pyavo.avotools package

Submodules

pyavo.avotools.approx module

Functions to compute Aki-Richards and Shuey 2-term & 3-term approximations.

pyavo.avotools.approx.aki_richards(vp1: numpy.ndarray, vs1: numpy.ndarray, rho1: numpy.ndarray, vp2: numpy.ndarray, vs2: numpy.ndarray, rho2: numpy.ndarray, theta1: numpy.ndarray) → numpy.ndarray

Computes the Reflection Coefficient with Aki and Richard’s (1980) equation for a two-layered model.

Parameters

  • vp1 – P-wave velocity in upper layer

  • vs1 – S-wave velocity in upper layer

  • rho1 – Density of upper layer

  • vp2 – P-wave velocity in lower layer

  • vs2 – S-wave velocity in lower layer

  • rho2 – Density in lower layer

  • theta1 – Angle of incidence

Returns

rc: Reflection coefficient

Reference: AVO - Chopra and Castagna, 2014, Page 62.

pyavo.avotools.approx.ref_coeff(imp: Union[numpy.ndarray, pandas.core.series.Series])

Computes the reflection coefficient for a plane incident P-wave.

Parameters

imp – Acoustic Impedance

Returns

rc: reflection coefficient

pyavo.avotools.approx.shuey(vp1: numpy.ndarray, vs1: numpy.ndarray, rho1: numpy.ndarray, vp2: numpy.ndarray, vs2: numpy.ndarray, rho2: numpy.ndarray, theta1: numpy.ndarray) → tuple

Computes the Reflectiviy parameters with Shuey (1985) 2 and 3 terms for a two-layered model.

Parameters

  • vp1 – P-wave velocity in upper layer

  • vs1 – S-wave velocity in lower layer

  • rho1 – Density in upper later

  • vp2 – P-wave velocity in lower layer

  • vs2 – S-wave velocity in lower layer

  • rho2 – Density in lower layer

  • theta1 – Angles of incidence

Returns

c : Intercept. m : Gradient. rc2 : Reflection coefficient for the 2-term approximation. rc3 : Reflection coefficient for the 3-term approximation.

Reference: Avseth et al., Quantitative seismic interpretation, 2006, Page 182.

pyavo.avotools.approx.shueyrc(vp0: Union[numpy.ndarray, pandas.core.series.Series, float], vs0: Union[numpy.ndarray, pandas.core.series.Series, float], rho0: Union[numpy.ndarray, pandas.core.series.Series, float], theta1: Union[numpy.ndarray, pandas.core.series.Series, float]) → tuple

Computes the P-wave reflectivity with Shuey (1985) 2 terms for a given well log.

Parameters

  • vp0 – P-wave velocities from Vp log

  • vs0 – S-Wave velocities from Vs log

  • rho0 – Density from RHOB log

  • theta1 – Angles of incidence

Returns

RC: Reflection coefficient for the 2-term approximation. c: Intercept. m: Gradient.

Reference: Avseth et al., Quantitative seismic interpretation, 2006, Page 182.

pyavo.avotools.approx.snell(vp1: numpy.ndarray, vp2: numpy.ndarray, theta1: float) → tuple

Computes the angles of refraction for an incident P-wave in a two-layered model.

Parameters

  • vp1 – P-wave velocity in upper layer

  • vp2 – P-wave velocity in lower layer

  • theta1 – Angle of incidence

Returns

theta2: Angle of Refraction p: Ray Parameter

Reference: AVO - Chopra and Castagna, 2014, Page 6.

pyavo.avotools.gassmann module

Class for modelling fluid properties for gas, oil and brine saturated sands.

References: Wang(2001), Batzle and Wang(1992), Geophysics.

class pyavo.avotools.gassmann.GassmannSub(vp: Union[int, float], vs: Union[int, float], rho: Union[int, float], rho_o: Union[int, float], rho_g: Union[int, float], vsh: float, phi: float, swi: float, swt: float, S: float, T: Union[int, float], P: Union[int, float], init_fluid: str, final_fluid: str, GOR: float)

Bases: object

Class to model Gassmann fluid substitution for brine sands, oil sands, and gas sands. It generates the P and S wave velocities and density after fluid substitution according to input parameters.

