bruges.rockphysics.anisotropy module

Anisotropy effects.

Backus anisotropy is from thin layers.

Hudson anisotropy is from crack defects.

copyright:2015 Agile Geoscience
license:Apache 2.0
bruges.rockphysics.anisotropy.backus(vp, vs, rho, lb, dz)[source]

Backus averaging. Using Liner’s algorithm (2014; see Notes).

Parameters:
  • vp (ndarray) – P-wave interval velocity.
  • vs (ndarray) – S-wave interval velocity.
  • rho (ndarray) – Bulk density.
  • lb (float) – The Backus averaging length in m.
  • dz (float) – The depth sample interval in m.
Returns:

the smoothed logs: vp, vs, plus rho. Useful for computing

other elastic parameters at a seismic scale.

Return type:

namedtuple

Notes

Liner, C (2014), Long-wave elastic attenuation produced by horizontal layering. The Leading Edge, June 2014, p 634-638.

bruges.rockphysics.anisotropy.backus_parameters(vp, vs, rho, lb, dz)[source]

Intermediate parameters for Backus averaging. This is expected to be a private function. You probably want backus() and not this.

Parameters:
  • vp (ndarray) – P-wave interval velocity.
  • vs (ndarray) – S-wave interval velocity.
  • rho (ndarray) – Bulk density.
  • lb (float) – The Backus averaging length in m.
  • dz (float) – The depth sample interval in m.
Returns:

Liner’s 5 intermediate parameters: A, C, F, L and M.

Return type:

tuple

Notes

Liner, C (2014), Long-wave elastic attenuation produced by horizontal layering. The Leading Edge, June 2014, p 634-638.

bruges.rockphysics.anisotropy.backus_quality_factor(vp, vs, rho, lb, dz)[source]

Compute Qp and Qs from Liner (2014) equation 10.

Parameters:
  • vp (ndarray) – P-wave interval velocity.
  • vs (ndarray) – S-wave interval velocity.
  • rho (ndarray) – Bulk density.
  • lb (float) – The Backus averaging length in m.
  • dz (float) – The depth sample interval in m.
Returns:

Qp and Qs.

Return type:

namedtuple

bruges.rockphysics.anisotropy.blangy(vp1, vs1, rho1, d1, e1, vp0, vs0, rho0, d0, e0, theta)[source]

Blangy, JP, 1994, AVO in transversely isotropic media-An overview. Geophysics 59 (5), 775-781. DOI: 10.1190/1.1443635

Provide Vp, Vs, rho, delta, epsilon for the upper and lower intervals, and theta, the incidence angle.

Parameters:
  • vp1 – The p-wave velocity of the upper medium.
  • vs1 – The s-wave velocity of the upper medium.
  • rho1 – The density of the upper medium.
  • d1 – Thomsen’s delta of the upper medium.
  • e1 – Thomsen’s epsilon of the upper medium.
  • vp0 – The p-wave velocity of the lower medium.
  • vs0 – The s-wave velocity of the lower medium.
  • rho0 – The density of the lower medium.
  • d0 – Thomsen’s delta of the lower medium.
  • e0 – Thomsen’s epsilon of the lower medium.
  • theta – A scalar [degrees].
Returns:

the isotropic and anisotropic reflectivities in a tuple. The isotropic result is equivalent to Aki-Richards.

TODO
Use rocks.
bruges.rockphysics.anisotropy.crack_density(porosity, aspect)[source]

Returns crack density from porosity and aspect ratio, phi and alpha respectively in the unnumbered equation between 15.40 and 15.41 in Dvorkin et al. 2014.

Parameters:
  • porosity (float) – Fractional porosity.
  • aspect (float) – Aspect ratio.
Returns:

Crack density.

Return type:

float

bruges.rockphysics.anisotropy.dispersion_parameter(qp)[source]

Kjartansson (1979). Journal of Geophysical Research, 84 (B9), 4737-4748. DOI: 10.1029/JB084iB09p04737.

bruges.rockphysics.anisotropy.hudson_delta_G(porosity, aspect, mu, lam=None, pmod=None)[source]

The approximate reduction in shear modulus G (or mu) in the direction normal to a set of aligned cracks. Eqn 15.42 in Dvorkin et al (2014).

