def forward_model_and_store(solver, shot, sparse_greens_matrix, freq):
generate_seismic_data([shot],
solver,
solver.model_parameters.without_padding(),
frequencies=freq)
n_receivers = len(shot.receivers.receiver_list)
source_pos = shot.sources.position
for i in xrange(n_receivers):
receiver = shot.receivers.receiver_list[i]
receiver_pos = receiver.position
recording = shot.receivers.data_dft[freq][0][i]
sparse_greens_matrix.set_value_by_position(source_pos, receiver_pos,
recording)
def adjoint_test_rho():
import numpy as np
from pysit import PML, RectangularDomain, CartesianMesh, PointSource, ReceiverSet, Shot, VariableDensityAcousticWave, generate_seismic_data, PointReceiver, RickerWavelet
from pysit.gallery.horizontal_reflector import horizontal_reflector
# Setup
# Define Domain
pmlx = PML(0.1, 1000, ftype='quadratic')
pmlz = PML(0.1, 1000, ftype='quadratic')
x_config = (0.1, 1.0, pmlx, pmlx)
z_config = (0.1, 1.0, pmlz, pmlz)
d = RectangularDomain( x_config, z_config )
m = CartesianMesh(d, 70,80 )
# Generate true wave speed
# (M = C^-2 - C0^-2)
C,C0,m,d = horizontal_reflector(m)
w=1.3
M = [w*C, C/w]
M0 = [C0, C0]
# Set up shots
Nshots = 1
shots = []
xmin = d.x.lbound
xmax = d.x.rbound
nx = m.x.n
zmin = d.z.lbound
zmax = d.z.rbound
for i in xrange(Nshots):
# Define source location and type
# source = PointSource(d, (xmax*(i+1.0)/(Nshots+1.0), 0.1), RickerWavelet(10.0))
source = PointSource(m, (.188888, 0.18888), RickerWavelet(10.0))
# Define set of receivers
zpos = zmin + (1./9.)*zmax
xpos = np.linspace(xmin, xmax, nx)
receivers = ReceiverSet(m, [PointReceiver(m, (x, zpos)) for x in xpos])
# Create and store the shot
shot = Shot(source, receivers)
shots.append(shot)
# Define and configure the wave solver
trange=(0.,3.0)
solver = VariableDensityAcousticWave(m,
formulation='scalar',
model_parameters={'kappa': M[0], 'rho' : M[1]},
spatial_accuracy_order=2,
trange=trange,
use_cpp_acceleration=False,
time_accuracy_order=2)
# Generate synthetic Seismic data
np.random.seed(1)
print('Generating data...')
wavefields=[]
base_model = solver.ModelParameters(m,{'kappa': M[0], 'rho':M[1]})
generate_seismic_data(shots, solver, base_model, wavefields=wavefields)
tools = TemporalModeling(solver)
m0 = solver.ModelParameters(m,{'kappa': M[0], 'rho':M[1]})
m1 = m0.perturbation()
v=uniform(.5,2.2,len(m0.rho)).reshape((len(m0.rho),1)) #pertubation of m2
m1.rho=1.0/v
fwdret = tools.forward_model(shot, m0, 1, ['wavefield', 'dWaveOp', 'simdata'])
dWaveOp0 = fwdret['dWaveOp']
inc_field = fwdret['wavefield']
data = fwdret['simdata']
#data += np.random.rand(*data.shape)
linfwdret = tools.linear_forward_model_rho(shot, m0, m1, ['simdata'],wavefield=inc_field)
lindata = linfwdret['simdata']
adjret = tools.adjoint_model(shot, m0, data, 1, return_parameters=['imaging_condition', 'adjointfield'], dWaveOp=dWaveOp0,wavefield=inc_field)
# multiplied adjmodel by an additional m2 model.
adjmodel = adjret['imaging_condition'].rho
#adjmodel = 1.0/adjmodel
#m1_C = m1.C
print "data space ", np.sum(data*lindata)*solver.dt
print "model space ", np.dot(v.T, adjmodel).squeeze()*np.prod(m.deltas)
print "their diff ", np.dot(v.T, adjmodel).squeeze()*np.prod(m.deltas)-np.sum(data*lindata)*solver.dt
def adjoint_test():
#if __name__ == '__main__':
import numpy as np
from pysit import PML, RectangularDomain, CartesianMesh, PointSource, ReceiverSet, Shot, ConstantDensityAcousticWave, generate_seismic_data, PointReceiver, RickerWavelet
from pysit.gallery import horizontal_reflector
# Setup
# Define Domain
pmlx = PML(0.1, 1000, ftype='quadratic')
pmlz = PML(0.1, 1000, ftype='quadratic')
x_config = (0.1, 1.0, pmlx, pmlx)
z_config = (0.1, 0.8, pmlz, pmlz)
d = RectangularDomain( x_config, z_config )
m = CartesianMesh(d, 90, 70)
# Generate true wave speed
# (M = C^-2 - C0^-2)
C0, C = horizontal_reflector(m)
# Set up shots
Nshots = 1
shots = []
xmin = d.x.lbound
xmax = d.x.rbound
nx = m.x.n
zmin = d.z.lbound
zmax = d.z.rbound
for i in xrange(Nshots):
# Define source location and type
# source = PointSource(d, (xmax*(i+1.0)/(Nshots+1.0), 0.1), RickerWavelet(10.0))
source = PointSource(m, (.188888, 0.18888), RickerWavelet(10.0))
# Define set of receivers
zpos = zmin + (1./9.)*zmax
xpos = np.linspace(xmin, xmax, nx)
receivers = ReceiverSet(m, [PointReceiver(m, (x, zpos)) for x in xpos])
# Create and store the shot
shot = Shot(source, receivers)
shots.append(shot)
# Define and configure the wave solver
trange=(0.,3.0)
solver = ConstantDensityAcousticWave(m,
formulation='ode',
# formulation='scalar',
model_parameters={'C': C},
spatial_accuracy_order=4,
# spatial_shifted_differences=True,
# cfl_safety=0.01,
trange=trange,
time_accuracy_order=4)
# Generate synthetic Seismic data
np.random.seed(1)
print('Generating data...')
wavefields=[]
base_model = solver.ModelParameters(m,{'C': C})
generate_seismic_data(shots, solver, base_model, wavefields=wavefields)
tools = TemporalModeling(solver)
m0 = solver.ModelParameters(m,{'C': C0})
m1 = m0.perturbation()
m1 += np.random.rand(*m1.data.shape)
fwdret = tools.forward_model(shot, m0, ['wavefield', 'dWaveOp', 'simdata'])
dWaveOp0 = fwdret['dWaveOp']
inc_field = fwdret['wavefield']
data = fwdret['simdata']
# data += np.random.rand(*data.shape)
linfwdret = tools.linear_forward_model(shot, m0, m1, ['simdata'])
lindata = linfwdret['simdata']
adjret = tools.adjoint_model(shot, m0, data, return_parameters=['imaging_condition', 'adjointfield'], dWaveOp=dWaveOp0)
adjmodel = adjret['imaging_condition'].asarray()
adj_field = adjret['adjointfield']
m1 = m1.asarray()
print data.shape, solver.nsteps
print np.sum(data*lindata)*solver.dt
print np.dot(m1.T, adjmodel).squeeze()*np.prod(m.deltas)
print np.dot(m1.T, adjmodel).squeeze()*np.prod(m.deltas)-np.sum(data*lindata)*solver.dt
