def compute_prem_load(station_array, load_array, disk_radius, greensfunc, max_distance):
# For a given station and a given set of loads,
# Compute the loading on a PREM earth structure
# Max distance is in degrees
total_disp_x, total_disp_y, total_disp_v = [], [], [];
for i in range(len(station_array.lon)): # for each station...
# Take a set of rectangular loads and tile them into disk loads.
CircleLoads = get_disks(load_array, disk_radius, max_distance, station_array.lon[i], station_array.lat[i]);
print("Number of circles: %d" % len(CircleLoads.lon));
disk_sum_v, disk_sum_x, disk_sum_y = 0, 0, 0;
for j in range(np.size(CircleLoads.lon)):
dist_from_center = haversine.distance([CircleLoads.lat[j], CircleLoads.lon[j]],
[station_array.lat[i], station_array.lon[i]]); # reported in km
myindex = find_closest_greens(greensfunc.km,
dist_from_center); # find the nearest answer in the Green's functions
vdisp = greensfunc.vload[myindex]; # in m
hdisp = greensfunc.hload[myindex]; # in m
[xdisp, ydisp] = az_decompose(hdisp, (station_array.lat[i], station_array.lon[i]), (
CircleLoads.lat[j], CircleLoads.lon[j])); # Decompose radial into x and y components
disk_sum_v = disk_sum_v + vdisp * CircleLoads.pressure[
j] * 1000 / 9.81; # THIS SHOULD BE DIVIDED BY 9.81! the PREM code already has it. Result in mm
disk_sum_x = disk_sum_x + xdisp * CircleLoads.pressure[
j] * 1000 / 9.81; # THIS SHOULD BE DIVIDED BY 9.81! the PREM code already has it. Result in mm
disk_sum_y = disk_sum_y + ydisp * CircleLoads.pressure[
j] * 1000 / 9.81; # THIS SHOULD BE DIVIDED BY 9.81! the PREM code already has it. Result in mm
total_disp_x.append(disk_sum_x);
total_disp_y.append(disk_sum_y);
total_disp_v.append(disk_sum_v);
return total_disp_x, total_disp_y, total_disp_v; # should exactly match length of input station_array fields.
def evaluate_gradients(point1, point2, ascending1, ascending2, descending1,
descending2):
mydistance = haversine.distance([point1[1], point1[0]],
[point2[1], point2[0]])
print(
"Gradient in ASCENDING track from point1 to point2: %f mm/yr in %f km "
% (np.abs(ascending1 - ascending2), mydistance))
print("Equal to: %f mm/yr per 100 km \n" %
(100 * np.abs(ascending1 - ascending2) / mydistance))
print(
"Gradient in DESCENDING track from point1 to point2: %f mm/yr in %f km "
% (np.abs(descending1 - descending2), mydistance))
print("Equal to: %f mm/yr per 100 km \n" %
(100 * np.abs(descending1 - descending2) / mydistance))
return
def compute_circle(myVelfield, center, radius):
close_stations = []
rad_distance = []
lon, lat = [], []
for station_vel in myVelfield:
mydist = haversine.distance([center[1], center[0]],
[station_vel.nlat, station_vel.elon])
if mydist <= radius:
rad_distance.append(mydist)
lon.append(station_vel.elon)
lat.append(station_vel.nlat)
close_stations.append(station_vel.name)
print("Returning %d stations within %.3f km of %.4f, %.4f" %
(len(close_stations), radius, center[0], center[1]))
return close_stations, lon, lat, rad_distance
def get_disks(load_array, disk_radius, threshold_distance, sta_lon, sta_lat):
# threshold_distance is in degrees
circle_lons, circle_lats, circle_radius, circle_pressure = [], [], [], [];
threshold_distance = threshold_distance * (np.pi / 180) * 6370; # converting to km (6370km = 1 radian).
