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volcano_lib.py
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volcano_lib.py
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#!/usr/bin/env python3
'''
## volcano_lib.py
Library of python functions to be used with volcano_practical.ipynb.
'''
# packages
import subprocess as subp
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.path as path
from mpl_toolkits.axes_grid1 import make_axes_locatable
from cmcrameri import cm
import warnings
#-------------------------------------------------------------------------------
def mogi_source(x,y,xcen=0,ycen=0,d=3e3,dV=1e6, nu=0.25):
'''
Based on the Mogi source provided by Scott Henderson at:
https://github.com/scottyhq/cov9/blob/master/mogi.py
Original Mogi source from:
Mogi 1958, Segall 2010 p.203
INPUTS:
x = x-coordinate grid (m)
y = y-coordinate grid (m)
xcen = y-offset of point source epicenter (m) (default = 0)
ycen = y-offset of point source epicenter (m) (default = 0)
d = depth to point (m) (default = 3e3)
dV = change in volume (m^3) (default = 1e6)
nu = poisson's ratio for medium (default = 0.25)
OUTPUTS:
ux = displacement in x-direction at each point in (x,y)
uy = displacement in y-direction at each point in (x,y)
uz = displacement in z-direction at each point in (x,y)
'''
# Centre coordinate grid on point source
x = x - xcen
y = y - ycen
# Convert to surface cylindrical coordinates
th, rho = cart2pol(x,y)
R = np.hypot(d,rho)
# Mogi displacement calculation
C = ((1-nu) / np.pi) * dV
ur = C * rho / R**3
uz = C * d / R**3
# Convert back to cartesian coordinates
ux, uy = pol2cart(th, ur)
# reshape to input grid size
ux = ux.reshape(x.shape)
uy = uy.reshape(x.shape)
uz = uz.reshape(x.shape)
return ux, uy, uz
#-------------------------------------------------------------------------------
def mogi_source_topo(x, y, elev, xcen=0, ycen=0, d=3e3, dV=1e6, nu=0.25):
'''
Based on the Mogi source provided by Scott Henderson at:
https://github.com/scottyhq/cov9/blob/master/mogi.py
Includes an adjustment for topography above the source.
Elevations are measured above sea level, source depth is measured below sea level.
Original Mogi source from:
Mogi 1958, Segall 2010 p.203
INPUTS:
x = x-coordinate grid (m)
y = y-coordinate grid (m)
xcen = y-offset of point source epicenter (m) (default = 0)
ycen = y-offset of point source epicenter (m) (default = 0)
d = depth to point (m) (default = 3e3)
dV = change in volume (m^3) (default = 1e6)
nu = poisson's ratio for medium (default = 0.25)
elev = array of elevations, same size as x and y (m)
OUTPUTS:
ux = displacement in x-direction at each point in (x,y)
uy = displacement in y-direction at each point in (x,y)
uz = displacement in z-direction at each point in (x,y)
'''
# Centre coordinate grid on point source
x = x - xcen
y = y - ycen
# Convert to surface cylindrical coordinates
th, rho = cart2pol(x,y)
R = np.hypot(d+elev,rho)
# Mogi displacement calculation
C = ((1-nu) / np.pi) * dV
ur = C * rho / R**3
uz = C * d / R**3
# Convert back to cartesian coordinates
ux, uy = pol2cart(th, ur)
# reshape to input grid size
ux = ux.reshape(x.shape)
uy = uy.reshape(x.shape)
uz = uz.reshape(x.shape)
return ux, uy, uz
#-------------------------------------------------------------------------------
def cart2pol(x1,x2):
'''
Conversion for cartesian (x,y) to polar coordinates (for mogi model).
'''
theta = np.arctan2(x2,x1)
r = np.hypot(x2,x1)
return theta, r
#-------------------------------------------------------------------------------
def pol2cart(theta,r):
'''
Conversion from polar coordinates to cartesian (for mogi model).
'''
x1 = r * np.cos(theta)
x2 = r * np.sin(theta)
return x1,x2
#-------------------------------------------------------------------------------
def profile_data(x,y,data,prof_start,prof_end,params):
'''
Generates a profile through gridded data.
