| 椭球体的视电阻率特征 |
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| 引用本文： | 张超,汤井田,强建科.椭球体的视电阻率特征[J].物探化探计算技术,2014(2):158-163. |
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| 作者姓名： | 张超 汤井田 强建科 |
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| 作者单位： | 中南大学地球科学与信息物理学院,长沙410083 |
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| 基金项目： | 国家自然科学基金（41174105） |
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| 摘 要： | 椭球体是最具代表性的典型三维地电体之一,它三个轴的长短经过变化后可以和多种形状的地电体相似。因此,实现了椭球体电阻率的求解,就可以模拟绝大多数三维地电体的电阻率曲线。从拉普拉斯方程的求解出发,得到了均匀空间中存在的水平椭球体异常表达式,并用简单加倍的方法得到了均匀半空间中水平椭球体的视电阻率公式,结合倾斜旋转椭球体的视电阻率公式的规律,得到了倾斜椭球体的视电阻率公式,再进行一系列简化得到板状体。最后分析对比了均匀电场中旋转椭球体和板状体的视电阻率曲线的形态和规律。结论表明:旋转椭球体与板状体的视电阻率曲线的走向大体相似,且板状体的曲线相比旋转椭球体较缓和。对于低阻情况,在异常体顶部附近的视电阻率异常为零,异常体的倾向一侧有极小值,反倾向一侧有极大值,曲线随倾角α的增大而逐渐变陡。对于高阻情况,视电阻率的极大值出现在异常体顶部附近,两侧有极小值,倾向一侧的曲线较缓和而反倾向一侧的曲线较陡峭,随着倾角α的增大,视电阻率异常变大。
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| 关 键 词： | 电场 椭球体 板状体 视电阻率 |
Characteristics of the apparent resistivity of ellipsoid |
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| ZHANG Chao,TANG Jing-tian,QIANG Jian-ke.Characteristics of the apparent resistivity of ellipsoid[J].Computing Techniques For Geophysical and Geochemical Exploration,2014(2):158-163. |
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| Authors: | ZHANG Chao TANG Jing-tian QIANG Jian-ke |
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| Institution: | (School of Geo science and Info Physics, Central South University, Changsha 410083, China) |
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| Abstract: | Ellipsoid is one of the most typical three-dinensional geo-electrical body, by changing the length of three axes it can be similar to a variety of geo electric models with different shapes. Therefore, most of the three dimensional geo elec trical bodys apparent resistivity can be given after calculating the apparent resistivity of ellipsoid. From the solution of Laplaceequation, a horizontal ellipsoid anomaly in uniform space was obtained, and the formula of apparent resistivity of ellipsoid in a homogeneous half space was given by using the method of double abnormality, Combined with the law of the resisitivity of the inclined rotating ellipsoid, the formula of apparent resistivity of inclined ellipsoid was obtained. And then with a sery of simpli fication to ellipsoid, a plate was obtained. Finally the shape of the apparent resistivity curve of rotating ellipsoid and plate was also compared. The conclusion shows that the trend of the apparent resistivity curve is similar between inclined rotating ellip soid and plate, and the curve of plate is tender than that of inclined rotating ellipsoid. In terms of low resistivity, the apparent resistivity anomaly is zero on the top of the abnormal body; the inclination direction has minimum value while the other direc tion has maximum value;the curve becomes steep with the increase of the inclination angle, In terms of high resistivity, the maximum of apparent resistivity is on the top of the abnormal body; while minimum value turns out on both sides; the curve in the inclination direction is tender while that in the other side is steep; the apparent resistivity anomaly increases as the inclination angle increases. |
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| Keywords: | electric fields ellipsoid plate apparent resistivity |
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