def interpolate(frame, field):
# read coordinate of nodes
fl = flac.Flac()
xx, zz = fl.read_mesh(frame)
x, z = flac.make_uniform_grid(xmin, xmax, zmin, zmax, dx, dz)
if field == 'phase':
## phase
# read marker location, age and phase
mx, mz, mage, mphase, mid = fl.read_markers(frame)
mx, mz, mphase = excluding(mx, mz, mphase, xmin-dx, xmax+dx, zmin-dz, zmax+dz)
ph = flac.nearest_neighbor_interpolation2d(mx, mz, mphase, x, z)
f = ph.astype(np.float32)
elif field in ('temperature', 'aps', 'density', 'eII', 'sII',
'sxx', 'szz', 'sxz', 'srII', 'pres', 'diss', 'visc'):
# read field
cf = getattr(fl, 'read_'+field)(frame)
cx, cz = flac.elem_coord(xx, zz)
cx, cz, cf = excluding(cx, cz, cf, xmin-dx, xmax+dx, zmin-dz, zmax+dz)
f = flac.gaussian_interpolation2d(cx, cz, cf, x, z)
else:
raise RuntimeError('unknown field %s' % field)
f = clip_topo(x, z, f, xx, zz)
return x, z, f
def interpolate(frame, field):
# read coordinate of nodes
fl = flac.Flac()
xx, zz = fl.read_mesh(frame)
x, z = flac.make_uniform_grid(xmin, xmax, zmin, zmax, dx, dz)
if field == 'phase':
## phase
# read marker location, age and phase
mx, mz, mage, mphase = fl.read_markers(frame)
mx, mz, mphase = excluding(mx, mz, mphase, xmin-dx, xmax+dx, zmin-dz, zmax+dz)
ph = flac.nearest_neighbor_interpolation2d(mx, mz, mphase, x, z)
f = ph.astype(np.float32)
elif field in ('temperature', 'aps', 'density', 'eII', 'sII',
'sxx', 'szz', 'sxz', 'srII', 'pres', 'diss', 'visc'):
# read field
cf = getattr(fl, 'read_'+field)(frame)
cx, cz = flac.elem_coord(xx, zz)
cx, cz, cf = excluding(cx, cz, cf, xmin-dx, xmax+dx, zmin-dz, zmax+dz)
f = flac.gaussian_interpolation2d(cx, cz, cf, x, z)
else:
raise RuntimeError('unknown field %s' % field)
f = clip_topo(x, z, f, xx, zz)
return x, z, f
def compute_gravity(frame):
## read data
fl = flac.Flac()
x, z = fl.read_mesh(frame) # in km
x *= 1e3
z *= 1e3
# surface coordinates
xx = x[:,0]
zz = z[:,0]
xmin = x[0,0]
xmax = x[-1,0]
# center of elements
cx, cz = flac.elem_coord(x, z)
# area of elements = 0.5 * | AC x BD | = 0.5 * |xdiag1*zdiag2 - xdiag2*zdiag1|
# A -- D
# | |
# B -- C
xdiag1 = x[0:-1, 0:-1] - x[1:, 1:]
zdiag1 = z[0:-1, 0:-1] - z[1:, 1:]
xdiag2 = x[1:, 0:-1] - x[0:-1, 1:]
zdiag2 = z[1:, 0:-1] - z[0:-1, 1:]
area = 0.5 * np.abs(xdiag1*zdiag2 - xdiag2*zdiag1)
rho = fl.read_density(frame) # in kg/m^3
# anything above sea level is removed
rho[cz > 0] = 0
## benchmark case: infinite-long cylinder with radius R
## buried at depth D
#R = 10e3
#D = -150e3
#drho = 1000
#rho = np.zeros(cx.shape)
#midx = 0.5 * (xmin + xmax)
#midz = 0.5 * z.min()
#dist2 = (x - midx)**2 + (z - D)**2
#rho[dist2 < R**2] = drho
#ocean_density = 0
mass = rho * area
## calculate gravity at these points
# px in uniform spacing
px = np.linspace(xmin, xmax, num=5*fl.nx)
# pz is a few km above the highest topography to avoid high frequency oscillation
pz_height = max(0, np.max(zz)) + 4e3
print 'gravity evaluated at %f km' % pz_height