INPUTS:
data = numpy array of values to profile
x = vector of coords for the x axis
y = vector of coords for the y axis
prof_start = (x, y) pair for the start of the profile line
prof_end = (x, y) pair for the end of the profile line
params = dictionary of parameters for the profiler (currently nbins and width)
'''
xx,yy = np.meshgrid(x,y)
prof_start = np.array(prof_start)
prof_end = np.array(prof_end)
# Profile dimensions relative to profile itself
prof_dist = np.sqrt((prof_start[1]-prof_end[1])**2 + (prof_start[0]-prof_end[0])**2)
prof_bin_edges = np.linspace(0, prof_dist ,params["nbins"]+1)
prof_bin_mids = (prof_bin_edges[:-1] + prof_bin_edges[1:]) / 2
# Profile points in lat long space
bin_mids = np.linspace(0,1,params["nbins"]+1)
bin_grad = prof_end - prof_start
x_mids = prof_start[0] + (bin_mids * bin_grad[0])
y_mids = prof_start[1] + (bin_mids * bin_grad[1])
# Gradient of line perpendicular to profile
bin_grad_norm = (params["width"]/2) * bin_grad / np.linalg.norm(bin_grad)
# Corner points of bins
bin_x1 = x_mids + bin_grad_norm[1]
bin_x2 = x_mids - bin_grad_norm[1]
bin_y1 = y_mids - bin_grad_norm[0]
bin_y2 = y_mids + bin_grad_norm[0]
# Pre-allocate outputs
bin_val = np.zeros_like((bin_x1[:-1]))
bin_std = np.zeros_like(bin_val)
# Trim data set to points inside any bin (improves run time)
full_poly = path.Path([(bin_x1[0], bin_y1[0]), (bin_x1[-1], bin_y1[-1]), (bin_x2[-1], bin_y2[-1]), (bin_x2[0], bin_y2[0])])
poly_points = full_poly.contains_points(np.transpose([xx.flatten(),yy.flatten()]))
poly_points = poly_points.reshape(data.shape)
trim_data = data[poly_points]
trim_xx = xx[poly_points]
trim_yy = yy[poly_points]
# Loop through each bin identifying the points that they contain
for ii in range(0,params["nbins"]):
poly_x = np.array([bin_x1[ii], bin_x1[ii+1], bin_x2[ii+1], bin_x2[ii]]);
poly_y = np.array([bin_y1[ii], bin_y1[ii+1], bin_y2[ii+1], bin_y2[ii]]);
poly = path.Path([(poly_x[0], poly_y[0]), (poly_x[1], poly_y[1]), (poly_x[2], poly_y[2]), (poly_x[3], poly_y[3])])
poly_points = poly.contains_points(np.transpose([trim_xx,trim_yy]))
in_poly_vals = trim_data[poly_points]
with warnings.catch_warnings():
warnings.simplefilter("ignore", category=RuntimeWarning)
bin_val[ii] = np.nanmean(in_poly_vals)
# get point cloud
poly_x = np.array([bin_x1[0], bin_x1[-1], bin_x2[-1], bin_x2[0]])
poly_y = np.array([bin_y1[0], bin_y1[-1], bin_y2[-1], bin_y2[0]])
points_poly = np.vstack((poly_x,poly_y)).T
points_poly = np.vstack((points_poly,np.array([points_poly[0,0],points_poly[0,1]])))
poly = path.Path([(poly_x[0], poly_y[0]), (poly_x[1], poly_y[1]), (poly_x[2], poly_y[2]), (poly_x[3], poly_y[3])])
poly_points = poly.contains_points(np.transpose([trim_xx,trim_yy]))
points_val = trim_data[poly_points]
points_x = trim_xx[poly_points]
points_y = trim_yy[poly_points]
prof_m = (prof_start[1] - prof_end[1]) / (prof_start[0] - prof_end[0])
points_m = (prof_start[1] - points_y) / (prof_start[0] - points_x)
points_prof_angle = np.arctan((points_m - prof_m) / (1 + prof_m * points_m))
points2prof_start = np.sqrt((prof_start[1] - points_y)**2 + (prof_start[0] - points_x)**2)
points_dist = points2prof_start * np.cos(points_prof_angle)
return bin_val, prof_bin_mids, points_val, points_dist, points_poly
#-------------------------------------------------------------------------------
def plot_comparison(ulos_asc, disp_asc, ulos_desc, disp_desc, xcen, ycen, extents, clim):
'''
Generates a plot comparing modelled, observed, and residual displacements for two frames.
Currently the frame names are hard-coded.
