Analytical formulas for geometrical factor and sensitivity for long electrodes.
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| Title: | Analytical formulas for geometrical factor and sensitivity for long electrodes. |
|---|---|
| Authors: | Butler, S. L.1 (AUTHOR) sam.butler@usask.ca |
| Source: | Geophysical Prospecting. Jan2025, Vol. 73 Issue 1, p130-141. 12p. |
| Subjects: | Electrical resistivity, Electric potential measurement, Archaeological surveying, Analytical solutions, Ideal sources (Electric circuits) |
| Abstract: | In the electrical resistivity method, electrodes are usually modelled as point current sources and point voltage measurements. If the burial depth of the electrode is significant compared with the spacing between electrodes, this point approximation may not be accurate. Common situations employing long electrodes include the use of metal‐cased boreholes as electrodes and small‐scale, high‐resolution environmental, engineering and archaeological surveys where electrode spacings may be very small. In this contribution, I present analytical expressions for the mutual resistance between long electrodes modelled as line current sources. Mutual resistances are then used to calculate geometrical factors. Additionally, I present an expression for the current density and use it to derive an analytical expression for the sensitivity of electrode arrays with long electrodes. The sensitivity is, in turn, used to calculate the mean depth and position which can be used as estimates of depth and position of investigation and as pseudosection plot points. Example calculations using the geometrical factor, sensitivity and mean depth are shown, and comparisons are made with simulations and lab‐scale experiments. [ABSTRACT FROM AUTHOR] |
| Copyright of Geophysical Prospecting is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 181804204 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Analytical formulas for geometrical factor and sensitivity for long electrodes. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Butler%2C+S%2E+L%2E%22">Butler, S. L.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> sam.butler@usask.ca</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Geophysical+Prospecting%22">Geophysical Prospecting</searchLink>. Jan2025, Vol. 73 Issue 1, p130-141. 12p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Electrical+resistivity%22">Electrical resistivity</searchLink><br /><searchLink fieldCode="DE" term="%22Electric+potential+measurement%22">Electric potential measurement</searchLink><br /><searchLink fieldCode="DE" term="%22Archaeological+surveying%22">Archaeological surveying</searchLink><br /><searchLink fieldCode="DE" term="%22Analytical+solutions%22">Analytical solutions</searchLink><br /><searchLink fieldCode="DE" term="%22Ideal+sources+%28Electric+circuits%29%22">Ideal sources (Electric circuits)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In the electrical resistivity method, electrodes are usually modelled as point current sources and point voltage measurements. If the burial depth of the electrode is significant compared with the spacing between electrodes, this point approximation may not be accurate. Common situations employing long electrodes include the use of metal‐cased boreholes as electrodes and small‐scale, high‐resolution environmental, engineering and archaeological surveys where electrode spacings may be very small. In this contribution, I present analytical expressions for the mutual resistance between long electrodes modelled as line current sources. Mutual resistances are then used to calculate geometrical factors. Additionally, I present an expression for the current density and use it to derive an analytical expression for the sensitivity of electrode arrays with long electrodes. The sensitivity is, in turn, used to calculate the mean depth and position which can be used as estimates of depth and position of investigation and as pseudosection plot points. Example calculations using the geometrical factor, sensitivity and mean depth are shown, and comparisons are made with simulations and lab‐scale experiments. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Geophysical Prospecting is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1111/1365-2478.13644 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 12 StartPage: 130 Subjects: – SubjectFull: Electrical resistivity Type: general – SubjectFull: Electric potential measurement Type: general – SubjectFull: Archaeological surveying Type: general – SubjectFull: Analytical solutions Type: general – SubjectFull: Ideal sources (Electric circuits) Type: general Titles: – TitleFull: Analytical formulas for geometrical factor and sensitivity for long electrodes. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Butler, S. L. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: Jan2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 00168025 Numbering: – Type: volume Value: 73 – Type: issue Value: 1 Titles: – TitleFull: Geophysical Prospecting Type: main |
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