@wikipedia
Motivation
Outputs
espatial geothermal temperature distribution | Inputs
| t | Astronomic time | Geothermal Temperature Gradient |
|
--uriencoded--\lambda(%7B\bf r%7D) | Rock thermal conductivity Inputs
| j_z(x,y) | True vertical component of Regional Earth's heat flux (usually --uriencoded--j_z = 25 \div 55 \ mW/m%5e2 | )Assumptions
Equations
| Annual average surface temperature variation based on weather reports |
| | | Period of annual temperature variation cycle: | LaTeX Math Inline |
|---|
| body | --uriencoded--A_T = 1 \, %7B\rm year%7D |
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|
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| True vertical component of regional Earth's Heat Flux | | Time shift of annual highest temperature with respect to January 1 |
| Local annual average surface temperature based on weather reports | | Daily average surface temperature variation based on weather reports |
| LaTeX Math Inline |
|---|
| body | --uriencoded--a_%7Ben%7D |
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|
| Local average Thermal diffusivity of the soil between Earth's surface and NTL | | Period of daily temperature variation cycle: | LaTeX Math Inline |
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| body | --uriencoded--A_D = 1 \, %7B\rm day%7D |
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|
|
| Subsurface Thermal Conductivity profile as function of TVDss | | Time shift of daily highest temperature with respect to Midnight 00:00 |
|
| | LaTeX Math Inline |
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| body | --uriencoded--\delta T_%7B\rm cut%7D |
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|
| Temperature measurement threshold (usually | LaTeX Math Inline |
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| body | --uriencoded--\delta T_%7B\rm cut%7D = 0.01 \, %7B\rm °C%7D |
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|
) |
where
| |
| TVDss of the Earth's surface in a given location. In case the Earth's surface is at sea level then |
Assumptions
Equations
| LaTeX Math Block |
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| T_G(t, {\bf r}) = T_{GS}({\bf r}) + T_Y(t, z) + T_D(t, z) |
| | LaTeX Math Block |
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| G_T(z) = \frac{j_z}{\lambda_r(z)} |
|
| LaTeX Math Block |
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| \nabla T_{GS} = \lambda^{-1}({\bf r}) \cdot {\bf j} |
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| LaTeX Math Block |
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| T_{GS}(x, y, z = z_s) = T_s |
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| LaTeX Math Block |
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| T_Y(t,z) = \delta T_A \, \exp \left[ \, {(z_s-z}) \sqrt{\frac{\pi}{a_{en} \, A_T}} \, \right] \, \cos \left[ \, 2 \pi \frac{t - \delta t_A}{A_T} + (z_s -z) \sqrt |
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| Below Neutral Temperature Layer | Above Neutral Temperature Layer |
| LaTeX Math Block |
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T_g(x,y,z) = T_n(x,y) + \int_{z_n}^z G_T(x,y,z) dz |
| LaTeX Math Block |
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|
T(t, x, y,z) = T_s + \frac{j_z(x,y)}{\lambda_e} (z-z_s) + T_A \, \exp \left[ \, {(z_s-z}) \sqrte\delta \right] |
| LaTeX Math Block |
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| T_D(t,z) = \delta T_D \, \ |
|
cos 2 \pi\frac{t - t_min}}{\delta_T} + e\delta
| LaTeX Math Block |
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G_T(x, y, z) =\frac{d T_g}{d z}= \frac{j_z(x,y,z)}{\lambda_e} |
where
где
\, \cos \left[ \, 2 \pi \frac{t - \delta t_D}{D_T} + (z_s -z) \sqrt {\frac{\pi}{a_{en} \, D_T}} \, \right] |
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| Neutral Layer |
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| LaTeX Math Block |
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| z_n = z_s + H_n |
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| LaTeX Math Block |
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| H_n = \sqrt{\frac{a_{en} \, A_T }{\pi}} \, \ln \frac{\delta T_A }{\delta T_{\rm cut} } |
|
| TVDss of the Earth's surface |
| Annual average surface temperature based on weather reports |
| Annual average surface temperature variation based on weather reports |
| Temperature variation cycle (usually | LaTeX Math Inline |
|---|
| body | --uriencoded--\delta t = 1 \, %7B\rm year%7D |
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|
) |
| Temperature variation cycle shift (time moment of minimal temperature with respect to astronomic midnight 0:00) |
| LaTeX Math Inline |
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| body | a_e = \frac{\lambda_e}{\rho_e \, c_e} |
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|
| Rock temperature conductivity |
| Rock density |
| Rock specific volumetric heat capacity at constant pressure
See Also
...
Geology / Geothermal Temperature Field
...
