def transFwdArchiePhi(rFluid=20, m=2):
r"""Archies law transformation function for resistivity(porosity).
.. math::
\rho & = a\rho_{\text{fl}}\phi^{-m}\S_w^{-n} \\
\rho & = \rho_{\text{fl}}\phi^(-m) =
\left(\phi/\rho_{\text{fl}}^{-1/n}\right)^{-n}
See also :py:mod:`pygimli.physics.petro.resistivityArchie`
Returns
-------
trans : :gimliapi:`GIMLI::RTransPower`
Transformation function
Examples
--------
>>> from pygimli.physics.petro import *
>>> phi = 0.3
>>> tFAPhi = transFwdArchiePhi(rFluid=20)
>>> r1 = tFAPhi.trans(phi)
>>> r2 = resistivityArchie(rFluid=20.0, porosity=phi,
... a=1.0, m=2.0, sat=1.0, n=2.0)
>>> print(r1-r2 < 1e-12)
True
>>> phi = [0.3]
>>> tFAPhi = transFwdArchiePhi(rFluid=20)
>>> r1 = tFAPhi.trans(phi)
>>> r2 = resistivityArchie(rFluid=20.0, porosity=phi,
... a=1.0, m=2.0, sat=1.0, n=2.0)
>>> print((r1-r2 < 1e-12)[0])
True
"""
return pg.RTransPower(-m, rFluid**(1. / m))
def transInvArchiePhi(rFluid=20, m=2): # phi(rho)
"""Inverse Archie transformation function porosity(resistivity).
# rFluid/rho = phi^m ==> phi = (rFluid/rho)^(1/m) = (rho/rFluid)^(-1/m)
See
---
:py:mod:`pygimli.physics.petro.transFwdArchiePhi`
"""
return pg.RTransPower(-1 / m, rFluid)
def transInvArchieS(rFluid=20, phi=0.4, m=2, n=2): # S(rho)
"""Inverse Archie transformation function saturation(resistivity)."""
# rFluid/rho = phi^m S^n => S=(rFluid/rho/phi^m)^(1/n)
# S = (rho/rFluid/phi^-m)^(-1/n)
return pg.RTransPower(-1 / n, rFluid * phi**(-m))
def transFwdArchieS(rFluid=20, phi=0.4, m=2, n=2): # rho(S)
"""Inverse Archie transformation function resistivity(saturation)."""
# rho = rFluid * phi^(-m) S^(-n)
return pg.RTransPower(-n, (rFluid * phi**(-m))**(1 / n))