Notebook

In [1]:

import numpy as np
import functions as fc
import fourier_continuation as fc_c
from timeit import default_timer as time
from fatiando.gravmag import polyprism, sphere
from fatiando import mesher, gridder,utils
from fatiando.constants import G, SI2MGAL
from scipy.sparse import diags
from matplotlib import pyplot as plt
import matplotlib.cm as cm
from scipy.interpolate import griddata
from scipy import interpolate
from fatiando.vis import mpl
import cPickle as pickle
%matplotlib inline

/home/vanderlei/Documents/fatiando/fatiando/vis/mpl.py:70: UserWarning: This module will be removed in v0.6. We recommend the use of matplotlib.pyplot module directly. Some of the fatiando specific functions will remain.
  "specific functions will remain.")

Open data and configuration¶

In [2]:

with open('synthetic_gz.pickle') as r:
    synthetic_gz = pickle.load(r)
    
xi = synthetic_gz['x']
yi = synthetic_gz['y']
zi = synthetic_gz['z']
zi_up = synthetic_gz['z_up']
zi_down = synthetic_gz['z_down']
dobs = synthetic_gz['gz_med']
dobs_up = synthetic_gz['gz_up']
dobs_down = synthetic_gz['gz_down']

shape = (100, 100)
area = [-5000, 5000, -4000, 4000]
R = 1000
xc, yc = -3000, 0

Equivalent Layer Depth¶

In [3]:

# Equivalent Layer depth
zj = np.ones_like(zi)*300

Fast Eq. Layer¶

In [4]:

# Predicted data
itmax = 40
s = time()
rho, gzp = fc.fast_eq(xi,yi,zi,zj,shape,dobs,itmax)
e = time()
tcpu = e - s
print tcpu, 'seconds'

10.3862431049 seconds

Fast Eq. Layer BCCB¶

In [5]:

# Predicted data
itmax = 40
s = time()
rho_c, gzp_bccb = fc.fast_eq_bccb(xi,yi,zi,zj,shape,dobs,itmax)
e = time()
tcpu = e - s
print tcpu, 'seconds'

0.0598001480103 seconds

Upward Continuation and Downward Continuation¶

In [6]:

N = shape[0]*shape[1]

#up BCCB
s = time()
#zi_up = np.ones_like(zi)*-300
BTTB_up = fc.bttb(xi,yi,zi_up,zj)
cev_up = fc.bccb(shape,N,BTTB_up)
gzp_bccb_up = fc.fast_forward_bccb(shape,N,rho_c,cev_up)
e = time()
tcpu = e - s
print tcpu, 'seconds'

s = time()
A = fc.sensibility_matrix(xi,yi,zi_up,zj,N)
gzp_up = A.dot(rho)
e = time()
tcpu = e - s
print tcpu, 'seconds'


#down BCCB
s = time()
#zi_down = np.ones_like(zi)*-50
BTTB_down = fc.bttb(xi,yi,zi_down,zj)
cev_down = fc.bccb(shape,N,BTTB_down)
gzp_bccb_down = fc.fast_forward_bccb(shape,N,rho_c,cev_down)
e = time()
tcpu = e - s
print tcpu, 'seconds'

s = time()
A = fc.sensibility_matrix(xi,yi,zi_down,zj,N)
gzp_down = A.dot(rho)
e = time()
tcpu = e - s
print tcpu, 'seconds'

0.00499701499939 seconds
8.85737490654 seconds
0.00388503074646 seconds
8.63595795631 seconds

Upward plot¶

In [7]:

delta_gz_bccb_up = dobs_up-gzp_bccb_up
delta_gz_up = dobs_up-gzp_up

In [8]:

#Projection_model
phi = np.linspace(0, 2.*np.pi, 36)  #36 points
x = xc + R*np.cos(phi)
y = yc + R*np.sin(phi)

x_p = [-3000., -3500, 0, 500, -3000.]
y_p = [-500., 0, 4500, 4000, -500.]