circle_area = np.pi * disk_radius * disk_radius; # Area = pi * r^2
square_side_length = np.sqrt(circle_area); # in same units as disk_radius
for i in range(len(load_array.lon)): # for each rectangular load cell
if abs(load_array.lat[i]) > 85: # ignoring the arctic and antarctic
continue;
dist_from_center = haversine.distance([load_array.lat[i], load_array.lon[i]],
[sta_lat, sta_lon]); # reported in km
if dist_from_center < threshold_distance:
# if the load cell is less than a certain distance from the station, discretize it.
center = [load_array.lon[i], load_array.lat[i]];
load_akm = load_array.east_width[i] * 111.0 * np.cos(center[1] * np.pi / 180);
load_bkm = load_array.north_width[i] * 111.0;
# The placement of each disk-shaped tile within the load
n_tiles_x = int(np.floor(load_akm * 2 / square_side_length));
n_tiles_y = int(np.floor(load_bkm * 2 / square_side_length)); # n tiles fitting in x and y dim of rectangle
x_array, y_array = [], [];
x_nodes = np.linspace(center[0] - load_array.east_width[i], center[0] + load_array.east_width[i],
n_tiles_x + 1, endpoint=True);
y_nodes = np.linspace(center[1] - load_array.north_width[i], center[1] + load_array.north_width[i],
n_tiles_y + 1, endpoint=True);
for j in range(len(x_nodes) - 1):
x_array.append((x_nodes[j] + x_nodes[j + 1]) * 0.5); # average of two nodes
for j in range(len(y_nodes) - 1):
y_array.append((y_nodes[j] + y_nodes[j + 1]) * 0.5); # average of two nodes
[centerx, centery] = np.meshgrid(x_array, y_array);
centerx = np.reshape(centerx, (np.size(centerx), 1))
centery = np.reshape(centery, (np.size(centery), 1))
# HERE WE RE-PACKAGE INTO CIRCULAR LOADS
for j in range(np.size(centerx)):
circle_lons.append(centerx[j]);
circle_lats.append(centery[j]);
circle_radius.append(disk_radius);
circle_pressure.append(load_array.pressure[i]);
CircleLoads = helper_functions.Load_Array(lon=circle_lons, lat=circle_lats, east_width=circle_radius,
north_width=[], pressure=circle_pressure);
return CircleLoads;
def create_los_rdr_geo_from_ground_ann_file(ann_file, x_axis, y_axis):
# Make los.rdr.geo given .ann file from JPL website's UAVSAR interferograms and the ground-range sample points.
# x-axis and y-axis are the x and y arrays where los vectors will be extracted on a corresponding grid.
near_angle, far_angle, heading = jpl_uav_read_write.get_nearrange_farrange_heading_angles(
ann_file)
heading_cartesian = insar_vector_functions.bearing_to_cartesian(heading)
# CCW from east
print("Heading is %f degrees CW from north" % heading)
print("Cartesian Heading is %f" % heading_cartesian)
# Get the upper and lower left corners, so we can compute the length of the across-track extent in km
ul_lon, ul_lat, ll_lon, ll_lat = jpl_uav_read_write.get_ground_range_left_corners(
ann_file)
cross_track_max = haversine.distance((ll_lat, ll_lon), (ul_lat, ul_lon))
