print(
"either ydata or xdata contain NaNs, or if incompatible options are used"
)
popt, pcov = [np.nan, np.nan], [[np.nan, np.nan], [np.nan, np.nan]]
except OptimizeWarning:
print("Covariance of the parameters could not be estimated.")
# popt, pcov = [np.nan, np.nan], [[np.nan, np.nan],[np.nan, np.nan]]
Sy = abs(popt[0])
T = abs(popt[1])
# calculate the fitted power spectra
Shh_fitted = shh_analytical((frequency_input, Sww),
Sy,
T,
x,
L,
m=n,
n=m,
norm=norm)
# get the characteristic time
tc = calc_tc(L, Sy, T, which="dupuit")
# define a (discharge constant)
# a = np.pi ** 2 * T / (4 * L ** 2)
# define tc (characteristic time scale)
# tc = Sy / a
data = np.vstack((Shh, Shh_fitted))
labels = ["Shh numerical", "Shh fitted"]
linestyle = ["-", "-"]
p0=initial_guess)
return popt, pcov
if __name__ == "__main__":
popt, pcov = shh_analytical_fit(
power_spectrum_input,
power_spectrum_output,
frequency_input,
location=500,
length=1000,
m=2,
n=2,
norm=False,
)
plt.loglog(power_spectrum_output, label="data", color="blue")
plt.loglog(
shh_analytical(
(frequency_input, power_spectrum_input),
popt[0],
popt[1],
x=500,
L=1000,
norm=False,
),
label="fit",
color="red",
)
plt.legend()
plt.show()
"aquifer_length": aquifer_length,
"aquifer_thickness": aquifer_thickness,
"len_scale": len_scale,
"variance": var,
"geomean": geomean,
"harmean": harmean,
"arimean": arimean,
"mean": mean,
"seed": seed,
"dim": dim
}
results = results.append(other=results_temp, ignore_index=True, sort=False)
# calculate the power spectra: Shh from ogs runs, Shh theoretical (geo, har, ari), Shh fitted
Shh_geo = shh_analytical(
(frequency, Sww), S, T_in_geo, obs_loc, aquifer_length, m=m, n=n, norm=norm
)
Shh_har = shh_analytical(
(frequency, Sww), S, T_in_har, obs_loc, aquifer_length, m=m, n=n, norm=norm
)
Shh_ari = shh_analytical(
(frequency, Sww), S, T_in_ari, obs_loc, aquifer_length, m=m, n=n, norm=norm
)
Shh_fitted = shh_analytical(
(frequency, Sww),
popt[0],
popt[1],
obs_loc,
aquifer_length,
m=n,
n=m,
"which": which,
"recharge": get_filename_from_rfd_top_com(path_to_project),
"aquifer_length": aquifer_length,
"aquifer_thickness": aquifer_thickness,
}
results = results.append(other=results_temp,
ignore_index=True,
sort=False)
# calculate the fitted power spectra
Shh_fitted = shh_analytical(
(frequency, Sww),
popt[0],
popt[1],
obs_loc,
aquifer_length,
m=n,
n=m,
norm=norm,
)
if norm == True:
data = np.vstack((Shh_Sww, Shh_fitted))
elif norm == False:
data = np.vstack((Shh, Shh_fitted))
labels = ["Shh numerical", "Shh fitted"]
linestyle = ["-", "-"]
# lims = [(1e-9,6e-6),(1e-6,1e5)]
marker = ["", "d"]
figtxt = "OGS Input Parameter: S = %1.3e, T1 = %1.3e, T2 = %1.3e" % (
"err_tc_ari": percent_difference_fraction(
calc_tc(aquifer_length, S, T_in_ari), calc_tc(aquifer_length, popt[0], popt[1])
),
"obs_loc": obs_loc,
"time_step_size": time_step_size,
"time_steps": time_steps,
"model_period": time_step_size * time_steps / 86400,
"which": which,
"recharge": get_filename_from_rfd_top_com(path_to_project)
}
results = results.append(other=results_temp, ignore_index=True, sort=False)
# plot the power spectra: Shh from ogs runs, Shh theoretical, Shh fitted
Shh_numerical = Shh
Shh_theoretical = shh_analytical(
(frequency, Sww), S, T, obs_loc, aquifer_length, m=5, n=5, norm=False
)
Shh_fitted = shh_analytical(
(frequency, Sww),
popt[0],
popt[1],
obs_loc,
aquifer_length,
m=5,
n=5,
norm=False,
)
data = np.vstack((Shh_numerical, Shh_fitted, Shh_geo, Shh_har, Shh_ari))
labels = ["Shh numerical", "Shh fitted", "Shh geometric mean", "Shh harmonic mean", "Shh arithmetic mean"]
linestyle = ["-", "-", "--", "--", "--"]
#lims = [(1e-9,6e-6),(1e-6,1e5)]
def plot_shh_anal_loc():
"""
Function to plot multiple analytical power spectra along e.g. an aquifer in a 3D plot.