x_p2 = [-3000, -2500, 3500, 3000, -3000.]
y_p2 = [4000, 4500, 0, -500, 4000]

plt.figure(figsize=(6,16)) plt.subplot(311) plt.title('(a)', y=0.91, x=-0.13, fontsize=14) plt.tricontourf(yi,xi,dobs_up,22,cmap='jet', vmin=synthetic_gz['gz_min'],vmax=synthetic_gz['gz_max']) plt.plot(x_p,y_p,color="k", linewidth=3) plt.plot(x_p2,y_p2,color="k", linewidth=3) plt.plot(y, x, color="k", linewidth=3) cb = plt.colorbar(shrink=1) #plt.axis('scaled') cb.set_label('$Gz$ ( $mGal$ )', rotation=90, fontsize=14) plt.xlim(np.min(yi),np.max(yi)) plt.ylim(np.min(xi),np.max(xi)) plt.xticks(fontsize=14) plt.yticks(fontsize=14) #plt.xlabel('Easting coordinate y (km)', fontsize=14) plt.ylabel('Northing coordinate x (m)', fontsize=14) mpl.m2km() #delta_gz_up = dobs_up-gzp_up plt.subplot(312) plt.title('(b)', y=0.91, x=-0.13, fontsize=14) plt.tricontourf(yi,xi,delta_gz_up,22,cmap='jet') plt.plot(x_p,y_p,color="k", linewidth=3) plt.plot(x_p2,y_p2,color="k", linewidth=3) plt.plot(y, x, color="k", linewidth=3) cb = plt.colorbar(shrink=1) #plt.axis('scaled') cb.set_label('$Gz$ ( $mGal$ )', rotation=90, fontsize=14) plt.xlim(np.min(yi),np.max(yi)) plt.ylim(np.min(xi),np.max(xi)) plt.xticks(fontsize=14) plt.yticks(fontsize=14) #plt.xlabel('Easting coordinate y (km)', fontsize=14) plt.ylabel('Northing coordinate x (m)', fontsize=14) mpl.m2km() #delta_gz_bccb_up = dobs_up-gzp_bccb_up plt.subplot(313) plt.title('(c)', y=0.91, x=-0.13, fontsize=14) plt.tricontourf(yi,xi,delta_gz_bccb_up,22,cmap='jet') plt.plot(x_p,y_p,color="k", linewidth=3) plt.plot(x_p2,y_p2,color="k", linewidth=3) plt.plot(y, x, color="k", linewidth=3) cb = plt.colorbar(shrink=1) #plt.axis('scaled') cb.set_label('$Gz$ ( $mGal$ )', rotation=90, fontsize=14) plt.xlim(np.min(yi),np.max(yi)) plt.ylim(np.min(xi),np.max(xi)) plt.xticks(fontsize=14) plt.yticks(fontsize=14) plt.xlabel('Easting coordinate y (km)', fontsize=14) plt.ylabel('Northing coordinate x (m)', fontsize=14) mpl.m2km() plt.tight_layout(True) #plt.savefig('../manuscript/Fig/upward_med.png', dpi=300)

In [9]:

mean = np.mean(delta_gz_up)
print mean
std = np.std(delta_gz_up)
print std
mean = np.mean(delta_gz_bccb_up)
print mean
std = np.std(delta_gz_bccb_up)
print std

0.0031299438371729044
0.03444145923923826
0.0031299438371728884
0.03444145923923814

Downward plot¶

In [10]:

