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Table 1 Partial derivatives of Φ, where Det[A]=A x x A y y A x y A y x is the determinant of A

From: Introducing inter-site phase tensors to suppress galvanic distortion in the telluric method

  Φ x x Φ x y Φ y x Φ y y
A x x \(\frac {-A_{yy}\varPhi _{xx}}{\text {Det}[\mathrm {A}]}\) \(\frac {-A_{yy}\varPhi _{xy}}{\text {Det}[\mathrm {A}]}\) \(\frac {B_{yx}-A_{yy}\varPhi _{yx}}{\text {Det}[\mathrm {A}]}\) \(\frac {B_{yy}-A_{yy}\varPhi _{yy}}{\text {Det}[\mathrm {A}]}\)
A x y \(\frac {-B_{yx}+A_{yx}\varPhi _{xx}}{\text {Det}[\mathrm {A}]}\) \(\frac {-B_{yy}+A_{yx}\varPhi _{xy}}{\text {Det}[\mathrm {A}]}\) \(\frac {A_{yx}\varPhi _{yx}}{\text {Det}[\mathrm {A}]}\) \(\frac {A_{yx}\varPhi _{yy}}{\text {Det}[\mathrm {A}]}\)
A y x \(\frac {A_{xy}\varPhi _{xx}}{\text {Det}[\mathrm {A}]}\) \(\frac {A_{xy}\varPhi _{xy}}{\text {Det}[\mathrm {A}]}\) \(\frac {-B_{xx}+A_{xy}\varPhi _{yx}}{\text {Det}[\mathrm {A}]}\) \(\frac {-B_{xy}+A_{xy}\varPhi _{yy}}{\text {Det}[\mathrm {A}]}\)
A y y \(\frac {B_{xx}-A_{xx}\varPhi _{xx}}{\text {Det}[\mathrm {A}]}\) \(\frac {B_{xy}-A_{xx}\varPhi _{xy}}{\text {Det}[\mathrm {A}]}\) \(\frac {-A_{xx}\varPhi _{yx}}{\text {Det}[\mathrm {A}]}\) \(\frac {A_{xx}\varPhi _{yy}}{\text {Det}[\mathrm {A}]}\)
B x x \(\frac {A_{yy}}{\text {Det}[\mathrm {A}]}\) 0 \(\frac {-A_{yx}}{\text {Det}[\mathrm {A}]}\) 0
B x y 0 \(\frac {A_{yy}}{\text {Det}[\mathrm {A}]}\) 0 \(\frac {-A_{yx}}{\text {Det}[\mathrm {A}]}\)
B y x \(\frac {-A_{xy}}{\text {Det}[\mathrm {A}]}\) 0 \(\frac {A_{xx}}{\text {Det}[\mathrm {A}]} \) 0
B y y 0 \(\frac {-A_{xy}}{\text {Det}[\mathrm {A}]}\) 0 \(\frac {A_{xx}}{\text {Det}[\mathrm {A}]}\)