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: Chong Zhang, Qingtian Lü, Jiayong Yan, Guang Qi
Format: Article
Language:English
Published: Wiley 2018-04-01
Series:Geophysical Research Letters
Subjects:
Online Access:https://doi.org/10.1002/2018GL076995
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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.
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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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AT qingtianlu numericalsolutionsofthemeanvaluetheoremnewmethodsfordownwardcontinuationofpotentialfields
AT jiayongyan numericalsolutionsofthemeanvaluetheoremnewmethodsfordownwardcontinuationofpotentialfields
AT guangqi numericalsolutionsofthemeanvaluetheoremnewmethodsfordownwardcontinuationofpotentialfields