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Motivation


In many subsurface applications which require the knowledge of subsurface temperature distributions the land area of the study is small enough to consider the subsurface heat flux  

LaTeX Math Inline
body--uriencoded--%7B \bf j%7D(x,y,z) = \%7B j_x, \, j_y, \, j_z \%7D
 to be independent on areal location:  
LaTeX Math Inline
body--uriencoded--%7B \bf j%7D(x,y,z) =%7B \bf j%7D(z)
 and vanishing lateral components: 
LaTeX Math Inline
body--uriencoded--%7B \bf j%7D(x,y,z) = \%7B j_x = 0, \, j_y = 0 , \, j_z(z) \%7D
.

Normally there are no heat sources within a subsurface3 volume under study other than Earth's Heat Flux which means that true vertical component 

LaTeX Math Inline
bodyj_z(z) = j_z = \rm const
 is constant along true vertical direction.

This simplifies the procedure of modelling the Geothermal Temperature Field 

LaTeX Math Inline
body--uriencoded--%7B \bf j%7D(x,y,z) = \%7B 0, \, 0 , \, j_z \%7D
 which called .


Outputs

LaTeX Math Inline
bodyT_e(t, l)

along-hole geothermal temperature profile

LaTeX Math Inline
bodyG_T(z)

temperature gradient

LaTeX Math Inline
bodyH_N

neutral layer

...

LaTeX Math Inline
bodyt

Astronomic time

LaTeX Math Inline
body\delta T_A

Annual average surface temperature variation based on weather reports

LaTeX Math Inline
bodyl

wellbore trajectory Measured Depth with reference to Earth's surface (

LaTeX Math Inline
bodyl=0
)

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
bodyz(l)

Wellbore trajectory. True Vertical Depth Sub-Sea (TVDss)

LaTeX Math Inline
body\delta t_A

Time moment of annual highest temperature with respect to January 1

LaTeX Math Inline
bodyj_z

True vertical component of regional Earth's Heat Flux

LaTeX Math Inline
body\delta T_D

Daily average surface temperature variation based on weather reports

LaTeX Math Inline
bodyT_s

Annual average surface temperature based on weather reports

LaTeX Math Inline
bodyD_T

Period of daily temperature variation cycle:

LaTeX Math Inline
body--uriencoded--A_D = 1 \, %7B\rm day%7D

LaTeX Math Inline
bodya_e

Average Thermal diffusivity of the soil between Earth's surface and neutral layer

LaTeX Math Inline
body\delta t_D

Time moment of daily highest temperature with respect to Midnight 00:00

LaTeX Math Inline
body\lambda_r(l)

Rock Thermal Conductivity along-hole profile

LaTeX Math Inline
body--uriencoded--\delta T_%7B\rm cut%7D

Temperature measurement threshold (usually

LaTeX Math Inline
body--uriencoded--\delta T_%7B\rm cut%7D = 0.001 \, %7B\rm °C%7D
) 

...