pz = np.ones(px.shape) * pz_height
# original topography defined in px grid
topo = np.interp(px, x[:,0], z[:,0])
## contribution of material inside the model
grav = np.empty(px.shape)
for i in range(len(grav)):
dx = px[i] - cx
dz = pz[i] - cz
dist2 = (dx**2 + dz**2)
# downward component of gravity of an infinite long line source of density anomaly
# see Turcotte & Schubert, 1st Ed., Eq 5-104
grav[i] = 2 * gn * np.sum(mass * dz / dist2)
## contribution of sedimentary basin, only to the right of trench
peaks = find_peaks(zz)
itrench = find_trench_index(zz)
basin_depth = -2000
sed_density = 2200
sed_thickness = np.zeros(fl.nx)
for ii in range(len(peaks)-1):
fill_height = min((basin_depth, zz[peaks[ii]], zz[peaks[ii+1]]))
for i in range(peaks[ii], peaks[ii+1]):
if zz[i] < fill_height:
sed_thickness[i] = fill_height - zz[i]
zz[i] = fill_height
for i in range(itrench, fl.nx-1):
sedz = 0.5 * (sed_thickness[i] + sed_thickness[i+1])
if sedz > 0:
midz = 0.5 * (zz[i] + zz[i+1])
midx = 0.5 * (xx[i] + xx[i+1])
m = (xx[i+1] - xx[i]) * sedz * sed_density
dx = px - midx
dz = pz - midz
dist2 = (dx**2 + dz**2)
grav += 2 * gn * m * dz / dist2
## contribution of ocean
for i in range(fl.nx-1):
midz = 0.5 * (zz[i] + zz[i+1])
if midz < 0:
midx = 0.5 * (xx[i] + xx[i+1])
m = (xx[i+1] - xx[i]) * -midz * ocean_density
dx = px - midx
dz = pz - midz
dist2 = (dx**2 + dz**2)
grav += 2 * gn * m * dz / dist2
# contribution of material outside left boundary
# assuming the leftmost element extend to negative infinity
# see Turcotte & Schubert, 1st Ed., Eq 5-106
for i in range(fl.nz-1):
sigma = rho[0,i] * (z[0,i] - z[0,i+1])
dx = px - xmin
dz = pz - 0.5 * (z[0,i] + z[0,i+1])
angle = np.arctan2(dx, dz)
grav += 2 * gn * sigma * (0.5*np.pi - angle)
if zz[0] < 0:
sigma = ocean_density * -zz[0]
dx = px - xmin
dz = pz - 0.5 * zz[0]
angle = np.arctan2(dx, dz)
grav += 2 * gn * sigma * (0.5*np.pi - angle)
# ditto for right boundary
for i in range(fl.nz-1):
sigma = rho[-1,i] * (z[-1,i] - z[-1,i+1])
dx = xmax - px
dz = pz - 0.5 * (z[-1,i] + z[-1,i+1])
angle = np.arctan2(dx, dz)
grav += 2 * gn * sigma * (0.5*np.pi - angle)
if zz[-1] < 0:
sigma = ocean_density * -zz[-1]
dx = xmax - px
dz = pz - 0.5 * zz[-1]
angle = np.arctan2(dx, dz)
grav += 2 * gn * sigma * (0.5*np.pi - angle)
## set reference gravity
## far right gravity to 0
grav -= grav[-1]
return px, topo, grav
def compute_gravity(frame):
## read data
fl = flac.Flac()
x, z = fl.read_mesh(frame) # in km
x *= 1e3
z *= 1e3
# surface coordinates
xx = x[:,0]
zz = z[:,0]
xmin = x[0,0]
xmax = x[-1,0]
# center of elements
cx, cz = flac.elem_coord(x, z)
# area of elements = 0.5 * | AC x BD | = 0.5 * |xdiag1*zdiag2 - xdiag2*zdiag1|
# A -- D
# | |
# B -- C
xdiag1 = x[0:-1, 0:-1] - x[1:, 1:]
zdiag1 = z[0:-1, 0:-1] - z[1:, 1:]
xdiag2 = x[1:, 0:-1] - x[0:-1, 1:]
zdiag2 = z[1:, 0:-1] - z[0:-1, 1:]
area = 0.5 * np.abs(xdiag1*zdiag2 - xdiag2*zdiag1)
rho = fl.read_density(frame) # in kg/m^3
