# -*- coding: utf-8 -*-
"""
Routines for multivariate pressure prediction
Created on Sep 20 2018
"""
from __future__ import (absolute_import, division, print_function,
unicode_literals)
__author__ = "yuhao"
import numpy as np
[docs]def multivariate_virgin(sigma, phi, vsh, a_0, a_1, a_2, a_3, B):
"""
Calculate velocity using multivariate virgin curve
Parameters
----------
sigma : 1-d ndarray
effective pressure
phi : 1-d ndarray
effective porosity
vsh : 1-d ndarray
shale volume
a_0, a_1, a_2, a_3 : float
coefficients of equation
B : float
effective pressure exponential
Returns
-------
out : 1-d ndarray
velocity array
Notes
-----
.. math:: V = a_0 + a_1\\phi + a_2{V}_{sh} + a_3 {\\sigma}^{B}
[5]_
.. [5] Sayers, C., Smit, T., van Eden, C., Wervelman, R., Bachmann, B.,
Fitts, T., et al. (2003). Use of reflection tomography to predict
pore pressure in overpressured reservoir sands. In submitted for
presentation at the SEG 2003 annual meeting.
"""
return a_0 - a_1 * phi - a_2 * vsh + a_3 * sigma**B
[docs]def invert_multivariate_virgin(vel, phi, vsh, a_0, a_1, a_2, a_3, B):
"""
Calculate effective stress using multivariate virgin curve
Parameters
----------
vel : 1-d ndarray
velocity array whose unit is m/s.
phi : 1-d ndarray
porosity array
vsh : 1-d ndarray
shale volume
a_0, a_1, a_2, a_3 : scalar
coefficients
Returns
-------
sigma: 1-d ndarray
"""
return ((vel - a_0 + a_1 * phi + a_2 * vsh) / a_3)**(1 / B)
[docs]def multivariate_unloading(sigma, phi, vsh, a_0, a_1, a_2, a_3, B, U, vmax):
"""
Calculate velocity using multivariate unloading curve
"""
sigma_max = invert_multivariate_virgin(
vmax, phi, vsh, a_0, a_1, a_2, a_3, B)
sigma_vc = sigma_max*(sigma/sigma_max)**(1/U)
return multivariate_virgin(sigma_vc, phi, vsh, a_0, a_1, a_2, a_3, B)
[docs]def invert_multivariate_unloading(vel, phi, vsh, a_0, a_1, a_2, a_3,
B, U, vmax):
"""
Calculate effective stress using multivariate unloading curve
"""
sigma_max = invert_multivariate_virgin(
vmax, phi, vsh, a_0, a_1, a_2, a_3, B)
sigma_vc = invert_multivariate_virgin(
vel, phi, vsh, a_0, a_1, a_2, a_3, B)
return sigma_max * (sigma_vc/sigma_max)**U
[docs]def effective_stress_multivariate(vel, phi, vsh, a_0, a_1, a_2, a_3,
B, U, vmax, start_idx, end_idx=None):
ves = invert_multivariate_virgin(vel, phi, vsh, a_0, a_1, a_2, a_3, B)
unloading = invert_multivariate_unloading(
vel, phi, vsh, a_0, a_1, a_2, a_3, B, U, vmax)
ves[start_idx: end_idx] = unloading[start_idx: end_idx]
return ves
[docs]def pressure_multivariate(obp, vel, phi, vsh, a_0, a_1, a_2, a_3,
B, U, vmax, start_idx, end_idx=None):
"""
Pressure Prediction using multivariate model
"""
ves = effective_stress_multivariate(
vel, phi, vsh, a_0, a_1, a_2, a_3, B, U, vmax, start_idx, end_idx)
return obp - ves
[docs]def pressure_multivariate_varu(obp, vel, phi, vsh, a_0, a_1, a_2, a_3,
B, U, vmax, start_idx, buf=20,
end_idx=None, end_buffer=10):
"""
Pressure Prediction using multivariate model
"""
ves = effective_stress_multivariate_varu(
vel, phi, vsh, a_0, a_1, a_2, a_3,
B, U, vmax, start_idx, buf, end_idx, end_buffer)
return obp - ves
[docs]def effective_stress_multivariate_varu(vel, phi, vsh, a_0, a_1, a_2, a_3,
B, U, vmax, start_idx, buf=20,
end_idx=None, end_buffer=10):
u_array = np.ones(vel.shape)
u_array[start_idx: end_idx] = U
# start buffer
u_buffer = np.linspace(1, U, buf)
u_array[start_idx-buf+1: start_idx + 1] = u_buffer
# end buffer
if end_idx is not None:
u_array[end_idx: end_idx + end_buffer] = np.linspace(U, 1, end_buffer)
ves = invert_multivariate_unloading(vel, phi, vsh, a_0, a_1, a_2, a_3,
B, u_array, vmax)
return ves