INPUTS:
ulos_asc = ascending model
disp_asc = ascending observations
ulos_desc = descending model
disp_desc = descending observations
xcen = x coord of mogi centre
ycen = y coord of mogi centre
extents = extents of displacement files [xmin, xmax, ymin, ymax]
clim = colour limits for model and observed
'''
# plot model, data, and residual
fig, axs = plt.subplots(2,3,figsize=(20,17))
fig.tight_layout(h_pad=10, w_pad = 10)
# ascending model
im = axs[0,0].imshow(ulos_asc, extent=extents, vmin=clim[0], vmax=clim[1], cmap=cm.batlow)
axs[0,0].scatter(xcen, ycen, color='red')
divider = make_axes_locatable(axs[0,0])
cax = divider.append_axes("right", size="5%", pad="5%")
cbar = plt.colorbar(im, cax=cax)
cbar.set_label(label='Line-of-sight displacement (mm)', fontsize=18)
cbar.ax.tick_params(labelsize=16)
axs[0,0].set_title('Model displacement', fontsize=20)
axs[0,0].set_xlabel('x-coord (km)', fontsize=18)
axs[0,0].set_ylabel('y-coord (km)', fontsize=18)
axs[0,0].tick_params(labelsize=16)
axs[0,0].set_xlim(extents[0], extents[1])
axs[0,0].set_ylim(extents[2], extents[3])
axs[0,0].annotate('018A_12668_131313', xy=(0, 0.5), xytext=(-axs[0,0].yaxis.labelpad - 40, 0),
xycoords=axs[0,0].yaxis.label, textcoords='offset points',
fontsize=20, ha='left', va='center', rotation=90, weight='bold')
# ascending data
im = axs[0,1].imshow(disp_asc, extent=extents, vmin=clim[0], vmax=clim[1], cmap=cm.batlow)
axs[0,1].scatter(xcen, ycen, color='red')
divider = make_axes_locatable(axs[0,1])
cax = divider.append_axes("right", size="5%", pad="5%")
cbar = plt.colorbar(im, cax=cax)
cbar.set_label(label='Line-of-sight displacement (mm)', fontsize=18)
cbar.ax.tick_params(labelsize=16)
axs[0,1].set_title('Observed displacement', fontsize=20)
axs[0,1].set_xlabel('x-coord (km)', fontsize=18)
axs[0,1].tick_params(labelsize=16)
axs[0,1].set_xlim(extents[0], extents[1])
axs[0,1].set_ylim(extents[2], extents[3])
# asceding residual (observed - model)
im = axs[0,2].imshow(disp_asc-ulos_asc, extent=extents, cmap=cm.batlow)
axs[0,2].scatter(xcen, ycen, color='red')
divider = make_axes_locatable(axs[0,2])
cax = divider.append_axes("right", size="5%", pad="5%")
cbar = plt.colorbar(im, cax=cax)
cbar.set_label(label='Residual displacement (mm)', fontsize=18)
cbar.ax.tick_params(labelsize=16)
axs[0,2].set_title('Residual (observed - model)', fontsize=20)
axs[0,2].set_xlabel('x-coord (km)', fontsize=18)
axs[0,2].tick_params(labelsize=16)
axs[0,2].set_xlim(extents[0], extents[1])
axs[0,2].set_ylim(extents[2], extents[3])
# descending model
im = axs[1,0].imshow(ulos_desc, extent=extents, vmin=clim[0], vmax=clim[1], cmap=cm.batlow)
axs[1,0].scatter(xcen, ycen, color='red')
divider = make_axes_locatable(axs[1,0])
cax = divider.append_axes("right", size="5%", pad="5%")
cbar = plt.colorbar(im, cax=cax)
cbar.set_label(label='Line-of-sight displacement (mm)', fontsize=18)
cbar.ax.tick_params(labelsize=16)
axs[1,0].set_xlabel('x-coord (km)', fontsize=18)
axs[1,0].set_ylabel('y-coord (km)', fontsize=18)
axs[1,0].tick_params(labelsize=16)
axs[1,0].set_xlim(extents[0], extents[1])
axs[1,0].set_ylim(extents[2], extents[3])
axs[1,0].annotate('083D_12636_131313', xy=(0, 0.5), xytext=(-axs[1,0].yaxis.labelpad - 40, 0),
xycoords=axs[1,0].yaxis.label, textcoords='offset points',
fontsize=20, ha='left', va='center', rotation=90, weight='bold')
# descending data
im = axs[1,1].imshow(disp_desc, extent=extents, vmin=clim[0], vmax=clim[1], cmap=cm.batlow)
axs[1,1].scatter(xcen, ycen, color='red')
divider = make_axes_locatable(axs[1,1])
cax = divider.append_axes("right", size="5%", pad="5%")
cbar = plt.colorbar(im, cax=cax)
cbar.set_label(label='Line-of-sight displacement (mm)', fontsize=18)
cbar.ax.tick_params(labelsize=16)
axs[1,1].set_title('Observed displacement', fontsize=20)
axs[1,1].set_xlabel('x-coord (km)', fontsize=18)
axs[1,1].tick_params(labelsize=16)
axs[1,1].set_xlim(extents[0], extents[1])
axs[1,1].set_ylim(extents[2], extents[3])
# descending residual (observed - model)
im = axs[1,2].imshow(disp_desc-ulos_desc, extent=extents, cmap=cm.batlow)
axs[1,2].scatter(xcen, ycen, color='red')
divider = make_axes_locatable(axs[1,2])
cax = divider.append_axes("right", size="5%", pad="5%")
cbar = plt.colorbar(im, cax=cax)
cbar.set_label(label='Residual displacement (mm)', fontsize=18)
cbar.ax.tick_params(labelsize=16)
axs[1,2].set_title('Residual (observed - model)', fontsize=20)
axs[1,2].set_xlabel('x-coord (km)', fontsize=18)
axs[1,2].tick_params(labelsize=16)
axs[1,2].set_xlim(extents[0], extents[1])
axs[1,2].set_ylim(extents[2], extents[3])
plt.show()