An efficient decoupled 3-D axial anisotropic resistivity inversion for magnetotelluric data with OpenMP parallelization

<jats:title>Abstract</jats:title> <jats:p>We have developed two novel axial anisotropic inversion codes for magnetotelluric (MT) data: a full axial inversion and a decoupled axial inversion. Both codes are based on the data space Gauss–Newton inversion method used in the WSINV3DMT code, enhanced with OpenMP parallelization and Intel MKL PARDISO direct solver for improved computational efficiency. The full axial inversion searches for three axial anisotropic resistivity elements <jats:inline-formula> <jats:alternatives> <jats:tex-math>$${\rho }_{xx}$$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mrow> <mml:mi>xx</mml:mi> </mml:mrow> </mml:msub> </mml:math> </jats:alternatives> </jats:inline-formula>, <jats:inline-formula> <jats:alternatives> <jats:tex-math>$${\rho }_{yy}$$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mrow> <mml:mi>yy</mml:mi> </mml:mrow> </mml:msub> </mml:math> </jats:alternatives> </jats:inline-formula>, and <jats:inline-formula> <jats:alternatives> <jats:tex-math>$${\rho }_{zz}$$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mrow> <mml:mi>zz</mml:mi> </mml:mrow> </mml:msub> </mml:math> </jats:alternatives> </jats:inline-formula>. Based on our prior influence studies, we identified contrasting influence patterns: <jats:inline-formula> <jats:alternatives> <jats:tex-math>$${\rho }_{xx}$$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mrow> <mml:mi>xx</mml:mi> </mml:mrow> </mml:msub> </mml:math> </jats:alternatives> </jats:inline-formula> has a strong influence on <jats:italic>Z</jats:italic> <jats:sub> <jats:italic>xy</jats:italic> </jats:sub> and <jats:italic>Z</jats:italic> <jats:sub> <jats:italic>yy</jats:italic> </jats:sub>, whereas <jats:inline-formula> <jats:alternatives> <jats:tex-math>$${\rho }_{yy}$$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mrow> <mml:mi>yy</mml:mi> </mml:mrow> </mml:msub> </mml:math> </jats:alternatives> </jats:inline-formula> has a strong influence on <jats:italic>Z</jats:italic> <jats:sub> <jats:italic>yx</jats:italic> </jats:sub> and <jats:italic>Z</jats:italic> <jats:sub> <jats:italic>xx</jats:italic> </jats:sub>, while <jats:inline-formula> <jats:alternatives> <jats:tex-math>$${\rho }_{zz}$$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mrow> <mml:mi>zz</mml:mi> </mml:mrow> </mml:msub> </mml:math> </jats:alternatives> </jats:inline-formula> has negligible impact on all responses. We, therefore, proposed a decoupled axial inversion. This novel technique splits the full axial inversion into two independent modes: <jats:inline-formula> <jats:alternatives> <jats:tex-math>$${\rho }_{xx}$$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mrow> <mml:mi>xx</mml:mi> </mml:mrow> </mml:msub> </mml:math> </jats:alternatives> </jats:inline-formula>- and <jats:inline-formula> <jats:alternatives> <jats:tex-math>$${\rho }_{yy}$$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml ...