def compute(myVelfield, MyParams):
print("Computing strain via delaunay method.")
z = np.array([myVelfield.elon, myVelfield.nlat])
z = z.T
tri = Delaunay(z)
triangle_vertices = z[tri.simplices]
trishape = np.shape(triangle_vertices)
# 516 x 3 x 2, for example
print(trishape[0])
# We are going to solve for the velocity gradient tensor at the centroid of each triangle.
centroids = []
for i in range(trishape[0]):
xcor_mean = np.mean([
triangle_vertices[i, 0, 0], triangle_vertices[i, 1, 0],
triangle_vertices[i, 2, 0]
])
ycor_mean = np.mean([
triangle_vertices[i, 0, 1], triangle_vertices[i, 1, 1],
triangle_vertices[i, 2, 1]
])
centroids.append([xcor_mean, ycor_mean])
xcentroid = [x[0] for x in centroids]
ycentroid = [x[1] for x in centroids]
# Initialize arrays.
I2nd = []
rot = []
max_shear = []
e1 = []
# eigenvalues
e2 = []
v00 = []
# eigenvectors
v01 = []
v10 = []
v11 = []
dilatation = []
# for each triangle:
for i in range(trishape[0]):
# Get the velocities of each vertex (VE1, VN1, VE2, VN2, VE3, VN3)
# Get velocities for Vertex 1 (triangle_vertices[i,0,0] and triangle_vertices[i,0,1])
xindex1 = np.where(myVelfield.elon == triangle_vertices[i, 0, 0])
yindex1 = np.where(myVelfield.nlat == triangle_vertices[i, 0, 1])
index1 = np.intersect1d(xindex1, yindex1)
xindex2 = np.where(myVelfield.elon == triangle_vertices[i, 1, 0])
yindex2 = np.where(myVelfield.nlat == triangle_vertices[i, 1, 1])
index2 = np.intersect1d(xindex2, yindex2)
xindex3 = np.where(myVelfield.elon == triangle_vertices[i, 2, 0])
yindex3 = np.where(myVelfield.nlat == triangle_vertices[i, 2, 1])
index3 = np.intersect1d(xindex3, yindex3)
VE1 = myVelfield.e[index1[0]]
VN1 = myVelfield.n[index1[0]]
VE2 = myVelfield.e[index2[0]]
VN2 = myVelfield.n[index2[0]]
VE3 = myVelfield.e[index3[0]]
VN3 = myVelfield.n[index3[0]]
obs_vel = np.array([[VE1], [VN1], [VE2], [VN2], [VE3], [VN3]])
# Get the distance between centroid and vertex (in km)
dE1 = (triangle_vertices[i, 0, 0] - xcentroid[i]) * 111.0 * np.cos(
np.deg2rad(ycentroid[i]))
dE2 = (triangle_vertices[i, 1, 0] - xcentroid[i]) * 111.0 * np.cos(
np.deg2rad(ycentroid[i]))
dE3 = (triangle_vertices[i, 2, 0] - xcentroid[i]) * 111.0 * np.cos(
np.deg2rad(ycentroid[i]))
dN1 = (triangle_vertices[i, 0, 1] - ycentroid[i]) * 111.0
dN2 = (triangle_vertices[i, 1, 1] - ycentroid[i]) * 111.0
dN3 = (triangle_vertices[i, 2, 1] - ycentroid[i]) * 111.0
Design_Matrix = np.array([[1, 0, dE1, dN1, 0,
0], [0, 1, 0, 0, dE1, dN1],
[1, 0, dE2, dN2, 0,
0], [0, 1, 0, 0, dE2, dN2],
[1, 0, dE3, dN3, 0, 0],
[0, 1, 0, 0, dE3, dN3]])
# Invert to get the components of the velocity gradient tensor.
DMinv = inv(Design_Matrix)
vel_grad = np.dot(DMinv, obs_vel)
# this is the money step.
VE_centroid = vel_grad[0][0]
VN_centroid = vel_grad[1][0]
dVEdE = vel_grad[2][0]
dVEdN = vel_grad[3][0]
dVNdE = vel_grad[4][0]
dVNdN = vel_grad[5][0]
# The components that are easily computed
[exx, exy, eyy,
rotation] = strain_tensor_toolbox.compute_strain_components_from_dx(
dVEdE, dVNdE, dVEdN, dVNdN)
# # Compute a number of values based on tensor properties.
I2nd_tri = np.log10(
np.abs(strain_tensor_toolbox.second_invariant(exx, exy, eyy)))
I2nd.append(I2nd_tri)
[e11, e22,
v] = strain_tensor_toolbox.eigenvector_eigenvalue(exx, exy, eyy)
e1.append(e11)
e2.append(e22)
rot.append(abs(rotation))
max_shear.append((e11 - e22) / 2)
v00.append(v[0][0])
v10.append(v[1][0])
v01.append(v[0][1])
v11.append(v[1][1])
dilatation.append(e11 + e22)
return [
xcentroid, ycentroid, triangle_vertices, I2nd, max_shear, rot, e1, e2,
v00, v01, v10, v11, dilatation
]
def compute(myVelfield, MyParams):
print("Computing strain via Numpy Spline method.");
interp_kind='linear';
# Scipy returns a function that you can use on a new set of x,y pairs.
f_east = interpolate.interp2d(myVelfield.elon, myVelfield.nlat, myVelfield.e, kind=interp_kind);
f_north = interpolate.interp2d(myVelfield.elon, myVelfield.nlat, myVelfield.n, kind=interp_kind);
# The new interpolation grid: a new set of points with some chosen spacing
xarray=np.arange(MyParams.coord_box[0],MyParams.coord_box[1],MyParams.grid_inc);
yarray=np.arange(MyParams.coord_box[2],MyParams.coord_box[3],MyParams.grid_inc);
[X,Y]=np.meshgrid(xarray,yarray);
# Evaluate the linear or cubic interpolation function at new points
new_east=np.zeros(np.shape(X));
new_north=np.zeros(np.shape(X));
for i in range(len(yarray)):
for j in range(len(xarray)):
new_east[i][j]=f_east(xarray[j],yarray[i]); # only want to give the functions one point at a time.
new_north[i][j]=f_north(xarray[j],yarray[i]);
# Grid increments
typical_lat=float(MyParams.map_range[2]);
xinc = MyParams.grid_inc * 111.000 * np.cos(np.deg2rad(typical_lat)); # in km (not degrees)
yinc = MyParams.grid_inc * 111.000; # in km (not degrees)
# Computing the elements of the strain tensor from the
rot=np.zeros(np.shape(X)); # 2nd invariant of rotation rate tensor
I2nd=np.zeros(np.shape(X)); # 2nd invariant of strain rate tensor
max_shear=np.zeros(np.shape(X)); # max shear of strain rate tensor
e1=np.zeros(np.shape(X)); # maximum principal strain (array of float)
e2=np.zeros(np.shape(X)); # minimum principal strain (array of float)
v00=np.zeros(np.shape(X)); # more complicated: eigenvectors (array of matrix 2x2)
v01=np.zeros(np.shape(X)); # more complicated: eigenvectors (array of matrix 2x2)
v10=np.zeros(np.shape(X)); # more complicated: eigenvectors (array of matrix 2x2)
v11=np.zeros(np.shape(X)); # more complicated: eigenvectors (array of matrix 2x2)
dilatation=np.zeros(np.shape(X));
# the strain calculation
for j in range(len(yarray)-1):
for i in range(len(xarray)-1):
up=new_east[j][i];
vp=new_north[j][i];
uq=new_east[j][i+1];
vq=new_north[j][i+1];
ur=new_east[j+1][i];
vr=new_north[j+1][i];
[dudx, dvdx, dudy, dvdy] = strain_tensor_toolbox.compute_displacement_gradients(up, vp, ur, vr, uq, vq, xinc, yinc);
# The components that are easily computed
# Units: nanostrain per year.
[exx, exy, eyy, rotation] = strain_tensor_toolbox.compute_strain_components_from_dx(dudx, dvdx, dudy, dvdy);
rot[j][i]=abs(rotation);
# Compute a number of values based on tensor properties.
I2nd[j][i] = np.log10(np.abs(strain_tensor_toolbox.second_invariant(exx, exy, eyy)));
[e11, e22, v1] = strain_tensor_toolbox.eigenvector_eigenvalue(exx, exy, eyy);
e1[j][i]= e11;
e2[j][i]= e22;
v00[j][i]=v1[0][0];
v10[j][i]=v1[1][0];
v01[j][i]=v1[0][1];
v11[j][i]=v1[1][1];
max_shear[j][i] = (e11 - e22)/2;
dilatation[j][i]= e11+e22;
print("Success computing strain via Numpy Spline method.\n");
return [xarray, yarray, I2nd, max_shear, rot, e1, e2, v00, v01, v10, v11, dilatation];
def compute(myVelfield, MyParams):
print("Computing strain via gpsgridder method.")