qs = adj_field
qhat = 0.0
dt = solver.dt
for k in xrange(solver.nsteps):
t = k * dt
qhat += qs[k]*(np.exp(-1j*2.0*np.pi*10.0*t)*dt)
def adjoint_test():
#if __name__ == '__main__':
# from pysit import *
import numpy as np
import matplotlib.pyplot as plt
from pysit import PML, Dirichlet, RectangularDomain, CartesianMesh, PointSource, ReceiverSet, Shot, ConstantDensityAcousticWave,ConstantDensityHelmholtz, generate_seismic_data, PointReceiver, RickerWavelet
from pysit.gallery import horizontal_reflector
# Define Domain
bc = PML(0.3, 100, ftype='quadratic')
# bc = Dirichlet()
x_config = (0.1, 1.0, bc, bc)
z_config = (0.1, 0.8, bc, bc)
d = RectangularDomain( x_config, z_config )
m = CartesianMesh(d, 90, 70)
# Generate true wave speed
# (M = C^-2 - C0^-2)
C0, C = horizontal_reflector(m)
# Set up shots
Nshots = 1
shots = []
xmin = d.x.lbound
xmax = d.x.rbound
nx = m.x.n
zmin = d.z.lbound
zmax = d.z.rbound
point_approx = 'delta'
for i in xrange(Nshots):
# Define source location and type
source = PointSource(m, (.188888, 0.18888), RickerWavelet(10.0), approximation=point_approx)
# Define set of receivers
zpos = zmin + (1./9.)*zmax
xpos = np.linspace(xmin, xmax, nx)
receivers = ReceiverSet(m, [PointReceiver(m, (x, zpos)) for x in xpos])
# Create and store the shot
shot = Shot(source, receivers)
shots.append(shot)
# Define and configure the wave solver
trange=(0.,3.0)
solver = ConstantDensityAcousticWave(m,
formulation='scalar',
model_parameters={'C': C},
spatial_accuracy_order=4,
trange=trange,
time_accuracy_order=6)
# Generate synthetic Seismic data
print('Generating data...')
base_model = solver.ModelParameters(m,{'C': C})
generate_seismic_data(shots, solver, base_model)
solver_frequency = ConstantDensityHelmholtz(m,
model_parameters={'C': C0},
spatial_shifted_differences=True,
spatial_accuracy_order=4)
tools = FrequencyModeling(solver_frequency)
m0 = solver_frequency.ModelParameters(m,{'C': C0})
np.random.seed(0)
m1 = m0.perturbation()
# m1 += M
m1 += np.random.rand(*m1.data.shape)
freqs = [10.0, 10.5, 10.123334145252]
# freqs = np.linspace(3,20,20)
fwdret = tools.forward_model(shot, m0, freqs, ['wavefield', 'dWaveOp', 'simdata'])
data = fwdret['simdata']
dWaveOp0 = fwdret['dWaveOp']
u0hat = fwdret['wavefield'][freqs[0]]
# data -= shot.receivers.interpolate_data(solver.ts())
# data *= -1
# for nu in freqs:
# data[nu] += np.random.rand(*data[nu].shape)
linfwdret = tools.linear_forward_model(shot, m0, m1, freqs, ['simdata','wavefield1'])
lindata = linfwdret['simdata']
u1hat = linfwdret['wavefield1'][freqs[0]]
adjret = tools.adjoint_model(shot, m0, data, freqs, return_parameters=['imaging_condition', 'adjointfield'], dWaveOp=dWaveOp0)
qhat = adjret['adjointfield'][freqs[0]]
adjmodel = adjret['imaging_condition'].data
# adjret2 = tools.adjoint_model(shot, m0, lindata_time, freqs, return_parameters=['imaging_condition', 'adjointfield'], dWaveOp=dWaveOp0)
## qhat = adjret['adjointfield'][freqs[0]]
# adjmodel2 = adjret2['imaging_condition'].view(np.ndarray)
m1 = m1.data
temp_data_prod = 0.0
for nu in freqs:
temp_data_prod += np.dot(lindata[nu].reshape(data[nu].shape).T, np.conj(data[nu]))
print temp_data_prod.squeeze()
print np.dot(m1.T, np.conj(adjmodel)).squeeze()*np.prod(m.deltas)
print np.dot(m1.T, np.conj(adjmodel)).squeeze()*np.prod(m.deltas) - temp_data_prod.squeeze()
def adjoint_test_rho():
import numpy as np
from pysit import PML, RectangularDomain, CartesianMesh, PointSource, ReceiverSet, Shot, VariableDensityAcousticWave, generate_seismic_data, PointReceiver, RickerWavelet
from pysit.gallery.horizontal_reflector import horizontal_reflector
# Setup
# Define Domain
pmlx = PML(0.1, 1000, ftype='quadratic')
pmlz = PML(0.1, 1000, ftype='quadratic')
x_config = (0.1, 1.0, pmlx, pmlx)
z_config = (0.1, 1.0, pmlz, pmlz)
d = RectangularDomain( x_config, z_config )
m = CartesianMesh(d, 70,80 )
# Generate true wave speed
# (M = C^-2 - C0^-2)
C,C0,m,d = horizontal_reflector(m)
w=1.3
M = [w*C, C/w]
M0 = [C0, C0]
# Set up shots
Nshots = 1
shots = []
xmin = d.x.lbound
xmax = d.x.rbound
nx = m.x.n
zmin = d.z.lbound
zmax = d.z.rbound
for i in xrange(Nshots):
# Define source location and type
# source = PointSource(d, (xmax*(i+1.0)/(Nshots+1.0), 0.1), RickerWavelet(10.0))
source = PointSource(m, (.188888, 0.18888), RickerWavelet(10.0))
# Define set of receivers
zpos = zmin + (1./9.)*zmax
xpos = np.linspace(xmin, xmax, nx)
receivers = ReceiverSet(m, [PointReceiver(m, (x, zpos)) for x in xpos])
# Create and store the shot
shot = Shot(source, receivers)
shots.append(shot)
# Define and configure the wave solver
trange=(0.,3.0)
solver = VariableDensityAcousticWave(m,
formulation='scalar',
model_parameters={'kappa': M[0], 'rho' : M[1]},
spatial_accuracy_order=2,
trange=trange,
use_cpp_acceleration=False,
time_accuracy_order=2)
# Generate synthetic Seismic data
np.random.seed(1)
print('Generating data...')
wavefields=[]
base_model = solver.ModelParameters(m,{'kappa': M[0], 'rho':M[1]})
generate_seismic_data(shots, solver, base_model, wavefields=wavefields)
tools = TemporalModeling(solver)
m0 = solver.ModelParameters(m,{'kappa': M[0], 'rho':M[1]})
m1 = m0.perturbation()
v=uniform(.5,2.2,len(m0.rho)).reshape((len(m0.rho),1)) #pertubation of m2
m1.rho=1.0/v
fwdret = tools.forward_model(shot, m0, 1, ['wavefield', 'dWaveOp', 'simdata'])
dWaveOp0 = fwdret['dWaveOp']
inc_field = fwdret['wavefield']
data = fwdret['simdata']
#data += np.random.rand(*data.shape)
linfwdret = tools.linear_forward_model_rho(shot, m0, m1, ['simdata'],wavefield=inc_field)
lindata = linfwdret['simdata']
adjret = tools.adjoint_model(shot, m0, data, 1, return_parameters=['imaging_condition', 'adjointfield'], dWaveOp=dWaveOp0,wavefield=inc_field)
# multiplied adjmodel by an additional m2 model.
adjmodel = adjret['imaging_condition'].rho
#adjmodel = 1.0/adjmodel
#m1_C = m1.C
print "data space ", np.sum(data*lindata)*solver.dt
print "model space ", np.dot(v.T, adjmodel).squeeze()*np.prod(m.deltas)
print "their diff ", np.dot(v.T, adjmodel).squeeze()*np.prod(m.deltas)-np.sum(data*lindata)*solver.dt
def adjoint_test():
#if __name__ == '__main__':
import numpy as np
from pysit import PML, RectangularDomain, CartesianMesh, PointSource, ReceiverSet, Shot, ConstantDensityAcousticWave, generate_seismic_data, PointReceiver, RickerWavelet
from pysit.gallery import horizontal_reflector
# Setup
# Define Domain
pmlx = PML(0.1, 1000, ftype='quadratic')
pmlz = PML(0.1, 1000, ftype='quadratic')
x_config = (0.1, 1.0, pmlx, pmlx)
z_config = (0.1, 0.8, pmlz, pmlz)
d = RectangularDomain( x_config, z_config )
m = CartesianMesh(d, 90, 70)
# Generate true wave speed
# (M = C^-2 - C0^-2)
C0, C = horizontal_reflector(m)
# Set up shots
Nshots = 1
shots = []
xmin = d.x.lbound
xmax = d.x.rbound
nx = m.x.n
zmin = d.z.lbound
zmax = d.z.rbound
for i in xrange(Nshots):
# Define source location and type
# source = PointSource(d, (xmax*(i+1.0)/(Nshots+1.0), 0.1), RickerWavelet(10.0))
source = PointSource(m, (.188888, 0.18888), RickerWavelet(10.0))
# Define set of receivers
zpos = zmin + (1./9.)*zmax
xpos = np.linspace(xmin, xmax, nx)
receivers = ReceiverSet(m, [PointReceiver(m, (x, zpos)) for x in xpos])
# Create and store the shot
shot = Shot(source, receivers)
shots.append(shot)
# Define and configure the wave solver
trange=(0.,3.0)
solver = ConstantDensityAcousticWave(m,
formulation='ode',
# formulation='scalar',
model_parameters={'C': C},
spatial_accuracy_order=4,
# spatial_shifted_differences=True,
# cfl_safety=0.01,
trange=trange,
time_accuracy_order=4)
# Generate synthetic Seismic data
np.random.seed(1)
print('Generating data...')
wavefields=[]
base_model = solver.ModelParameters(m,{'C': C})
generate_seismic_data(shots, solver, base_model, wavefields=wavefields)
tools = TemporalModeling(solver)
m0 = solver.ModelParameters(m,{'C': C0})
m1 = m0.perturbation()
m1 += np.random.rand(*m1.data.shape)
fwdret = tools.forward_model(shot, m0, ['wavefield', 'dWaveOp', 'simdata'])
dWaveOp0 = fwdret['dWaveOp']
inc_field = fwdret['wavefield']
data = fwdret['simdata']
# data += np.random.rand(*data.shape)
linfwdret = tools.linear_forward_model(shot, m0, m1, ['simdata'])
lindata = linfwdret['simdata']
adjret = tools.adjoint_model(shot, m0, data, return_parameters=['imaging_condition', 'adjointfield'], dWaveOp=dWaveOp0)
adjmodel = adjret['imaging_condition'].asarray()
adj_field = adjret['adjointfield']
m1 = m1.asarray()
print data.shape, solver.nsteps
print np.sum(data*lindata)*solver.dt
print np.dot(m1.T, adjmodel).squeeze()*np.prod(m.deltas)
print np.dot(m1.T, adjmodel).squeeze()*np.prod(m.deltas)-np.sum(data*lindata)*solver.dt
qs = adj_field
qhat = 0.0
dt = solver.dt
for k in xrange(solver.nsteps):
t = k * dt
qhat += qs[k]*(np.exp(-1j*2.0*np.pi*10.0*t)*dt)
def adjoint_test():
#if __name__ == '__main__':
# from pysit import *
import numpy as np
import matplotlib.pyplot as plt
from pysit import PML, Dirichlet, RectangularDomain, CartesianMesh, PointSource, ReceiverSet, Shot, ConstantDensityAcousticWave,ConstantDensityHelmholtz, generate_seismic_data, PointReceiver, RickerWavelet
from pysit.gallery import horizontal_reflector
# Define Domain
bc = PML(0.3, 100, ftype='quadratic')
# bc = Dirichlet()
x_config = (0.1, 1.0, bc, bc)
z_config = (0.1, 0.8, bc, bc)
d = RectangularDomain( x_config, z_config )
m = CartesianMesh(d, 90, 70)
# Generate true wave speed
# (M = C^-2 - C0^-2)
C0, C = horizontal_reflector(m)
# Set up shots
Nshots = 1
shots = []
xmin = d.x.lbound
xmax = d.x.rbound
nx = m.x.n
zmin = d.z.lbound
zmax = d.z.rbound
point_approx = 'delta'
for i in xrange(Nshots):
# Define source location and type
source = PointSource(m, (.188888, 0.18888), RickerWavelet(10.0), approximation=point_approx)
# Define set of receivers
zpos = zmin + (1./9.)*zmax
xpos = np.linspace(xmin, xmax, nx)
receivers = ReceiverSet(m, [PointReceiver(m, (x, zpos)) for x in xpos])
# Create and store the shot
shot = Shot(source, receivers)
shots.append(shot)
# Define and configure the wave solver
trange=(0.,3.0)
solver = ConstantDensityAcousticWave(m,
formulation='scalar',
model_parameters={'C': C},
spatial_accuracy_order=4,
trange=trange,
time_accuracy_order=6)
# Generate synthetic Seismic data
print('Generating data...')
base_model = solver.ModelParameters(m,{'C': C})
generate_seismic_data(shots, solver, base_model)
solver_frequency = ConstantDensityHelmholtz(m,
model_parameters={'C': C0},
spatial_shifted_differences=True,
spatial_accuracy_order=4)
tools = FrequencyModeling(solver_frequency)
m0 = solver_frequency.ModelParameters(m,{'C': C0})
np.random.seed(0)
m1 = m0.perturbation()
# m1 += M
m1 += np.random.rand(*m1.data.shape)
freqs = [10.0, 10.5, 10.123334145252]
# freqs = np.linspace(3,20,20)
fwdret = tools.forward_model(shot, m0, freqs, ['wavefield', 'dWaveOp', 'simdata'])
data = fwdret['simdata']
dWaveOp0 = fwdret['dWaveOp']
u0hat = fwdret['wavefield'][freqs[0]]
# data -= shot.receivers.interpolate_data(solver.ts())
# data *= -1
# for nu in freqs:
# data[nu] += np.random.rand(*data[nu].shape)
linfwdret = tools.linear_forward_model(shot, m0, m1, freqs, ['simdata','wavefield1'])
lindata = linfwdret['simdata']
u1hat = linfwdret['wavefield1'][freqs[0]]
adjret = tools.adjoint_model(shot, m0, data, freqs, return_parameters=['imaging_condition', 'adjointfield'], dWaveOp=dWaveOp0)
qhat = adjret['adjointfield'][freqs[0]]
adjmodel = adjret['imaging_condition'].data
# adjret2 = tools.adjoint_model(shot, m0, lindata_time, freqs, return_parameters=['imaging_condition', 'adjointfield'], dWaveOp=dWaveOp0)
## qhat = adjret['adjointfield'][freqs[0]]
# adjmodel2 = adjret2['imaging_condition'].view(np.ndarray)
m1 = m1.data
temp_data_prod = 0.0
for nu in freqs:
temp_data_prod += np.dot(lindata[nu].reshape(data[nu].shape).T, np.conj(data[nu]))
print temp_data_prod.squeeze()
print np.dot(m1.T, np.conj(adjmodel)).squeeze()*np.prod(m.deltas)
print np.dot(m1.T, np.conj(adjmodel)).squeeze()*np.prod(m.deltas) - temp_data_prod.squeeze()
def adjoint_test_rho():
#if __name__ == '__main__':
# from pysit import *
import numpy as np
import matplotlib.pyplot as plt
from numpy.random import uniform
from pysit import PML, Dirichlet, RectangularDomain, CartesianMesh, PointSource, ReceiverSet, Shot, ConstantDensityAcousticWave,VariableDensityHelmholtz, generate_seismic_data, PointReceiver, RickerWavelet
from pysit.gallery.horizontal_reflector import horizontal_reflector
# Define Domain
bc = PML(0.3, 100, ftype='quadratic')
# bc = Dirichlet()
x_config = (0.1, 1.0, bc, bc)
z_config = (0.1, 0.8, bc, bc)
d = RectangularDomain( x_config, z_config )
m = CartesianMesh(d, 70, 90)
# Generate true wave speed
# (M = C^-2 - C0^-2)
C,C0,m,d = horizontal_reflector(m)
w=1.3
M = [w*C, C/w]
M0 = [C0, C0]
# Set up shots
Nshots = 1
shots = []
xmin = d.x.lbound