# in km
# Get the azimuth angle for the pixels looking up to the airplane
# My own documentation says CCW from north, even though that's really strange.
azimuth = heading_cartesian - 90
# 90 degrees to the right of the airplane heading
# (for the look vector from ground to plane)
azimuth = insar_vector_functions.cartesian_to_ccw_from_north(azimuth)
# degrees CCW from North
print("azimuth from ground to plane is:", azimuth)
[X, Y] = np.meshgrid(x_axis, y_axis)
(ny, nx) = np.shape(X)
grid_az = azimuth * np.ones(np.shape(X))
grid_inc = np.zeros(np.shape(X))
print("Computing incidence angles for all pixels")
for i in range(ny):
for j in range(nx):
xtp = cross_track_pos(X[i, j], Y[i, j], ll_lon, ll_lat,
heading_cartesian)
# THIS WILL HAVE TO CHANGE FOR ASCENDING AND DESCENDING
inc = incidence_angle_trig(xtp, cross_track_max, near_angle,
far_angle)
grid_inc[i, j] = inc
# Finally, write the 2 bands for los.rdr.geo
isce_read_write.write_isce_unw(grid_inc, grid_az, nx, ny, "FLOAT",
'los.rdr.geo')
return
def vert_adjust_by_reference_stations(names, coords, slope_obj):
# How do we adjust the verticals for large-scale drought signatures?
reference_station = 'P208'
coord_box = [-123, -121, 39, 42]
eq_coords = [-124.81, 40.53]
radius = 250
max_radius = 350
reference_type = 'radius' # options = 'radius','box','station'
new_slope_obj = []
background_slopes_before = []
background_slopes_after = []
for i in range(len(names)):
if reference_type == 'station':
if names[i] == reference_station:
background_slopes_before.append(slope_obj[i][0])
background_slopes_after.append(slope_obj[i][1])
elif reference_type == 'box':
if coord_box[0] < coords[i][0] < coord_box[1]:
if coord_box[2] < coords[i][1] < coord_box[3]:
background_slopes_before.append(slope_obj[i][0])
background_slopes_after.append(slope_obj[i][1])
elif reference_type == 'radius':
mydistance = haversine.distance([coords[i][1], coords[i][0]],
[eq_coords[1], eq_coords[0]])
if radius < mydistance < max_radius:
background_slopes_before.append(slope_obj[i][0])
background_slopes_after.append(slope_obj[i][1])
vert_reference_before = np.nanmean(background_slopes_before)
vert_reference_after = np.nanmean(background_slopes_after)
print("Vert slope before: %f " % vert_reference_before)
print("Vert slope after: %f " % vert_reference_after)
for i in range(len(slope_obj)):
new_slope_obj.append([
slope_obj[i][0] - vert_reference_before,
slope_obj[i][1] - vert_reference_after, slope_obj[i][2]
])
return new_slope_obj
def cross_track_pos(target_lon, target_lat, nearrange_lon, nearrange_lat,
heading_cartesian):
# Given the heading of a plane and the coordinates of one near-range point
# Get the cross-track position of point in a coordinate system centered
# at (nearrange_lon, nearrange_lat) with given heading
distance = haversine.distance((target_lat, target_lon),
(nearrange_lat, nearrange_lon))
compass_bearing = haversine.calculate_initial_compass_bearing(
(nearrange_lat, nearrange_lon), (target_lat, target_lon))
# this comes CW from north
theta = insar_vector_functions.bearing_to_cartesian(compass_bearing)
# angle of position vector, cartesian coords
# heading_cartesian is the angle between the east unit vector and the flight direction
x0 = distance * np.cos(np.deg2rad(theta))
y0 = distance * np.sin(np.deg2rad(theta))
# in the east-north coordinate systeem
x_prime, y_prime = insar_vector_functions.rotate_vector_by_angle(
x0, y0, heading_cartesian)
return y_prime
def get_nearest_pixel_in_raster(raster_lon, raster_lat, target_lon, target_lat):
"""Take a raster (2d arrays with lat and lon)
and find the grid location closest to the target location
This could be optimized with a distance formula or walking algorithm in the future.
"""
dist = np.zeros(np.shape(raster_lon));
lon_shape = np.shape(raster_lon);
for i in range(lon_shape[0]):
for j in range(lon_shape[1]):
mypt = [raster_lat[i][j], raster_lon[i][j]];
dist[i][j] = haversine.distance((target_lat, target_lon), mypt);
minimum_distance = np.nanmin(dist);
if minimum_distance < 0.25: # if we're inside the domain.
idx = np.where(dist == np.nanmin(dist));
i_found = idx[0][0];
j_found = idx[1][0];
print(raster_lon[i_found][j_found], raster_lat[i_found][j_found]);
else:
i_found, j_found = np.nan, np.nan; # error codes
return i_found, j_found, minimum_distance;
def latlon2xy_single(loni, lati, lon0, lat0):
"""
Convert lon/lat coordinate into cartesian x/y coordinate using reference point.
