def model_grad_rand_2d(c=2000,
randc=100,
dc=1,
freq=25,
dx=5,
dt=0.0001,
nx=[20, 20],
propagator=None,
prop_kwargs=None):
"""Create a point scatterer model, and the gradient.
"""
nt = int((3 * nx[0] * dx / c + 0.1) / dt)
middle = int(nx[1] / 2)
x_s, x_s_idx = _set_coords([[1, middle]], dx)
x_r, x_r_idx = _set_coords([[1, middle]], dx)
x_p, x_p_idx = _set_coords([[nx[0] - 5, middle]], dx)
f = ricker(freq, nt, dt, 0.05)
model_init = (np.random.rand(nx[0], nx[1]).astype(np.float32) * randc) + c
model_true = model_init.copy()
model_true += np.random.rand(nx[0], nx[1]).astype(np.float32) * dc
fwi_grad, true_grad = grad_2d_fd(model_true, model_init, x_r, x_s, dx, dt,
dc, f, propagator, prop_kwargs)
return fwi_grad, true_grad
def model_grad_const_2d(c=1500,
dc=1,
freq=25,
dx=5,
dt=0.0001,
nx=[20, 20],
propagator=None,
prop_kwargs=None):
"""Create a point scatterer model, and the gradient.
"""
nt = int((3 * nx[0] * dx / c + 0.1) / dt)
middle = int(nx[1] / 2)
x_s, x_s_idx = _set_coords([[1, middle]], dx)
x_r, x_r_idx = _set_coords([[1, middle]], dx)
x_p, x_p_idx = _set_coords([[nx[0] - 5, middle]], dx)
f = ricker(freq, nt, dt, 0.05)
model_init = np.ones(nx, dtype=np.float32) * c
model_true = model_init.copy()
model_true[x_p_idx[0, 0], x_p_idx[0, 1]] += dc
expected = grad_2d(nx, x_r, x_s, x_p, dx, dt, c, dc, f)
fwi_grad, true_grad = grad_2d_fd(model_true, model_init, x_r, x_s, dx, dt,
dc, f, propagator, prop_kwargs)
return expected, fwi_grad, true_grad
def model_direct_2d(c=1500,
freq=25,
dx=5,
dt=0.0001,
nx=[50, 50],
propagator=None,
prop_kwargs=None):
"""Create a constant model, and the expected waveform at point,
and the forward propagated wave.
"""
model = np.ones(nx, dtype=np.float32) * c
nt = int(2 * nx[0] * dx / c / dt)
middle = int(nx[1] / 2)
x_s, x_s_idx = _set_coords([[1, middle]], dx)
x_r, x_r_idx = _set_coords([[nx[0] - 1, middle]], dx)
#x_r, x_r_idx = _set_coords([[1, middle]], dx)
f = ricker(freq, nt, dt, 0.05)
expected = direct_2d_approx(x_r, x_s, dx, dt, c, f)
source, receiver_locations = _make_source_receiver(x_s_idx, x_r_idx, f)
if propagator is None:
propagator = Scalar2D
if prop_kwargs is None:
prop_kwargs = {}
prop = propagator(model, dx, dt, source, **prop_kwargs)
actual, _ = forward_model(prop, receiver_locations)
return expected, actual.receivers.ravel()
def model_scatter_2d(c=1500,
dc=150,
freq=25,
dx=5,
dt=0.0001,
nx=[50, 50],
propagator=None,
prop_kwargs=None):
"""Create a point scatterer model, and the expected waveform at point,
and the forward propagated wave.
"""
nx = np.array(nx)
model = np.ones(nx, dtype=np.float32) * c
nt = int((3 * nx[0] * dx / c + 0.05) / dt)
middle = int(nx[1] / 2)
x_s, x_s_idx = _set_coords([[1, middle]], dx)
x_r, x_r_idx = _set_coords([[1, middle]], dx)
x_p, x_p_idx = _set_coords([[nx[0] - 10, middle]], dx)
f = ricker(freq, nt, dt, 0.05)
model[x_p_idx[0, 0], x_p_idx[0, 1]] += dc
expected = scattered_2d(x_r, x_s, x_p, dx, dt, c, dc, f)
source, receiver_locations = _make_source_receiver(x_s_idx, x_r_idx, f)
if propagator is None:
propagator = Scalar2D
if prop_kwargs is None:
prop_kwargs = {}
prop = propagator(model, dx, dt, source, **prop_kwargs)
actual, _ = forward_model(prop, receiver_locations)
return expected, actual.receivers.ravel()
def _setup_propagator(c, freq, dx, dt, nt, nx, num_shots, num_sources_per_shot,
num_receivers_per_shot, prop_kwargs):
model = np.ones(nx, np.float32) * c
x_s_idx = np.ones([num_shots, num_sources_per_shot, 2], np.int)
x_s_idx[:, :, 1] = np.tile(np.linspace(1, nx[1] - 1, num_sources_per_shot),
[num_shots, 1])
f = ricker(freq, nt, dt, 0.05)
source = {}
source['amplitude'] = np.tile(f, [num_shots, num_sources_per_shot, 1])
source['locations'] = x_s_idx
x_r_idx = np.ones([num_shots, num_receivers_per_shot, 2], np.int)
x_r_idx[:, :,
1] = np.tile(np.linspace(1, nx[1] - 1, num_receivers_per_shot),
[num_shots, 1])
x_r_idx[:, :, 0] = nx[0] - 1
prop_args = (model, dx, dt, source)
if len(prop_kwargs) == 0:
prop_kwargs = {'pml_width': 30}
return prop_args, prop_kwargs, x_r_idx