xmax = d.x.rbound
nx = m.x.n
zmin = d.z.lbound
zmax = d.z.rbound
point_approx = 'delta'
for i in xrange(Nshots):
# Define source location and type
source = PointSource(m, (.188888, 0.18888), RickerWavelet(10.0), approximation=point_approx)
# Define set of receivers
zpos = zmin + (1./9.)*zmax
xpos = np.linspace(xmin, xmax, nx)
receivers = ReceiverSet(m, [PointReceiver(m, (x, zpos)) for x in xpos])
# Create and store the shot
shot = Shot(source, receivers)
shots.append(shot)
# Define and configure the wave solver
#trange=(0.,3.0)
freqs = [3.0,5.0,7.0]
solver = VariableDensityHelmholtz(m,
model_parameters={'kappa': M[0], 'rho' : M[1]},
spatial_shifted_differences=False,
spatial_accuracy_order=2)
# Generate synthetic Seismic data
print('Generating data...')
base_model = solver.ModelParameters(m,{'kappa': M[0], 'rho' : M[1]})
generate_seismic_data(shots, solver, base_model,frequencies=freqs)
tools = FrequencyModeling(solver)
m0 = solver.ModelParameters(m,{'kappa': M[0], 'rho' : M[1]})
np.random.seed(0)
m1 = m0.perturbation()
# v is pertubation of model 1/rho. (which we have declared as m1). Thus, rho is 1/v.
v = uniform(0.5,1.5,len(m0.rho)).reshape((len(m0.rho),1))
m1.rho += 1.0/v
# freqs = np.linspace(3,20,20)
fwdret = tools.forward_model(shot, m0, freqs, ['wavefield', 'dWaveOp', 'simdata'])
data = fwdret['simdata']
dWaveOp0 = fwdret['dWaveOp']
u0hat = fwdret['wavefield']
# data -= shot.receivers.interpolate_data(solver.ts())
# data *= -1
# for nu in freqs:
# data[nu] += np.random.rand(*data[nu].shape)
linfwdret = tools.linear_forward_model_rho(shot, m0, m1, freqs, ['simdata','wavefield1'], wavefield=u0hat)
lindata = linfwdret['simdata']
#u1hat = linfwdret['wavefield1'][freqs[0]]
adjret = tools.adjoint_model(shot, m0, data, freqs, return_parameters=['imaging_condition', 'adjointfield'], dWaveOp=dWaveOp0,wavefield=u0hat)
qhat = adjret['adjointfield'][freqs[0]]
adjmodel = adjret['imaging_condition'].rho
# adjret2 = tools.adjoint_model(shot, m0, lindata_time, freqs, return_parameters=['imaging_condition', 'adjointfield'], dWaveOp=dWaveOp0)
## qhat = adjret['adjointfield'][freqs[0]]
# adjmodel2 = adjret2['imaging_condition'].view(np.ndarray)
temp_data_prod = 0.0
for nu in freqs:
temp_data_prod += np.dot(lindata[nu].reshape(data[nu].shape).T, np.conj(data[nu]))
print "data space: ", temp_data_prod.squeeze()
print "model space: ", np.dot(v.T, np.conj(adjmodel)).squeeze()*np.prod(m.deltas)
print "their diff: ", np.dot(v.T, np.conj(adjmodel)).squeeze()*np.prod(m.deltas) - temp_data_prod.squeeze()