outfile = open("tempgps.txt", 'w')
for i in range(len(myVelfield.n)):
outfile.write("%f %f %f %f %f %f 0.0\n" %
(myVelfield.elon[i], myVelfield.nlat[i], myVelfield.e[i],
myVelfield.n[i], myVelfield.se[i], myVelfield.sn[i]))
outfile.close()
subprocess.call(
"gmt gpsgridder tempgps.txt -R" + MyParams.map_range + " -I" +
str(MyParams.grid_inc) +
" -S0.5 -Fd0.01 -C0.0005 -Emisfitfile.txt -fg -r -Gnc4_%s.nc",
shell=True)
# makes a netcdf grid file
# -R = range. -I = interval. -E prints the model and data fits at the input stations (very useful).
# -S = poisson's ratio. -Fd = fudge factor. -C = eigenvalues below this value will be ignored.
# -fg = flat earth approximation. -G = output netcdf files (x and y displacements).
# You should experiment with Fd and C values to find something that you like (good fit without overfitting).
# For Northern California, I like -Fd0.01 -C0.005. -R-125/-121/38/42.2
# I had Ff0.1 -C0.005 -fg
# For large domains, GMT netcdf4 files instead of netcdf3. We must turn them all into netcdf3 for python to read them.
subprocess.call('nccopy -k classic nc4_u.nc gps_u.nc', shell=True)
subprocess.call('nccopy -k classic nc4_v.nc gps_v.nc', shell=True)
subprocess.call(['rm', 'tempgps.txt'], shell=False)
subprocess.call(['rm', 'gmt.history'], shell=False)
subprocess.call(['mv', 'misfitfile.txt', MyParams.outdir], shell=False)
subprocess.call(['mv', 'nc4_u.nc', MyParams.outdir], shell=False)
subprocess.call(['mv', 'nc4_v.nc', MyParams.outdir], shell=False)
subprocess.call(['mv', 'gps_u.nc', MyParams.outdir], shell=False)
subprocess.call(['mv', 'gps_v.nc', MyParams.outdir], shell=False)
# Get ready to do strain calculation.
file1 = MyParams.outdir + "gps_u.nc"
file2 = MyParams.outdir + "gps_v.nc"
[xdata, ydata,
udata] = netcdf_io_functions.read_grd_xyz(file1, 'lon', 'lat', 'z')
[vdata] = netcdf_io_functions.read_grd_z(file2, 'z')
xinc = float(
subprocess.check_output('gmt grdinfo -M -C ' + file1 +
' | awk \'{print $8}\'',
shell=True))
# the x-increment
yinc = float(
subprocess.check_output('gmt grdinfo -M -C ' + file1 +
' | awk \'{print $9}\'',
shell=True))
# the y-increment
typical_lat = float(MyParams.map_range[2])
xinc = xinc * 111.000 * np.cos(np.deg2rad(typical_lat))
# in km (not degrees)
yinc = yinc * 111.000
# in km (not degrees)
xdata = np.flipud(xdata)
ydata = np.flipud(ydata)
udata = np.flipud(udata)
vdata = np.flipud(vdata)
[ydim, xdim] = np.shape(udata)
rot = np.zeros(np.shape(vdata))
# 2nd invariant of rotation rate tensor
I2nd = np.zeros(np.shape(vdata))
# 2nd invariant of strain rate tensor
max_shear = np.zeros(np.shape(vdata))
# max shear of strain rate tensor
e1 = np.zeros(np.shape(vdata))
# maximum principal strain (array of float)
e2 = np.zeros(np.shape(vdata))
# minimum principal strain (array of float)
v00 = np.zeros(np.shape(vdata))
# more complicated: eigenvectors (array of matrix 2x2)
v01 = np.zeros(np.shape(vdata))
# more complicated: eigenvectors (array of matrix 2x2)
v10 = np.zeros(np.shape(vdata))
# more complicated: eigenvectors (array of matrix 2x2)
v11 = np.zeros(np.shape(vdata))
# more complicated: eigenvectors (array of matrix 2x2)
dilatation = np.zeros(np.shape(vdata))
# dilatation
# the strain calculation
for j in range(ydim - 1):
for i in range(xdim - 1):
up = udata[j][i]
vp = vdata[j][i]
uq = udata[j][i + 1]
vq = vdata[j][i + 1]
ur = udata[j + 1][i]
vr = vdata[j + 1][i]
[dudx, dvdx, dudy,
dvdy] = strain_tensor_toolbox.compute_displacement_gradients(
up, vp, ur, vr, uq, vq, xinc, yinc)
