AUTHOR=Tian Hongjun , Qiang Jianke , Li Kun , Tan Zhangkun , Zhang Ying , Zhu Dexiang 

TITLE=Wide field electromagnetic method calculation in arbitrary orientation and its effectiveness analysis

JOURNAL=Frontiers in Earth Science

VOLUME=11

YEAR=2023

URL=https://www.frontiersin.org/journals/earth-science/articles/10.3389/feart.2023.1158702

DOI=10.3389/feart.2023.1158702

ISSN=2296-6463

ABSTRACT=<p>The wide field electromagnetic method <inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>E</mml:mi><mml:mo>_</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> observation method requires the horizontal electrical field source (AB) to be parallel to the measure station (MN), but the complex terrain conditions make it difficult to meet the AB parallel MN in field construction, and there is always an azimuthal difference <inline-formula id="inf2"><mml:math id="m2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:math></inline-formula> between them, which will bring a large calculation error and cause distortion of the interpretation parameters if the calculation method <inline-formula id="inf3"><mml:math id="m3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>E</mml:mi><mml:mo>_</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> continues to be used. In order to tackle this problem, we analyse and study the <inline-formula id="inf4"><mml:math id="m4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>E</mml:mi><mml:mo>_</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> method and derive the new calculation method of <inline-formula id="inf5"><mml:math id="m5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>E</mml:mi><mml:mo>_</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>M</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> for the wide field electromagnetic method along the MN (<inline-formula id="inf6"><mml:math id="m6" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>E</mml:mi><mml:mo>_</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>M</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>). The method is based on the intrinsic relationship between the electric field components <inline-formula id="inf7"><mml:math id="m7" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula id="inf8"><mml:math id="m8" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and the azimuthal difference <inline-formula id="inf9"><mml:math id="m9" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:math></inline-formula> and derives the expression for the electric field <inline-formula id="inf10"><mml:math id="m10" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mrow><mml:mi>E</mml:mi><mml:mo>_</mml:mo><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>M</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> along the MN direction, and then uses the <inline-formula id="inf11"><mml:math id="m11" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>E</mml:mi><mml:mo>_</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>M</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> to calculate the wide field apparent resistivity. In this paper, we design a three-layer geoelectric model and calculate the azimuthal angle difference <inline-formula id="inf12"><mml:math id="m12" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:math></inline-formula> = 0° and <inline-formula id="inf13"><mml:math id="m13" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:math></inline-formula> = 15°wide field apparent resistivity parameters, respectively. The results show that the relative error between the calculated apparent resistivity and the theoretical value is less than 1%, which verifies the correctness and validity of the method. To further verify the accuracy of the method, experimental work on azimuthal difference <inline-formula id="inf14"><mml:math id="m14" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:math></inline-formula> was carried out next to a known well in Sichuan. The results show that: firstly, when <inline-formula id="inf15"><mml:math id="m15" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:math></inline-formula> is 1°, 3°, 5°, 10°, and 15°, respectively, the relative error of each frequency point increases with <inline-formula id="inf16"><mml:math id="m16" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:math></inline-formula> increasing. Secondly, when <inline-formula id="inf17"><mml:math id="m17" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:math></inline-formula> is 1°, 3°, 5°, 10°, and 15°, respectively, the relative error of each frequency point is less than 10% when the <inline-formula id="inf18"><mml:math id="m18" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>M</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> method is used to calculate the wide field apparent resistivity value; thirdly, taking <inline-formula id="inf19"><mml:math id="m19" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:math></inline-formula> = 15° as an example, single-station inversions are performed with <inline-formula id="inf20"><mml:math id="m20" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula id="inf21"><mml:math id="m21" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>M</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> apparent resistivity parameters, in which the <inline-formula id="inf22"><mml:math id="m22" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inversion results are more different from the trend of the logging curve, while the <inline-formula id="inf23"><mml:math id="m23" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>M</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> inversion results are relatively more consistent with the trend of the logging curve. The arbitrary orientation <inline-formula id="inf24"><mml:math id="m24" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>M</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> calculation method proposed in this paper can effectively reduce the influence of <inline-formula id="inf25"><mml:math id="m25" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:math></inline-formula> on the interpretation parameters and improve the accuracy of interpretation, and also greatly expand the applicability and flexibility of <inline-formula id="inf26"><mml:math id="m26" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> wide field electromagnetic method in the observation of complex terrain areas, which has important theoretical research and practical production significance.</p>