def backus_parameters(vp, vs, rho, lb, dz):
"""
Backus parameters.
Liner, C (2014), Long-wave elastic attenuation produced by horizontal
layering. The Leading Edge, June 2014, p 634-638.
"""
lam = moduli.lam(vp, vs, rho)
mu = moduli.mu(vp, vs, rho)
# Compute the layer parameters from Liner (2014) equation 2:
a = rho * np.power(vp, 2.0) # Acoustic impedance
# Compute the Backus parameters from Liner (2014) equation 4:
A1 = 4 * moving_average(mu * (lam + mu) / a, lb / dz, mode='same')
A = A1 + np.power(moving_average(lam/a, lb/dz, mode='same'), 2.0)\
/ moving_average(1.0/a, lb/dz, mode='same')
C = 1.0 / moving_average(1.0 / a, lb / dz, mode='same')
F = moving_average(lam/a, lb/dz, mode='same')\
/ moving_average(1.0/a, lb/dz, mode='same')
L = 1.0 / moving_average(1.0 / mu, lb / dz, mode='same')
M = moving_average(mu, lb / dz, mode='same')
return A, C, F, L, M
def backus_parameters(vp, vs, rho, lb, dz):
"""
Backus parameters.
Liner, C (2014), Long-wave elastic attenuation produced by horizontal
layering. The Leading Edge, June 2014, p 634-638.
"""
lam = moduli.lam(vp, vs, rho)
mu = moduli.mu(vp, vs, rho)
# Compute the layer parameters from Liner (2014) equation 2:
a = rho * np.power(vp, 2.0) # Acoustic impedance
# Compute the Backus parameters from Liner (2014) equation 4:
A1 = 4 * moving_average(mu*(lam+mu)/a, lb/dz, mode='same')
A = A1 + np.power(moving_average(lam/a, lb/dz, mode='same'), 2.0)\
/ moving_average(1.0/a, lb/dz, mode='same')
C = 1.0 / moving_average(1.0/a, lb/dz, mode='same')
F = moving_average(lam/a, lb/dz, mode='same')\
/ moving_average(1.0/a, lb/dz, mode='same')
L = 1.0 / moving_average(1.0/mu, lb/dz, mode='same')
M = moving_average(mu, lb/dz, mode='same')
return A, C, F, L, M
def backus(vp, vs, rho, lb, dz):
"""
Backus averaging. Using Liner's algorithm (2014; see Notes).
Args:
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:
namedtuple: the smoothed logs: vp, vs, plus rho. Useful for computing
other elastic parameters at a seismic scale.
Notes:
Liner, C (2014), Long-wave elastic attenuation produced by horizontal
layering. The Leading Edge, June 2014, p 634-638.
"""
# Compute the Backus parameters:
A, C, F, L, M = backus_parameters(vp, vs, rho, lb, dz)
# Compute the vertical velocities from Liner (2014) equation 5:
R = moving_average(rho, lb / dz, mode='same')
vp0 = np.sqrt(C / R)
vs0 = np.sqrt(L / R)
BackusResult = namedtuple('BackusResult', ['Vp', 'Vs', 'rho'])
return BackusResult(Vp=vp0, Vs=vs0, rho=R)
def backus(vp, vs, rho, lb, dz):
"""
Backus averaging. Using Liner's algorithm (2014; see Notes).
Args:
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:
namedtuple: the smoothed logs: vp, vs, plus rho. Useful for computing
other elastic parameters at a seismic scale.
Notes:
Liner, C (2014), Long-wave elastic attenuation produced by horizontal
layering. The Leading Edge, June 2014, p 634-638.
"""
# Compute the Backus parameters:
A, C, F, L, M = backus_parameters(vp, vs, rho, lb, dz)
# Compute the vertical velocities from Liner (2014) equation 5:
R = moving_average(rho, lb/dz, mode='same')
vp0 = np.sqrt(C / R)
vs0 = np.sqrt(L / R)
BackusResult = namedtuple('BackusResult', ['Vp', 'Vs', 'rho'])
return BackusResult(Vp=vp0, Vs=vs0, rho=R)
def backus(vp, vs, rho, lb, dz):
"""
Backus averaging.
