Numerical Solutions of the Mean‐Value Theorem: New Methods for Downward Continuation of Potential Fields
Abstract Downward continuation can enhance small‐scale sources and improve resolution. Nevertheless, the common methods have disadvantages in obtaining optimal results because of divergence and instability. We derive the mean‐value theorem for potential fields, which could be the theoretical basis o...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-04-01
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| Series: | Geophysical Research Letters |
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| Online Access: | https://doi.org/10.1002/2018GL076995 |
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| _version_ | 1850260792265408512 |
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| author | Chong Zhang Qingtian Lü Jiayong Yan Guang Qi |
| author_facet | Chong Zhang Qingtian Lü Jiayong Yan Guang Qi |
| author_sort | Chong Zhang |
| collection | DOAJ |
| description | Abstract Downward continuation can enhance small‐scale sources and improve resolution. Nevertheless, the common methods have disadvantages in obtaining optimal results because of divergence and instability. We derive the mean‐value theorem for potential fields, which could be the theoretical basis of some data processing and interpretation. Based on numerical solutions of the mean‐value theorem, we present the convergent and stable downward continuation methods by using the first‐order vertical derivatives and their upward continuation. By applying one of our methods to both the synthetic and real cases, we show that our method is stable, convergent and accurate. Meanwhile, compared with the fast Fourier transform Taylor series method and the integrated second vertical derivative Taylor series method, our process has very little boundary effect and is still stable in noise. We find that the characters of the fading anomalies emerge properly in our downward continuation with respect to the original fields at the lower heights. |
| format | Article |
| id | doaj-art-9c0f164c45f04d43b59f60ab7e5d65f4 |
| institution | OA Journals |
| issn | 0094-8276 1944-8007 |
| language | English |
| publishDate | 2018-04-01 |
| publisher | Wiley |
| record_format | Article |
| series | Geophysical Research Letters |
| spelling | doaj-art-9c0f164c45f04d43b59f60ab7e5d65f42025-08-20T01:55:33ZengWileyGeophysical Research Letters0094-82761944-80072018-04-014583461347010.1002/2018GL076995Numerical Solutions of the Mean‐Value Theorem: New Methods for Downward Continuation of Potential FieldsChong Zhang0Qingtian Lü1Jiayong Yan2Guang Qi3China Deep Exploration Center (SinoProbe Center) Chinese Academy of Geological Sciences Beijing ChinaChina Deep Exploration Center (SinoProbe Center) Chinese Academy of Geological Sciences Beijing ChinaChina Deep Exploration Center (SinoProbe Center) Chinese Academy of Geological Sciences Beijing ChinaChina Deep Exploration Center (SinoProbe Center) Chinese Academy of Geological Sciences Beijing ChinaAbstract Downward continuation can enhance small‐scale sources and improve resolution. Nevertheless, the common methods have disadvantages in obtaining optimal results because of divergence and instability. We derive the mean‐value theorem for potential fields, which could be the theoretical basis of some data processing and interpretation. Based on numerical solutions of the mean‐value theorem, we present the convergent and stable downward continuation methods by using the first‐order vertical derivatives and their upward continuation. By applying one of our methods to both the synthetic and real cases, we show that our method is stable, convergent and accurate. Meanwhile, compared with the fast Fourier transform Taylor series method and the integrated second vertical derivative Taylor series method, our process has very little boundary effect and is still stable in noise. We find that the characters of the fading anomalies emerge properly in our downward continuation with respect to the original fields at the lower heights.https://doi.org/10.1002/2018GL076995Potential fieldsMean‐value theoremDownward continuation |
| spellingShingle | Chong Zhang Qingtian Lü Jiayong Yan Guang Qi Numerical Solutions of the Mean‐Value Theorem: New Methods for Downward Continuation of Potential Fields Geophysical Research Letters Potential fields Mean‐value theorem Downward continuation |
| title | Numerical Solutions of the Mean‐Value Theorem: New Methods for Downward Continuation of Potential Fields |
| title_full | Numerical Solutions of the Mean‐Value Theorem: New Methods for Downward Continuation of Potential Fields |
| title_fullStr | Numerical Solutions of the Mean‐Value Theorem: New Methods for Downward Continuation of Potential Fields |
| title_full_unstemmed | Numerical Solutions of the Mean‐Value Theorem: New Methods for Downward Continuation of Potential Fields |
| title_short | Numerical Solutions of the Mean‐Value Theorem: New Methods for Downward Continuation of Potential Fields |
| title_sort | numerical solutions of the mean value theorem new methods for downward continuation of potential fields |
| topic | Potential fields Mean‐value theorem Downward continuation |
| url | https://doi.org/10.1002/2018GL076995 |
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