:param loni: longitude of target point
:type loni: float
:param lati: latitude of target point
:type lati: float
:param lon0: longitude of reference point
:type lon0: float
:param lat0: latitude of reference point
:type lat0: float
:returns: x, y of target point, in km
:rtype: float, float
"""
radius = haversine.distance([lat0, lon0], [lati, loni])
bearing = haversine.calculate_initial_compass_bearing((lat0, lon0),
(lati, loni))
azimuth = 90 - bearing
x = radius * np.cos(np.deg2rad(azimuth))
y = radius * np.sin(np.deg2rad(azimuth))
return x, y
def get_nearest_pixel_in_raster(raster_lon, raster_lat, target_lon,
target_lat):
"""
A very general function
Take a 2D raster of lons and lats and find the grid location closest to the target location
"""
dist = np.zeros(np.shape(raster_lon))
lon_shape = np.shape(raster_lon)
for i in range(lon_shape[0]):
for j in range(lon_shape[1]):
mypt = [raster_lat[i][j], raster_lon[i][j]]
dist[i][j] = haversine.distance((target_lat, target_lon), mypt)
minimum_distance = np.nanmin(dist)
if minimum_distance < 0.25: # if we're inside the domain.
idx = np.where(dist == np.nanmin(dist))
i_found = idx[0][0]
j_found = idx[1][0]
print(raster_lon[i_found][j_found], raster_lat[i_found][j_found])
else:
i_found, j_found = -1, -1
# error codes
return i_found, j_found
def split_fault_trace(fault_trace, typical_spacing_km):
"""
Algorithm: Walk up the fault in chunks. If the chunk is smaller than typical_spacing_km, it becomes one segment.
Otherwise we split the segment into something similar to typical_spacing_km.
Returns: (starting lon, starting_lat, strike, length, ending_lon, ending_lat) for each fault trace segment
"""
all_fault_segments = [];
for i in range(1, len(fault_trace[0])):
start_point = (fault_trace[1][i-1], fault_trace[0][i-1]);
end_point = (fault_trace[1][i], fault_trace[0][i]);
segment_distance = haversine.distance(start_point, end_point);
strike = haversine.calculate_initial_compass_bearing(start_point, end_point);
if segment_distance < typical_spacing_km: # for the really small segments
one_fault_segment = (fault_trace[0][i-1], fault_trace[1][i-1], strike, segment_distance,
fault_trace[0][i], fault_trace[1][i]);
all_fault_segments.append(one_fault_segment);
else: # the segments greater than 2x the characteristic spacing
num_subsegments = int(np.ceil(segment_distance / typical_spacing_km)); # making segments < typical_spacing
counter = [x for x in range(0, num_subsegments+1)];
lon_difference = fault_trace[0][i] - fault_trace[0][i-1];
lon_step = lon_difference / num_subsegments;
lon_subarray = [fault_trace[0][i-1] + lon_step*x for x in counter];
# for x subsegments, we have x+1 elements in lon_subarray
lat_difference = fault_trace[1][i] - fault_trace[1][i-1];
lat_step = lat_difference / num_subsegments;
lat_subarray = [fault_trace[1][i-1] + lat_step*x for x in counter];
for j in range(1, len(lon_subarray)):
one_fault_segment = (lon_subarray[j-1], lat_subarray[j-1], strike, segment_distance/num_subsegments,
lon_subarray[j], lat_subarray[j]);
all_fault_segments.append(one_fault_segment);
print("Meshed fault trace of %d segments into %d segments " % (len(fault_trace[0]), len(all_fault_segments)));
return all_fault_segments;