Arguments:

vp = P-wave velocity from log (ft/s)

vs = S-wave velocity from log (ft/s)

rho = Bulk density form log (g/cc)

rho_o = Oil gravity (deg API)

rho_g = Gas gravity (API)

vsh = Shale volume from log

phi = Porosity

swi = Initial water saturation from log

swt = Target water saturation

S = Salinity (ppm)

T = Temperature (deg)

P = Pressure (psi)

init_fluid = Fluid type of initial hydrocarbon (gas or oil)

final_fluid = Fluid type of desired output where (gas or oil)

GOR = Gas-Oil ratio

final_hc() → tuple

Computes the bulk modulus and density of the desired hydrocarbon (oil or gas).

Returns

k_hyc: bulk modulus, rho_hyc: density

init_hyc() → tuple

Computes Bulk modulus and density of initial hydrocarbon.

Returns

k_hyc: Bulk modulus, rho_hyc: Density

insitu_moduli(rho_fluid: float, rho_matrix: float, d_phi=True) → tuple

Computes the initial original moduli for saturated insitu rock. Density of the insitu saturated rock is calculated from the porosity log using the mass balance equation.

Parameters

  • rho_fluid – density of insitu pore fluid phase (g/cc)

  • rho_matrix – density of rock matrix (g/cc)

  • d_phi – density derived from input RHOB log.

Returns

k_sat_init: Bulk modulus, mu_sat_init: Shear modulus

k_frame(k_mat: float, k_fld: float, k_sat: float) → float

Computes the bulk modulus of porous rock frame.

Parameters

  • k_mat – Bulk modulus of rock matrix

  • k_fld – Bulk modulus of pore fluid phase

  • k_sat – Bulk modulus of saturated insitu rock

Returns

k_frame: Bulk modulus

k_rho_brine() → tuple

Computes the bulk modulus(Gpa) and density(g/cc) of brine.

Returns

Bulk Modulus, Density

k_rho_fluid() → tuple

Computes the Bulk modulus and density of the mixed pore fluid phase (Initial insitu model)

Returns

k_fld: Bulk modulus of pore fluid, rho_fld: Density of pore fluid

k_rho_sat(k_mat: float, rho_mat: float, k_frame: float) → tuple

Computes the Gassmann bulk modulus and density of saturated rock after fluid substitution. The desired fluid is defined by the target water saturation and type of hydrocarbon.

Parameters

  • k_mat – Bulk modulus of rock matrix (GPa)

  • rho_mat – Density of rock matrix (g/cc)

  • k_frame – Bulk modulus of rock frame (Gpa)

Returns

k_sat_new: Bulk modulus, rho_sat_new: Density

pyavo.avotools.gassmann.k_rho_matrix(v_cly: float, k_cly: float, k_qtz: float, rho_cly: float, rho_qtz: float) → tuple

Calculate the Bulk modulus and Density of rock matrix.

Parameters

  • v_cly – Volume of clay assumed to be 70% of Shale volume

  • k_cly – Bulk modulus of clay (Gpa)

  • k_qtz – Bulk modulus of quartz (Gpa)

  • rho_cly – Density of clay (g/cc)

  • rho_qtz – Density of quartz (g/cc)

Returns

k_mat : Bulk modulus of rock matrix, rho_mat : Density of rock matrix

pyavo.avotools.gassmann.vel_sat(k_sat: float, rho_sat: float, mu: float) → tuple

Estimate the seismic velocities after Gassmann fluid substitution using density and elastic moduli of saturated rock.

Returns

vp_new : P-wave velocity, vs_new : S-wave velocity

pyavo.avotools.impedance module

Functions to calculate acoustic and elastic impedance from well logs

pyavo.avotools.impedance.ai(vp: float, rho: float)

Calculates the acoustic impedance of a layer given velocities and densities.

Parameters

  • vp – P-wave velocity (m/s)

  • rho – Density (g/cc)

Returns

z: Acoustic Impedance

pyavo.avotools.impedance.ei(vp: float, vs: float, rho: float, ang: int)

Computes the elastic impedance of a layer given velocities, densities and incidence angle.

