rockphypy.Anisotropy

Module Contents

Classes

Anisotropy

Effective models, coordinate transform, anisotropic parameters and phase velocities that can be applied to anisotropic media.

class rockphypy.Anisotropy.Anisotropy

Effective models, coordinate transform, anisotropic parameters and phase velocities that can be applied to anisotropic media.

static Thomsen(C11, C33, C13, C44, C66, den, theta)

Compute thomsen parameters and three phase velocities for weak anisotropic TI media with vertical symmetry axis.

Parameters:

• Cij (float) – Stiffnesses in GPa

• den (float) – density of the effective medium, for backus average, the effective density can be computed using VRH method for Voigt average.

• theta (float or array-like) – angle of incidence

Returns:

float or array-like – VP, VSV, VSH: wave velocities propagating along given direction

static Thomsen_Tsvankin(C11, C22, C33, C12, C13, C23, C44, C55, C66)

Elastic constants of an orthorhombic elastic medium defined by Tsvankin’s notation for weak elastic anisotropy assuming the vertical symmetry axis is along the x3 direction.

Parameters:

Cij (float) – Stiffnesses in GPa

Returns:

floats – Thomsen-Tsvankin parameters

static Backus(V, lamda, G)

Computes stiffnesses of a layered medium using backus average model.

Parameters:

• V (float or array-like) – volumetric fractions of N isotropic layering materials

• lamda (float or array-like) – Lamé coefficients of N isotropic layering materials

• G (float or array-like) – shear moduli of N isotropic layering materials

Returns:

float or array-like – C11,C33,C13,C44,C66:Elastic moduli of the anisotropic layered media

static Backus_log(Vp, Vs, Den, Depth)

Computes Backus Average from log data, notice that the Depth is 1d Vector including each top depth of layer and also the bottom of last layer.

Parameters:

• Vp (array) – P wave velocities of layers [Vp1,Vp2…Vpn], Km/s, size N

• Vs (array) – S wave velocities of layers [Vs1,Vs2…Vsn],Km/s size N

• Den (array) – Densities of layers, size N

• Depth (array) – 1d depth, ATTENTION: each depth point corresponds to the top of thin isotropic layer, the bottom of the sedimentary package is the last depth point. [dep1,dep2,,,,,,depn, depn+1], size N+1

Returns:

array-like – Stiffness coeffs and averaged density

static vel_azi_HTI(C, Den, azimuth)

Given stiffnesses and density of the HTI medium, compute the azimuth dependent phase velocities.

Parameters:

• C (2d array) – stiffness matrix of the HTI medium

• Den (float) – density of the fractured medium

• azimuth (float or array like) – azimuth angle, degree

Returns:

float or array like – VP,VSH, VSV: phase velocities

static vel_azi_VTI(C, Den, azimuth)

Given stiffnesses and density of the VTI medium, compute the azimuth dependent phase velocities.

Parameters:

• C (2d array) – stiffness matrix of the VTI medium

• Den (float) – density of the fractured medium

• azimuth (float or array like) – azimuth angle, degree

Returns:

float or array like – VP,VSH, VSV: phase velocities

static Bond_trans(C, theta, axis=3)

Coordinate Transformations for stiffness matrix in 6x6 Voigt notation using Bond transformation matrix.

Parameters:

• C (2d array) – original stiffness matrix

• theta (float) – rotational angle

• axis (int, optional) – axis=1: fix 1-axis, rotate 2 and 3 axis, examples can be a TTI(Tilted TI) resulted from the rotation of VTI with horizontal aligned fracture sets wrt the vertical x3 axis. In this case, the input C should be a VTI matrix axis=3: fix 3-axis, rotate 1 and 2 axis, E.g. seismic measurements of HTI media e.g caused by vertically aligned fractures. The angle theta may be assigned to be the angle between the fracture normal and a seismic line.

Returns:

2d array – C_trans, new stiffness matrix wrt to the original right-hand rectangular Cartesian coordinates

References

• Bond, W., Jan. 1943, The mathematics of the physical properties of crystals, The Bell System Technical Journal, 1-72.