Inversion of the satellite observations of the tidally induced magnetic field in terms of 3-D upper-mantle electrical conductivity: Method and synthetic tests
Authors: Šachl Libor , Velímský Jakub , Fullea Javier 
Published: March 2021

&lt;p&gt;&lt;span&gt;&lt;span&gt;We have developed and tested a new frequency-domain, spherical harmonic-finite element approach to the inverse problem of global electromagnetic (EM) induction. It is based on the quasi-Newton minimization of data misfit and regularization, and uses the adjoint approach for fast calculation of misfit gradients in the model space. Thus, it allows for an effective inversion of satellite-observed magnetic field induced by tidally driven flows in the Earth's oceans in terms of 3-D structure of the electrical conductivity in the upper mantle.&lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt; Before proceeding to the inversion of Swarm-derived models of tidal magnetic signatures, we have performed a series of &lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt;parametric studies&lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt;, using a 3-D conductivity model WINTERC-e as a testbed.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;The WINTERC-e model has been derived using state-of-the-art laboratory conductivity measurements of mantle minerals, and thermal and compositional model of the lithosphere and upper mantle WINTERC-grav. The latter model is based on the inversion of global surface waveforms, satellite gravity and gradiometry measurements, surface elevation, and heat flow data &lt;/span&gt;&lt;span&gt;&lt;span&gt;in a thermodynamically self-consistent framework. &lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt;Therefore, the WINTERC-e model, independent of any EM data, represents an ideal target for synthetic tests of the 3-D EM inversion.&lt;/span&gt;&lt;/span&gt;&lt;span&gt; &lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;&lt;span&gt;We tested the impact of &lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt;the &lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt;satellite &lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt;altitude&lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt;, &lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt;the truncation degree of the &lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt;spherical-harmonic &lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt;expansion of the tidal signals, the random&lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt; noise in data&lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt;,&lt;/span&gt;&lt;/span&gt;&lt;span&gt; &lt;/span&gt;&lt;span&gt;&lt;span&gt;and &lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt;of the &lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt;sub-&lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt;continental conductivity&lt;/span&gt;&lt;/span&gt;&lt;span&gt; &lt;/span&gt;&lt;span&gt;&lt;span&gt;on the &lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt;ability to recover the sub-oceanic upper-mantle conductivity structure.&lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt; We &lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt;demonstrate &lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt;that &lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt;with &lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt;suitable regularization &lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt;we&lt;/span&gt;&lt;/span&gt;&lt;span&gt; &lt;/span&gt;&lt;span&gt;&lt;span&gt;can successfully reconstruct the 3D upper-mantle conductivity below world oceans.&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;