Parameters

  • vp – P-wave velocity (m/s)

  • vs – S-wave velocity (m/s)

  • rho – Density (g/cc)

  • ang – Angle of incidence (deg)

Returns

ei: Elastic impedance

Reference: Connolly, P., 1999, Elastic impedance: The Leading Edge, 18, 438–452.

pyavo.avotools.impedance.lame(vp: float, vs: float, rho: float)

Computes Lamé parameters - lambda_rho and mu_rho.

Parameters

  • vp – P-wave velocity (m/s)

  • vs – S-wave velocity (m/s)

  • rho – Density (g/cc)

Returns

lambda_rho: Lamé first parameter, mu_rho: Lamé second parameter

Reference: Goodway, B., T. Chen, and J. Downton, 1997, Improved AVO fluid detection and lithology discrimination using Lamé petrophysical parameters; “λρ”, “μρ”, & “λ/μ fluid stack” from P and S inversions: 67th Annual International Meeting, SEG, Expanded Abstracts, 183-186.

pyavo.avotools.impedance.norm_ei(vp: float, vs: float, rho: float, vp_sh: float, vs_sh: float, rho_sh: float, ang: int)

Computes the normalized elastic impedance.

Parameters

  • vp – P-wave velocity. (m/s)

  • vs – S-wave velocity. (m/s)

  • rho – Density. (g/cc)

  • vp_sh – P-wave velocity in shale (m/s)

  • vs_sh – S-wave velocity in shale (m/s)

  • rho_sh – Shale reference density.

  • ang – Angle of incidence

Returns

nei: Normalized elastic impedance.

Reference:

Whitcombe, D, 2002, Elastic impedance normalization, Geophysics, 67 (1), 60–62.

pyavo.avotools.log_crossplot module

Functions to create well log plots & crossplots of P-wave reflectivity vs angles, and gradient vs intercept.

pyavo.avotools.log_crossplot.avo_plot(angle: numpy.ndarray, shuey: float, intercept: float, gradient: float, lim=1.5)

Generates crossplots of P-wave reflectivity vs angles, and gradient vs intercept.

Parameters

  • angle – Angle of incidence

  • shuey – Shuey 2-term approximation of reflectivity

  • gradient – Gradient from shuey approximation

  • intercept – Intercept from shuey approximation

pyavo.avotools.log_crossplot.crossplot(vp, vs, vpvs, rho, phi, GR, AI, NEI, lambda_rho, mu_rho)

Generates cross plots of elastic impedance, porosity, density and velocities.

Parameters

  • vp – P-wave velocity from Vp log (m/s)

  • vs – S-wave velocity from Vs log (m/s)

  • vpvs – VpVS ratio from VP-VS log (m/s)

  • rho – Density from RHOB log (g/cc)

  • phi – Porosity from PHI log

  • GR – Gamma ray from GR log

  • AI – Acoustic impedance

  • NEI – Normalized acoustic impedance

  • lambda_rho – Lame’s first parameter

  • mu_rho – Lame’s second parameter

pyavo.avotools.log_crossplot.plot_imp(vpvs: Union[numpy.ndarray, pandas.core.series.Series, float], vp: Union[numpy.ndarray, pandas.core.series.Series, float], vs: Union[numpy.ndarray, pandas.core.series.Series, float], rho: Union[numpy.ndarray, pandas.core.series.Series, float], angle: Union[float, int], h_well: Union[numpy.ndarray, pandas.core.series.Series], h_ref: Union[int, float])

Creates log plots of Poisson ratio, Acoustic impedance-Normalized Elastic Impedance(AI-NEI) and Lame’s Parameters (lambda-rho & mu-rho).

Parameters

  • vpvs – Vp/Vs values form VP/VS Log (m/s)

  • vp – P-wave velocities form Vp log (m/s)

  • vs – S-wave velocities from Vs Log (m/s)

  • rho – Density form RHOB log (g/cc)

  • angle – Angle of incidence (deg)

  • h_well – Depth of well from Depth log (m)

  • h_ref – closest location of the top on the depth array as reference to normal elastic impedance

Returns

Poisson ratio, Acoustic impedance, lambda_rho, mu_rho, NEI

pyavo.avotools.moduli module

Functions to convert between various acoustic/elastic parameters, and provides a way to calculate all the elastic moduli from Vp, Vs, and rho.

