Physics

These functions provide physical equations that either can be accessed directly or are used to support the TSP class and subclasses.

tsp.physics.analytical_fourier(depths: ndarray, times: ndarray, Q: float = 0.2, c: float = 1600000.0, k: float = 2.5, A: float = 6, MAGST: float = -0.5) → ndarray

Create sinusoidal synthetic data for examples and testing

Parameters:

  • depths (np.ndarray) – array of depths in m

  • times (np.ndarray) – array of times in seconds

  • Q (Optional[float], optional) – Geothermal heat flux [W m-2], by default 0.2

  • c (Optional[float], optional) – heat capacity [J m-3 K-1], by default 1.6e6

  • k (Optional[float], optional) – thermal conductivity [W m-1 K-1], by default 2.5

  • A (Optional[float], optional) – Amplitude of temperature fluctuation [C], by default 6

  • MAGST (Optional[float], optional) – mean annual ground surface temperature [C], by default -0.5

Returns:

_description_

Return type:

TSP

tsp.physics.initial_analytic(MAGST: float, Q: float, k: float, z: ndarray) → ndarray

Initial conditions for steady-state analytical temperature oscillation

Parameters:

  • MAGST (float) – mean annual ground surface temperature [C]

  • Q (float) – Geothermal heat flux [W m-2]

  • k (float) – thermal conductivity [W m-1 K-1]

  • z (np.ndarray) – ordered list of depths [m]

Returns:

initial temperature conditions [C]

Return type:

np.ndarray

tsp.physics.delta_analytic(A0: float, z: ndarray, w: float, alpha: float, t: ndarray) → ndarray

Analytical solution to heat conduction equation

Parameters:

  • A0 (float) – Amplitude of temperature fluctuation [C]

  • z (np.ndarray) – depth [m]

  • w (float) – period of temperature fluctuation [s]

  • kappa (float) – thermal diffusivity [W m-1 K-1]

  • t (np.ndarray) – time in seconds [s]

Return type:

np.ndarray