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Below Neutral Temperature LayerAbove Neutral Temperature Layer


LaTeX Math Block
anchorT_g
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T_g(l) = T_n + \int_{z_n}^z G_T(z) dz



LaTeX Math Block
anchorT_z
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T(t, z) = T_s + \frac{j_z}{\lambda_e} (z-z_s) + T_Y(t, z) + T_D(t, z)



LaTeX Math Block
anchorG_T
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G_T(z) =\frac{d T_g}{d z}= \frac{j_z}{\lambda_e}



LaTeX Math Block
anchorT_z
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T_A(t,z) = \delta T_A \, \exp \left[ \, {(z_s-z}) \sqrt{\frac{\pi}{a_e \, A_T}} \, \right] \, \cos \left[  \, 2 \pi \frac{t - \delta t_A}{A_T} + (z_s -z) \sqrt {\frac{\pi}{a_e \, A_T}} \, \right]




LaTeX Math Block
anchorT_z
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T_D(t,z) = \delta T_AD \, \exp \left[ \, {(z_s-z}) \sqrt{\frac{\pi}{a_e \, \deltaA_TD}} \, \right] \, \cos \left[  \, 2 \pi \frac{t - \delta t_{min}D}{\deltaD_T} + (z_{srf}s -z) \sqrt {\frac{\pi}{a_e \, \deltaD_T}} \, \right]


where

где

LaTeX Math Inline
bodyz_s

TVDss of the Earth's surface

LaTeX Math Inline
bodyT_{srf}

Annual average surface temperature based on weather reports

LaTeX Math Inline
bodyT_A

Annual average surface temperature variation based on weather reports

LaTeX Math Inline
bodyA_T

Period of annual temperature variation cycle:

LaTeX Math Inline
body--uriencoded--A_T = 1 \, %7B\rm year%7D
)

LaTeX Math Inline
body\delta t_A

Temperature variation cycle shift (time moment of minimal temperature with respect to astronomic midnight 0:00)

LaTeX Math Inline
bodya_e = \frac{\lambda_e}{\rho_e \, c_e}

Rock temperature conductivity

LaTeX Math Inline
body\rho_e

Rock density

LaTeX Unit
bodyc_e

Rock specific volumetric heat capacity at constant pressure

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