# The components that are easily computed
# Units: nanostrain per year.
[exx, exy, eyy, rotation
] = strain_tensor_toolbox.compute_strain_components_from_dx(
dudx, dvdx, dudy, dvdy)
rot[j][i] = abs(rotation)
# Compute a number of values based on tensor properties.
I2nd[j][i] = np.log10(
np.abs(strain_tensor_toolbox.second_invariant(exx, exy, eyy)))
[e11, e22,
v1] = strain_tensor_toolbox.eigenvector_eigenvalue(exx, exy, eyy)
e1[j][i] = e11
e2[j][i] = e22
v00[j][i] = v1[0][0]
v10[j][i] = v1[1][0]
v01[j][i] = v1[0][1]
v11[j][i] = v1[1][1]
max_shear[j][i] = (e11 - e22) / 2
dilatation[j][i] = e11 + e22
return [
xdata, ydata, I2nd, max_shear, rot, e1, e2, v00, v01, v10, v11,
dilatation
]
def make_output_grids_from_strain_out(infile):
ifile = open(infile, 'r')
x = []
y = []
rotation = []
exx = []
exy = []
eyy = []
for line in ifile:
temp = line.split()
if 'index' in temp or 'longitude' in temp or 'deg' in temp:
continue
else:
x.append(float(temp[0]))
y.append(float(temp[1]))
rotation.append(float(temp[7]))
exx.append(float(temp[9]))
exy.append(float(temp[11]))
eyy.append(float(temp[13]))
ifile.close()
ax1 = set(x)
ax2 = set(y)
xlen = len(ax1)
ylen = len(ax2)
xaxis = sorted(ax1)
yaxis = sorted(ax2)
if xlen == 0 and ylen == 0:
print("ERROR! No valid strains have been computed. Try again.")
sys.exit(0)
# Loop through x and y lists, find the index of the coordinates in the xaxis and yaxis sets,
# Then place them into the 2d arrays.
# Then go compute I2nd, eigenvectors and eigenvalues.
I2nd = np.zeros((ylen, xlen))
max_shear = np.zeros((ylen, xlen))
rot = np.zeros((ylen, xlen))
e1 = np.zeros((ylen, xlen))
e2 = np.zeros((ylen, xlen))
dilatation = np.zeros((ylen, xlen))
v00 = np.zeros((ylen, xlen))
v01 = np.zeros((ylen, xlen))
v10 = np.zeros((ylen, xlen))
v11 = np.zeros((ylen, xlen))
print(np.shape(xaxis))
print(np.shape(I2nd))
for i in range(len(x)):
xindex = xaxis.index(x[i])
yindex = yaxis.index(y[i])
rot[yindex][xindex] = rotation[i]
I2nd[yindex][xindex] = np.log10(
np.abs(
strain_tensor_toolbox.second_invariant(exx[i], exy[i],
eyy[i])))
[e11, e22, v1] = strain_tensor_toolbox.eigenvector_eigenvalue(
exx[i], exy[i], eyy[i])
e1[yindex][xindex] = e11
e2[yindex][xindex] = e22
v00[yindex][xindex] = v1[0][0]
v10[yindex][xindex] = v1[1][0]
v01[yindex][xindex] = v1[0][1]
v11[yindex][xindex] = v1[1][1]
dilatation[yindex][xindex] = e11 + e22
max_shear[yindex][xindex] = (e11 - e22) / 2
return [
xaxis, yaxis, I2nd, max_shear, rot, e1, e2, v00, v01, v10, v11,
dilatation
]
def compute(myVelfield, MyParams):
print("Computing strain via Hammond method.")
z = np.array([myVelfield.elon, myVelfield.nlat])
z = z.T
tri = Delaunay(z)
triangle_vertices = z[tri.simplices]
trishape = np.shape(triangle_vertices)
# 516 x 3 x 2, for example
print("Number of triangle elements: %d" % (trishape[0]))
# We are going to solve for the velocity gradient tensor at the centroid of each triangle.
centroids = []
for i in range(trishape[0]):
xcor_mean = np.mean([
triangle_vertices[i, 0, 0], triangle_vertices[i, 1, 0],
triangle_vertices[i, 2, 0]
])
ycor_mean = np.mean([
triangle_vertices[i, 0, 1], triangle_vertices[i, 1, 1],
triangle_vertices[i, 2, 1]
])
centroids.append([xcor_mean, ycor_mean])
xcentroid = [x[0] for x in centroids]
ycentroid = [x[1] for x in centroids]