Still not working because plot3d has issues with log scale ...
"""
# set parameters
data_points = 8000
time_step_size = 86400
aquifer_length = 1000
Sy = 1e-1
T = 0.001
from calc_tc import calc_tc
tc = calc_tc(aquifer_length, Sy, T)
print(tc)
import sys
# add search path for own modules
sys.path.append("/Users/houben/PhD/python/scripts/spectral_analysis")
from shh_analytical import shh_analytical
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm
from mpl_toolkits.mplot3d import Axes3D
import scipy.fftpack as fftpack
# create an input signal
np.random.seed(123456789)
input = np.random.rand(data_points)
spectrum = fftpack.fft(input)
# erase first half of spectrum
spectrum = abs(spectrum[:round(len(spectrum) / 2)])**2
spectrum = spectrum # [1:]
# X contains the different locations
X = np.linspace(0, aquifer_length - 1, 10)
X = [100, 900]
# Y contains the frequencies, erase first data point because it's 0
Y = abs(fftpack.fftfreq(len(input),
time_step_size))[:round(len(input) / 2)]
Y = np.log10(Y[1:])
Z = np.zeros((len(Y), len(X)))
for i, loc in enumerate(X):
Z[:, i] = np.log10(
shh_analytical((Y, spectrum),
Sy=Sy,
T=T,
x=loc,
L=aquifer_length,
m=5,
n=5,
norm=False))
# erase first data point from Z for each location
print(Z)
print(Y)
import matplotlib.pyplot as plt
plt.plot(Y, Z[:, 0])
# plt.loglog(Y,Z[:,0])
# X, Y = np.meshgrid(X, Y)
# fig = plt.figure()
# ax = Axes3D(fig)
# surf = ax.plot_surface(
# X, Y, Z, rstride=1, cstride=2, shade=False, linewidth=1, cmap="Spectral_r"
# )
# surf = ax.plot_wireframe(X, Y, Z, rstride=0, cstride=1, cmap=cm.magma)
# surf.set_edgecolors(surf.to_rgba(surf._A))
# surf.set_facecolors("white")
# ax1 = ax.plot_wireframe(X, Y, Z, rstride=1, cstride=0)
# ax.set_xlabel("Location [m]")
# ax.set_ylabel("Frequency [Hz]")
# ax.set_zlabel("log Spectral Density")
# ax.set_zscale("log")
# ax.yaxis.set_scale("log")
# ax.zaxis._set_scale('log')
# ax.set_yscale("log")
plt.show()
"either ydata or xdata contain NaNs, or if incompatible options are used"
)
popt, pcov = [np.nan, np.nan], [[np.nan, np.nan], [np.nan, np.nan]]
except OptimizeWarning:
print("Covariance of the parameters could not be estimated.")
#popt, pcov = [np.nan, np.nan], [[np.nan, np.nan],[np.nan, np.nan]]
x = abs(popt[0])
L = abs(popt[1])
print("Obtained " + str(x) + "for x and " + str(L) + " for L.")
# calculate the fitted power spectra
Shh_fitted = shh_analytical(
(frequency_input, Sww),
Sy=Sy,
T=T,
x=x,
L=L,
m=n,
n=m,
norm=norm,
)
Shh_target = shh_analytical(
(frequency_input, Sww),
Sy=Sy,
T=T,
x=200,
L=1000,
m=n,
n=m,
norm=norm,
)
import numpy as np
import matplotlib.pyplot as plt
plt.ioff()
T_list = [1e-2, 1e-3, 1e-4, 1e-5]
S_list = [0.5, 0.4, 0.3, 0.2, 1e-1, 1e-2, 1e-3, 1e-4, 1e-5]
length_list = [100, 200, 500, 1000, 2000, 5000, 10000, 20000, 50000]
sww = np.loadtxt("/Users/houben/Desktop/shh_analytical_multi/sww.txt")
frequency = np.loadtxt(
"/Users/houben/Desktop/shh_analytical_multi/frequency.txt")
directory = "/Users/houben/Desktop/shh_analytical_multi"
X = (frequency, sww)
for T in T_list:
for S in S_list:
for L in length_list:
for x in np.linspace(0, L, 5):
shh = shh_analytical(X, S, T, x, L, m=5, n=5, norm=False)
plt.title("Transmissivity: " + str(T) + "\n" +
"Storativity: " + str(S) + "\n" + "Length: " +
str(L) + "\n" + "Location: " + str(x))
plt.loglog(frequency, shh)
plt.ylim(10e-7, 10e13)
plt.savefig(directory + "/" + str(T) + "_" + str(S) + "_" +
str(L) + "_" + str(x) + ".png")
print("saving " + str(T) + "_" + str(S) + "_" + str(L) + "_" +
str(x) + ".png")
plt.close()