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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

\(\frac {A_{xx}}{\text {Det}[\mathrm {A}]}\)