrical resistivity were observed at the same site. This kind of interference is characterized by short interference time, fixed interference waveform and fixed appearance time, and it will cause difficulties in identifying normal variation of geo-electric field and analyzing data. This paper deals with approaches of eliminating the interference data by using interpolation method. The fractal interpolation method and traditional Lagrange interpolation method were separately used. On the basis of introducing the principle of the two interpolation method, the processing result of the two methods on simulation data and actual data are compared, it demonstrates that fractal interpolation method has higher accuracy than that of Lagrange interpolation method. Then the fractal interpolation method was used in the actual data processing. The result shows that the method not only retrieves the section information effectively, but also preserves the overall original variation tendency of the observation data.
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图 1 2020年2月1日江苏高邮台（a）和陕西宝鸡台（b）受地电阻率供电干扰的地电场观测数据
Figure 1. The interference waveforms of geo-electric field at the seismic observatories Gaoyou （a） and Baoji （b） on 1 February 2020
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图 2 高邮台2020年2月1日正常地电场NS向观测数据
Figure 2. The curve of normal geo-electric field data of Gaoyou seismic observatory on 1 February 2020
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图 3 高邮台地电阻率供电干扰波形模板
Figure 3. The waveform of interference from current for Gaoyou seismic observatory
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图 4 地电场干扰数据模拟曲线
Figure 4. The curve of simulated interference data of geo-electric field
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图 5 插值结果与原始数据差值的均方根误差σ
Figure 5. The RMS error σ of difference between original data and reconstructed data
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图 6 模拟干扰数据（左）及分形插值处理结果（右）
（a） 2020年2月7日；（b） 2020年2月25日
Figure 6. The curves of simulated interference data （left） and processing result （right）
（a） On 7 February 2020；（b） On 25 February 2020
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图 7 分形插值数据与原始数据的对比
（a） 2020年2月7日；（b） 2020年2月25日
Figure 7. Comparison of original data with data reconstructed by fractal interpolation
（a） On 7 February 2020；（b） On 25 February 2020
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图 8 高邮台（a）、宝鸡台 （b）和榆树台（c）受干扰地电场数据（左）及其相应的分形插值结果（右）
Figure 8. The actual interference geo-electric field data （left panels） and corresponding fractal interpolation result （right panels） for the seismic observatories Gaoyou （a），Baoji （b） and Yushu （c）
表 1 插值数据与原始数据差值的均方根误差
Table 1 The RMS error of difference between original data and reconstructed data
序号 数据日期
年-月-日均方根误差σ 序号 数据日期
年-月-日均方根误差σ 拉格朗日插值 分形插值 拉格朗日插值 分形插值 1 2020-02-01 0.048 0.033 14 2020-02-14 0.034 0.032 2 2020-02-02 0.039 0.028 15 2020-02-15 0.043 0.028 3 2020-02-03 0.051 0.028 16 2020-02-16 0.030 0.025 4 2020-02-04 0.040 0.023 17 2020-02-17 0.040 0.028 5 2020-02-05 0.030 0.024 18 2020-02-18 0.055 0.028 6 2020-02-06 0.045 0.027 19 2020-02-19 0.053 0.035 7 2020-02-07 0.071 0.042 20 2020-02-20 0.038 0.034 8 2020-02-08 0.054 0.033 21 2020-02-21 0.046 0.023 9 2020-02-09 0.034 0.030 22 2020-02-22 0.047 0.032 10 2020-02-10 0.042 0.025 23 2020-02-23 0.031 0.029 11 2020-02-11 0.043 0.025 24 2020-02-24 0.045 0.023 12 2020-02-12 0.050 0.026 25 2020-02-25 0.029 0.019 13 2020-02-13 0.033 0.026 
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