Liner, C (2014), Long-wave elastic attenuation produced by horizontal
layering. The Leading Edge, June 2014, p 634-638.
"""
# Compute the Backus parameters:
A, C, F, L, M = backus_parameters(vp, vs, rho, lb, dz)
# Compute the vertical velocities from Liner (2014) equation 5:
R = moving_average(rho, lb / dz, mode='same')
vp0 = np.sqrt(C / R)
vs0 = np.sqrt(L / R)
return vp0, vs0
def backus(vp, vs, rho, lb, dz):
"""
Backus averaging.
Liner, C (2014), Long-wave elastic attenuation produced by horizontal
layering. The Leading Edge, June 2014, p 634-638.
"""
# Compute the Backus parameters:
A, C, F, L, M = backus_parameters(vp, vs, rho, lb, dz)
# Compute the vertical velocities from Liner (2014) equation 5:
R = moving_average(rho, lb/dz, mode='same')
vp0 = np.sqrt(C / R)
vs0 = np.sqrt(L / R)
return vp0, vs0
def backus_parameters(vp, vs, rho, lb, dz):
"""
Intermediate parameters for Backus averaging. This is expected to be a
private function. You probably want backus() and not this.
Args:
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:
tuple: Liner's 5 intermediate parameters: A, C, F, L and M.
Notes:
Liner, C (2014), Long-wave elastic attenuation produced by horizontal
layering. The Leading Edge, June 2014, p 634-638.
"""
lam = moduli.lam(vp, vs, rho)
mu = moduli.mu(vp, vs, rho)
# Compute the layer parameters from Liner (2014) equation 2:
a = rho * np.power(vp, 2.0) # Acoustic impedance
# Compute the Backus parameters from Liner (2014) equation 4:
A1 = 4 * moving_average(mu * (lam + mu) / a, lb / dz, mode='same')
A = A1 + np.power(moving_average(lam/a, lb/dz, mode='same'), 2.0)\
/ moving_average(1.0/a, lb/dz, mode='same')
C = 1.0 / moving_average(1.0 / a, lb / dz, mode='same')
F = moving_average(lam/a, lb/dz, mode='same')\
/ moving_average(1.0/a, lb/dz, mode='same')
L = 1.0 / moving_average(1.0 / mu, lb / dz, mode='same')
M = moving_average(mu, lb / dz, mode='same')
BackusResult = namedtuple('BackusResult', ['A', 'C', 'F', 'L', 'M'])
return BackusResult(A, C, F, L, M)
def backus_parameters(vp, vs, rho, lb, dz):
"""
Intermediate parameters for Backus averaging. This is expected to be a
private function. You probably want backus() and not this.
Args:
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:
tuple: Liner's 5 intermediate parameters: A, C, F, L and M.
Notes:
Liner, C (2014), Long-wave elastic attenuation produced by horizontal
layering. The Leading Edge, June 2014, p 634-638.
"""
lam = moduli.lam(vp, vs, rho)
mu = moduli.mu(vp, vs, rho)
# Compute the layer parameters from Liner (2014) equation 2:
a = rho * np.power(vp, 2.0) # Acoustic impedance
# Compute the Backus parameters from Liner (2014) equation 4:
A1 = 4 * moving_average(mu*(lam+mu)/a, lb/dz, mode='same')
A = A1 + np.power(moving_average(lam/a, lb/dz, mode='same'), 2.0)\
/ moving_average(1.0/a, lb/dz, mode='same')
C = 1.0 / moving_average(1.0/a, lb/dz, mode='same')
F = moving_average(lam/a, lb/dz, mode='same')\
/ moving_average(1.0/a, lb/dz, mode='same')
L = 1.0 / moving_average(1.0/mu, lb/dz, mode='same')
M = moving_average(mu, lb/dz, mode='same')
BackusResult = namedtuple('BackusResult', ['A', 'C', 'F', 'L', 'M'])
return BackusResult(A, C, F, L, M)