Magnetotelluric static correction of two-dimensional model based on the highest frequency phase method and spatial filtering method
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摘要: 静态效应一直是影响大地电磁测深法精确性的主要原因之一。在相位校正法的基础上提出了一种更适用于电性变化较为平缓的地质情况的静态校正方法—最高频相位法，其核心是用需要校正测点两侧受静态效应影响较小测点的最高频视电阻率的算术平均值代替相位法递推公式中每个频点前一个频点的视电阻率值，以消除相位法中的误差积累。以二维模型的正反演为例，通过对比空间滤波法、相位法和最高频相位法对不同模型静态校正前后的正反演结果，证明了最高频相位法的有效性和优越性，同时表明，对于电阻率变化大并且静态位移严重的水平层状地层模型，采用与空间滤波法相结合的联合校正效果更佳。Abstract: Static effect is one of the main reasons for affecting the accuracy of magnetotelluric sounding. In this paper, a static correction method, the highest frequency phase method, is proposed on the basis of the phase correction method, which is more suitable for geological conditions with smooth electrical changes. Its principle is to eliminate the error accumulation in the phase correction method by replacing the apparent resistivity value of the previous frequency point in the recurrence formula with the arithmetic mean of the highest frequency apparent resistivity of the measuring points on both sides of the measuring points that need to be corrected and are less affected by the static effect. Taking the forward and inversion of two-dimensional model as an example, the effectiveness and superiority of the highest frequency phase method are proved by comparing the forward and inversion results from spatial filtering method, phase correction method and highest frequency phase method before and after static correction for different models. It also shows that for the horizontal layered formation model with sharp resistivity difference and severe static shift, the static correction effect of joint correction which combines highest frequency phase method with spatial filtering method is much better.
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图 1 无地形（a）、含地垒（b）、含地堑（c）的均匀半空间介质近地表存在低阻和高阻电性异常体的模型
测线长3 km，测点数为30，点距为100 m；左侧低阻异常体长200 m，高40 m，电阻率为1 Ω·m；右侧高阻异常体长200 m，高40 m，电阻率为105 Ω·m
Figure 1. Schematic of the half space model with low and high resistivity anomaly near surface for the model of flat surface （a），horst terrain （b） and graben terrain （c），respectively
The measuring line is 3 km long，and there are 30 measuring points，and the point spacing is 100 m；the left low resistivity anomaly body and the right high resistivity body are both 200 m in length and 40 m in height，while the electrical resistivity are 1 Ω·m and 105 Ω·m，respectively；the horst is 300 m high and the graben is 300 m deep. The same below
图 2 利用三种静态校正方法对无地形（a）、含地垒（b）、含地堑（c）的均匀半空间介质近地表低阻异常体正上方测点的静态校正效果对比
Figure 2. Comparison of static correction effects of the measuring point above the near surface low resistivity anomaly body of homogeneous half-space with flat surface （a），horst terrain （b） and graben terrain （c），respectively
图 3 无地形（a）、含地垒（b）、含地堑（c）的均匀半空间介质近地表高阻异常体正上方测点静态校正效果对比
Figure 3. Comparison of static correction effects of the measuring point above near surface high resistivity anomaly of homogeneous half-space with flat surface （a），horst terrain （b） and graben terrain （c），respectively
图 4 三层地层加近地表低阻和高阻异常体的模型
（a） 无地形；（b） 含地垒地形；（c） 含地堑地形
Figure 4. Schematic model of three-layer strata with low and high resistivity anomaly near surface
（a） The flat surface；（b） With the horst terrain；（c） With the graben terrain
图 5 使用四种方法对无地形（a）、含地垒（b）、含地堑（c）的水平层状介质近地表低阻异常体正上方测点进行静态校正效果对比
Figure 5. Comparison of static correction effects of measuring points above near surface low resistivity anomaly of the horizontal layered medium with flat surface （a），horst terrain （b） and graben terrain （c） using four methods，respectively
图 6 使用三种不同方法对无地形（a）、含地垒（b）、含地堑（c） 的水平层状介质近地表低阻异常体正上方测点的静态校正误差e对比
Figure 6. Comparison of static correction errors of measuring points above near surface low resistivity anomaly of the horizontal layered medium with flat surface （a），horst terrain （b）， and graben terrain （c） using three methods，respectively
图 7 使用四种方法对无地形（a）、含地垒（b）、含地堑（c）的水平层状介质近地表高阻异常体正上方测点静态校正效果对比
Figure 7. Comparison of static correction effects of the measuring points above near surface high resistivity anomaly of the horizontal layered medium with flat surface （a），horst terrain （b）， and graben terrain （c） using four methods，respectively
图 8 无地形（a）、含地垒（b）、含地堑（c）的均匀半空间介质近地表存在低阻和高阻且深部存在低阻电性异常体的模型
Figure 8. Schematic of the homogeneous half space model with near surface electrical anomaly bodies and deep embedding anomaly bodies with flat surface （a），horst terrain （b） and graben terrain （c），respectively
图 9 无地形（a）、含地垒（b）、含地堑（c）的三层地层近地表和深部存在电性异常体的模型
Figure 9. Schematic of three-layer strata model with near surface electrical anomalies and deep embedding anomaly with flat surface （a），horst terrain （b） and graben terrain （c），respectively
图 10 无地形（a）、含地垒（b）、含地堑（c）的均匀半空间介质中利用最高频相位法静态校正前后的正演（左侧两列）与反演（右侧两列）效果对比（白色矩形区域为模型中异常体的位置，下同）
Figure 10. Comparison of correction effects of the forward （left two columns） and inversion （right two columns） results before and after correction by the highest frequency phase method for homogeneous half-space with flat surface （a），horst terrain （b） and graben terrain （c），respectively （The white rectangle represents the anomalous body，the same below）
图 11 无地形（a）、含地垒（b）、含地堑（c）时水平均匀层状介质的联合校正法校正前后的正演（左侧两列）与反演（右侧两列）效果对比
Figure 11. Comparison of correction effects of the forward （left two columns） and inversion （right two columns） results before and after correction by the joint correction method for three-layer stratum model with flat surface （a），horst terrain （b） and graben terrain （c），respectively
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