# anything above sea level is removed
rho[cz > 0] = 0
## benchmark case: infinite-long cylinder with radius R
## buried at depth D
#R = 10e3
#D = -150e3
#drho = 1000
#rho = np.zeros(cx.shape)
#midx = 0.5 * (xmin + xmax)
#midz = 0.5 * z.min()
#dist2 = (x - midx)**2 + (z - D)**2
#rho[dist2 < R**2] = drho
#ocean_density = 0
mass = rho * area
## calculate gravity at these points
# px in uniform spacing
px = np.linspace(xmin, xmax, num=5*fl.nx)
# pz is a few km above the highest topography to avoid high frequency oscillation
pz_height = max(0, np.max(zz)) + 4e3
print ('gravity evaluated at %f km' % pz_height)
pz = np.ones(px.shape) * pz_height
# original topography defined in px grid
topo = np.interp(px, x[:,0], z[:,0])
## contribution of material inside the model
grav = np.empty(px.shape)
for i in range(len(grav)):
dx = px[i] - cx
dz = pz[i] - cz
dist2 = (dx**2 + dz**2)
# downward component of gravity of an infinite long line source of density anomaly
# see Turcotte & Schubert, 1st Ed., Eq 5-104
grav[i] = 2 * gn * np.sum(mass * dz / dist2)
## contribution of sedimentary basin, only to the right of trench
peaks = find_peaks(zz)
itrench = find_trench_index(zz)
basin_depth = -2000
sed_density = 2200
sed_thickness = np.zeros(fl.nx)
for ii in range(len(peaks)-1):
fill_height = min((basin_depth, zz[peaks[ii]], zz[peaks[ii+1]]))
for i in range(peaks[ii], peaks[ii+1]):
if zz[i] < fill_height:
sed_thickness[i] = fill_height - zz[i]
zz[i] = fill_height
for i in range(itrench, fl.nx-1):
sedz = 0.5 * (sed_thickness[i] + sed_thickness[i+1])
if sedz > 0:
midz = 0.5 * (zz[i] + zz[i+1])
midx = 0.5 * (xx[i] + xx[i+1])
m = (xx[i+1] - xx[i]) * sedz * sed_density
dx = px - midx
dz = pz - midz
dist2 = (dx**2 + dz**2)
grav += 2 * gn * m * dz / dist2
## contribution of ocean
for i in range(fl.nx-1):
midz = 0.5 * (zz[i] + zz[i+1])
if midz < 0:
midx = 0.5 * (xx[i] + xx[i+1])
m = (xx[i+1] - xx[i]) * -midz * ocean_density
dx = px - midx
dz = pz - midz
dist2 = (dx**2 + dz**2)
grav += 2 * gn * m * dz / dist2
# contribution of material outside left boundary
# assuming the leftmost element extend to negative infinity
# see Turcotte & Schubert, 1st Ed., Eq 5-106
for i in range(fl.nz-1):
sigma = rho[0,i] * (z[0,i] - z[0,i+1])
dx = px - xmin
dz = pz - 0.5 * (z[0,i] + z[0,i+1])
angle = np.arctan2(dx, dz)
grav += 2 * gn * sigma * (0.5*np.pi - angle)
if zz[0] < 0:
sigma = ocean_density * -zz[0]
dx = px - xmin
dz = pz - 0.5 * zz[0]
angle = np.arctan2(dx, dz)
grav += 2 * gn * sigma * (0.5*np.pi - angle)
# ditto for right boundary
for i in range(fl.nz-1):
sigma = rho[-1,i] * (z[-1,i] - z[-1,i+1])
dx = xmax - px
dz = pz - 0.5 * (z[-1,i] + z[-1,i+1])
angle = np.arctan2(dx, dz)
grav += 2 * gn * sigma * (0.5*np.pi - angle)
if zz[-1] < 0:
sigma = ocean_density * -zz[-1]
dx = xmax - px
dz = pz - 0.5 * zz[-1]
angle = np.arctan2(dx, dz)
grav += 2 * gn * sigma * (0.5*np.pi - angle)
## set reference gravity
## far right gravity to 0
grav -= grav[-1]
return px, topo, grav