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<front>
<journal-meta>
<journal-id journal-id-type="publisher">SED</journal-id>
<journal-title-group>
<journal-title>Solid Earth Discussions</journal-title>
<abbrev-journal-title abbrev-type="publisher">SED</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Solid Earth Discuss.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1869-9537</issn>
<publisher><publisher-name></publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.5194/se-2020-201</article-id>
<title-group>
<article-title>An upward continuation method based on spherical harmonic 
analysis and its application in the calibration of satellite gravity 
gradiometry data</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Qu</surname>
<given-names>Qingliang</given-names>
<ext-link>https://orcid.org/0000-0002-4059-0434</ext-link>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Yu</surname>
<given-names>Shengwen</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Zhu</surname>
<given-names>Guangbin</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Chang</surname>
<given-names>Xiaotao</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Zhou</surname>
<given-names>Miao</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Liu</surname>
<given-names>Wei</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>College of Geomatics, Shandong University of Science and Technology, Qingdao 266510, China</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>Land Satellite Remote Sensing Application Center of the Ministry of Natural Resources, Beijing 100048,  China</addr-line>
</aff>
<pub-date pub-type="epub">
<day>09</day>
<month>02</month>
<year>2021</year>
</pub-date>
<volume>2021</volume>
<fpage>1</fpage>
<lpage>17</lpage>
<permissions>
<copyright-statement>Copyright: &#x000a9; 2021 Qingliang Qu et al.</copyright-statement>
<copyright-year>2021</copyright-year>
<license license-type="open-access">
<license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri"  xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p>
</license>
</permissions>
<self-uri xlink:href="https://se.copernicus.org/preprints/se-2020-201/">This article is available from https://se.copernicus.org/preprints/se-2020-201/</self-uri>
<self-uri xlink:href="https://se.copernicus.org/preprints/se-2020-201/se-2020-201.pdf">The full text article is available as a PDF file from https://se.copernicus.org/preprints/se-2020-201/se-2020-201.pdf</self-uri>
<abstract>
<p>&lt;p&gt;The ground gravity anomalies can be used to calibrate and validate the satellite gravity gradiometry data. In this study, an upward continuation method of ground gravity data based on spherical harmonic analysis is proposed, which can be applied to the calibration of satellite observations from the European Space Agency&apos;s Gravity Field and Steady-State Ocean Circulation Explorer (GOCE). Here, the following process was conducted to apply this method. The accuracy of the upward continuation method based on spherical harmonic analysis was verified using simulated ground gravity anomalies. The DTU13 global gravity anomaly data were used to determine the calibration parameters of the GOCE gravitational gradients based on the spherical harmonic analysis method. The trace and the tensor invariants &lt;i&gt;I&lt;sub&gt;2&lt;/sub&gt;&lt;/i&gt;, &lt;i&gt;I&lt;sub&gt;3&lt;/sub&gt;&lt;/i&gt; of the gravitational gradients were used to verify the calibration results. The results revealed that the upward continuation errors based on spherical harmonic analysis were much smaller than the noise level in the measurement bandwidth of the GOCE gravity gradiometer. The scale factors of the &lt;i&gt;V&lt;sub&gt;xx&lt;/sub&gt;&lt;/i&gt;, &lt;i&gt;V&lt;sub&gt;yy&lt;/sub&gt;&lt;/i&gt;, &lt;i&gt;V&lt;sub&gt;zz&lt;/sub&gt;&lt;/i&gt;, and &lt;i&gt;V&lt;sub&gt;yz&lt;/sub&gt;&lt;/i&gt; components were determined at an order of magnitude of approximately 10&lt;sup&gt;&amp;minus;2&lt;/sup&gt;, the &lt;i&gt;V&lt;sub&gt;xz&lt;/sub&gt;&lt;/i&gt; component was approximately 10&lt;sup&gt;&amp;minus;3&lt;/sup&gt;, and the &lt;i&gt;V&lt;sub&gt;xy&lt;/sub&gt;&lt;/i&gt; component was approximately 10&lt;sup&gt;&amp;minus;1&lt;/sup&gt;. The traces of gravitational gradients after calibration were improved when compared with the traces before calibration and were slightly better than the EGG_TRF_2 data released by the European Space Agency (ESA). In addition, the relative errors of the tensor invariants &lt;i&gt;I&lt;sub&gt;2&lt;/sub&gt;&lt;/i&gt;, &lt;i&gt;I&lt;sub&gt;3&lt;/sub&gt;&lt;/i&gt; of the gravitational gradients after calibration were significantly better than those before calibration. In conclusion, the upward continuation method based on spherical harmonic analysis could meet the external calibration accuracy requirements of the gradiometer.&lt;/p&gt;</p>
</abstract>
<counts><page-count count="17"/></counts>
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