Parameters:
  • porosity (float) – Fractional porosity, phi.
  • aspect (float) – Aspect ratio, alpha.
  • mu (float) – Shear modulus, sometimes called G.
  • lam (float) – Lame’s first parameter, lambda.
  • pmod (float) – Compressional modulus, M.
Returns:

M_inf - M_0 = Delta c_11.

Return type:

float

bruges.rockphysics.anisotropy.hudson_delta_M(porosity, aspect, mu, lam=None, pmod=None)[source]

The approximate reduction in compressional modulus M in the direction normal to a set of aligned cracks. Eqn 15.40 in Dvorkin et al (2014).

Parameters:
  • porosity (float) – Fractional porosity, phi.
  • aspect (float) – Aspect ratio, alpha.
  • mu (float) – Shear modulus, sometimes called G.
  • lam (float) – Lame’s first parameter.
  • pmod (float) – Compressional modulus, M.
Returns:

M_inf - M_0 = Delta c_11.

Return type:

float

bruges.rockphysics.anisotropy.hudson_inverse_Q_ratio(mu=None, pmod=None, pr=None, vp=None, vs=None, aligned=True)[source]

Dvorkin et al. (2014), Eq 15.44 (aligned) and 15.48 (not aligned). You must provide one of the following: pr, or vp and vs, or mu and pmod.

Parameters:
  • mu (float) – Shear modulus, sometimes called G.
  • pmod (float) – Compressional modulus, M.
  • pr (float) – Poisson’s ratio, somtimes called v.
  • vp (ndarray) – P-wave interval velocity.
  • vs (ndarray) – S-wave interval velocity.
  • aligned (bool) – Either treats cracks as alligned (Default, True) or assumes defects are randomly oriented (False)
Returns:

2Q_s^-1

Return type:

float

bruges.rockphysics.anisotropy.hudson_quality_factor(porosity, aspect, mu, lam=None, pmod=None)[source]

Returns Q_p and Q_s for cracked media. Equations 15.41 and 15.43 in Dvorkin et al. (2014).

Parameters:
  • porosity (float) – Fractional porosity, phi.
  • aspect (float) – Aspect ratio, alpha.
  • mu (float) – Shear modulus, sometimes called G.
  • lam (float) – Lame’s first parameter, lambda.
  • pmod (float) – Compressional modulus, M.
Returns:

Q_p float: Q_s

Return type:

float

bruges.rockphysics.anisotropy.ruger(vp1, vs1, rho1, d1, e1, vp2, vs2, rho2, d2, e2, theta)[source]

Coded by Alessandro Amato del Monte and (c) 2016 by him https://github.com/aadm/avo_explorer/blob/master/avo_explorer_v2.ipynb

Rüger, A., 1997, P -wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry: Geophysics, v. 62, no. 3, p. 713–722.

Provide Vp, Vs, rho, delta, epsilon for the upper and lower intervals, and theta, the incidence angle.

Parameters:
  • vp1 – The p-wave velocity of the upper medium.
  • vs1 – The s-wave velocity of the upper medium.
  • rho1 – The density of the upper medium.
  • d1 – Thomsen’s delta of the upper medium.
  • e1 – Thomsen’s epsilon of the upper medium.
  • vp0 – The p-wave velocity of the lower medium.
  • vs0 – The s-wave velocity of the lower medium.
  • rho0 – The density of the lower medium.
  • d0 – Thomsen’s delta of the lower medium.
  • e0 – Thomsen’s epsilon of the lower medium.
  • theta – A scalar [degrees].
Returns:

anisotropic reflectivity.

bruges.rockphysics.anisotropy.thomsen_parameters(vp, vs, rho, lb, dz)[source]

Liner, C, and T Fei (2006). Layer-induced seismic anisotropy from full-wave sonic logs: Theory, application, and validation. Geophysics 71 (6), p D183–D190. DOI:10.1190/1.2356997

Parameters:
  • vp (ndarray) – P-wave interval velocity.
  • vs (ndarray) – S-wave interval velocity.
  • rho (ndarray) – Bulk density.
  • lb (float) – The Backus averaging length in m.
  • dz (float) – The depth sample interval in m.
Returns:

delta, epsilon and gamma.

Return type:

namedtuple