Using equations http://www.subsurfwiki.org/wiki/Elastic_modulus from Mavko, G, T Mukerji and J Dvorkin (2003), The Rock Physics Handbook, Cambridge University Press

Created by Matt Hall, 2014. Modified by Tola Abiodun, 2021.

pyavo.avotools.moduli.bulk(vp=None, vs=None, rho=None, mu=None, lam=None, youngs=None, pr=None, pmod=None)

Calculate the Bulk modulus given either P-wave Velocity, S-wave velocity, and Density, or any two elastic moduli (e.g. lambda and mu, or bulk and P moduli). SI units only.

Args:

vp, vs, and rho or any 2 from lam, mu, youngs, pr, and pmod

Returns

Bulk modulus in pascals, Pa

pyavo.avotools.moduli.comp_vel(youngs=None, vs=None, rho=None, mu=None, lam=None, bulk=None, pr=None, pmod=None)

Calculates the P-wave velocity given bulk density and any two elastic moduli (e.g. lambda and mu, or Young’s and P moduli). SI units only.

Args:

Any 2 from lam, mu, youngs, pr, pmod, bulk and Rho

Returns

Vp in m/s

pyavo.avotools.moduli.elastic_mod(vp, vs, rho) → dict

Computes elastic moduli given P-wave velocity, S-wave velocity, and Density. SI units only.

Args:

Vp, Vs, and rho

Returns

A dict of elastic moduli, plus P-wave impedance.

pyavo.avotools.moduli.lame_param(vp=None, vs=None, rho=None, pr=None, mu=None, youngs=None, bulk=None, pmod=None)

Computes Lame’s first parameter given either P-wave velocity, S-wave velocity, and Density, or any two elastic moduli (e.g. bulk and mu, or Young’s and P moduli). SI units only.

Args:

vp, vs, and rho or any 2 from bulk, mu, youngs, pr, and pmod

Returns

Lambda in pascals, Pa

pyavo.avotools.moduli.mu(vp=None, vs=None, rho=None, pr=None, lam=None, youngs=None, bulk=None, pmod=None)

Computes shear modulus given either Vp, Vs, and rho, or any two elastic moduli (e.g. lambda and bulk modulus, or Young’s and P moduli). SI units only.

Args:

vp, vs, and rho or any 2 from lam, bulk, youngs, pr, and pmod

Returns

Shear modulus in pascals, Pa

pyavo.avotools.moduli.p_mod(vp=None, vs=None, rho=None, pr=None, mu=None, lam=None, youngs=None, bulk=None)

Computes P-wave modulus given either P-wave velocity, S-wave velocity, and Density, or any two elastic moduli (e.g. lambda and mu, or Young’s and bulk moduli). SI units only.

Args:

vp, vs, and rho or any 2 from lam, mu, youngs, pr, and bulk

Returns

P-wave modulus in pascals, Pa

pyavo.avotools.moduli.poisson(vp=None, vs=None, rho=None, mu=None, lam=None, youngs=None, bulk=None, pmod=None)

Calculate the Poisson ratio given either P-wave Velocity, S-wave velocity, and Density, or any two elastic moduli (e.g. lambda and mu, or bulk and P moduli). SI units only.

Args:

vp, vs, and rho or any 2 from lam, mu, youngs, bulk, and pmod

Returns

Poisson’s ratio, dimensionless

pyavo.avotools.moduli.shear_vel(rho=None, mu=None)

Computes the Shear wave velocity given bulk density and shear modulus. SI units only.

Args:

Mu, Rho

Returns

Vs in m/s

pyavo.avotools.moduli.youngs(vp=None, vs=None, rho=None, mu=None, lam=None, bulk=None, pr=None, pmod=None)

Computes Young’s modulus given either P-wave Velocity, S-wave velocity, and Density, or any two elastic moduli (e.g. lambda and mu, or bulk and P moduli). SI units only.

Args:

vp, vs, and rho or any 2 from lam, mu, bulk, pr, and pmod

Returns

Young’s modulus in pascals, Pa

Module contents