# Initialize arrays.
I2nd = []
rot = []
max_shear = []
e1 = []
# eigenvalues
e2 = []
v00 = []
# eigenvectors
v01 = []
v10 = []
v11 = []
dilatation = []
# dilatation = e1+e2
# for each triangle:
for i in range(trishape[0]):
# Get the velocities of each vertex (VE1, VN1, VE2, VN2, VE3, VN3)
# Get velocities for Vertex 1 (triangle_vertices[i,0,0] and triangle_vertices[i,0,1])
xindex1 = np.where(myVelfield.elon == triangle_vertices[i, 0, 0])
yindex1 = np.where(myVelfield.nlat == triangle_vertices[i, 0, 1])
index1 = int(np.intersect1d(xindex1, yindex1)[0])
xindex2 = np.where(myVelfield.elon == triangle_vertices[i, 1, 0])
yindex2 = np.where(myVelfield.nlat == triangle_vertices[i, 1, 1])
index2 = int(np.intersect1d(xindex2, yindex2)[0])
xindex3 = np.where(myVelfield.elon == triangle_vertices[i, 2, 0])
yindex3 = np.where(myVelfield.nlat == triangle_vertices[i, 2, 1])
index3 = int(np.intersect1d(xindex3, yindex3)[0])
phi = np.array([
triangle_vertices[i, 0, 0], triangle_vertices[i, 1, 0],
triangle_vertices[i, 2, 0]
])
theta = np.array([
triangle_vertices[i, 0, 1], triangle_vertices[i, 1, 1],
triangle_vertices[i, 2, 1]
])
theta = [i - 90 for i in theta]
u_phi = np.array(
[myVelfield.e[index1], myVelfield.e[index2], myVelfield.e[index3]])
u_theta = np.array(
[myVelfield.n[index1], myVelfield.n[index2], myVelfield.n[index3]])
u_theta = np.array([-i for i in u_theta])
# colatitude needs negative theta values.
s_phi = np.array([
myVelfield.se[index1], myVelfield.se[index2], myVelfield.se[index3]
])
s_theta = np.array([
myVelfield.sn[index1], myVelfield.sn[index2], myVelfield.sn[index3]
])
# HERE WE PLUG IN BILL'S CODE!
weight = 1
paramsel = 0
[
e_phiphi, e_thetaphi, e_thetatheta, omega_r, U_theta, U_phi,
s_omega_r, s_e_phiphi, s_e_thetaphi, s_e_thetatheta, s_U_theta,
s_U_phi, chi2, OMEGA, THETA_p, PHI_p, s_OMEGA, s_THETA_p, s_PHI_p,
r_PHITHETA, u_phi_p, u_theta_p
] = strain_sphere(phi, theta, u_phi, u_theta, s_phi, s_theta, weight,
paramsel)
# print_all_values(e_phiphi,e_thetaphi,e_thetatheta,omega_r,U_theta,U_phi,s_omega_r,s_e_phiphi,s_e_thetaphi,s_e_thetatheta,s_U_theta,s_U_phi,chi2,OMEGA,THETA_p,PHI_p,s_OMEGA,s_THETA_p,s_PHI_p,r_PHITHETA,u_phi_p,u_theta_p);
# The components that are easily computed
# Units: nanostrain per year.
exx = e_phiphi * 1e6
exy = -e_thetaphi * 1e6
eyy = e_thetatheta * 1e6
# # Compute a number of values based on tensor properties.
I2nd_tri = np.log10(
np.abs(strain_tensor_toolbox.second_invariant(exx, exy, eyy)))
I2nd.append(I2nd_tri)
rot.append(OMEGA * 1000 * 1000)
[e11, e22,
v] = strain_tensor_toolbox.eigenvector_eigenvalue(exx, exy, eyy)
e1.append(-e11)
# the convention of this code returns negative eigenvalues compared to my other codes.
e2.append(-e22)
max_shear.append((e11 - e22) / 2)
v00.append(v[0][0])
v10.append(v[1][0])
v01.append(v[0][1])
v11.append(v[1][1])
dilatation.append(-e11 + -e22)
# # the convention of this code returns negative eigenvalues compared to my other codes.
print("Success computing strain via Hammond method.\n")
return [
xcentroid, ycentroid, triangle_vertices, I2nd, max_shear, rot, e1, e2,
v00, v01, v10, v11, dilatation
]