delta_gz_down = dobs_down-gzp_down
delta_gz_bccb_down = dobs_down-gzp_bccb_down

plt.figure(figsize=(6,16)) plt.subplot(311) plt.title('(a)', y=0.91, x=-0.13, fontsize=14) plt.tricontourf(yi,xi,dobs_down,22,cmap='jet', vmin=synthetic_gz['gz_min'],vmax=synthetic_gz['gz_max']) plt.plot(x_p,y_p,color="k", linewidth=3) plt.plot(x_p2,y_p2,color="k", linewidth=3) plt.plot(y, x, color="k", linewidth=3) cb = plt.colorbar(shrink=1) #plt.axis('scaled') cb.set_label('$Gz$ ( $mGal$ )', rotation=90, fontsize=14) plt.xlim(np.min(yi),np.max(yi)) plt.ylim(np.min(xi),np.max(xi)) plt.xticks(fontsize=14) plt.yticks(fontsize=14) #plt.xlabel('Easting coordinate y (km)', fontsize=14) plt.ylabel('Northing coordinate x (m)', fontsize=14) mpl.m2km() #delta_gz_down = dobs_down-gzp_down plt.subplot(312) plt.title('(b)', y=0.91, x=-0.13, fontsize=14) plt.tricontourf(yi,xi,delta_gz_down,22,cmap='jet') plt.plot(x_p,y_p,color="k", linewidth=3) plt.plot(x_p2,y_p2,color="k", linewidth=3) plt.plot(y, x, color="k", linewidth=3) cb = plt.colorbar(shrink=1) #plt.axis('scaled') cb.set_label('$Gz$ ( $mGal$ )', rotation=90, fontsize=14) plt.xlim(np.min(yi),np.max(yi)) plt.ylim(np.min(xi),np.max(xi)) plt.xticks(fontsize=14) plt.yticks(fontsize=14) #plt.xlabel('Easting coordinate y (km)', fontsize=14) plt.ylabel('Northing coordinate x (m)', fontsize=14) mpl.m2km() #delta_gz_bccb_down = dobs_down-gzp_bccb_down plt.subplot(313) plt.title('(c)', y=0.91, x=-0.13, fontsize=14) plt.tricontourf(yi,xi,delta_gz_bccb_down,22,cmap='jet') plt.plot(x_p,y_p,color="k", linewidth=3) plt.plot(x_p2,y_p2,color="k", linewidth=3) plt.plot(y, x, color="k", linewidth=3) cb = plt.colorbar(shrink=1) #plt.axis('scaled') cb.set_label('$Gz$ ( $mGal$ )', rotation=90, fontsize=14) plt.xlim(np.min(yi),np.max(yi)) plt.ylim(np.min(xi),np.max(xi)) plt.xticks(fontsize=14) plt.yticks(fontsize=14) plt.xlabel('Easting coordinate y (km)', fontsize=14) plt.ylabel('Northing coordinate x (m)', fontsize=14) mpl.m2km() plt.tight_layout(True) #plt.savefig('../manuscript/Fig/downward_med.png', dpi=300)

In [11]:

mean = np.mean(delta_gz_down)
print mean
std = np.std(delta_gz_down)
print std
mean = np.mean(delta_gz_bccb_down)
print mean
std = np.std(delta_gz_bccb_down)
print std

-0.001007217244496282
0.03831202233877217
-0.0010072172444962715
0.038312022338772185

Comparison Upward - BCCB vs. Fast vs. Fourier¶

In [12]:

# Up Fourier
gzp_fourier_up = fc_c.upcontinue(xi, yi, dobs, shape, 200)

In [13]:

# define the scale for residuals
delta_gz_fourier_up = dobs_up-np.ravel(gzp_fourier_up)
scale_max = np.max([delta_gz_bccb_up, delta_gz_up, delta_gz_fourier_up])
scale_min = np.min([delta_gz_bccb_up, delta_gz_up, delta_gz_fourier_up])

print scale_min, scale_max

-1.9005183543218769 1.9026002023084692

In [14]:

colorbar_ranges = np.linspace(-2, 2, 21)

In [15]:

colorbar_ranges

Out[15]:

array([-2. , -1.8, -1.6, -1.4, -1.2, -1. , -0.8, -0.6, -0.4, -0.2,  0. ,
        0.2,  0.4,  0.6,  0.8,  1. ,  1.2,  1.4,  1.6,  1.8,  2. ])

In [16]:

font_title = 8
font_ticks = 5
font_labels = 6


height=9.
width = 10.
height_per_width = height/width
#plt.figure(figsize=(10,9))
plt.figure(figsize=(4.33,4.33*height_per_width))

plt.subplot(221)
plt.title('(a)', y=0.95, x=-0.18, fontsize=font_title)
# plt.tricontourf(yi,xi,dobs_up,22,cmap='jet',
#                 vmin=synthetic_gz['gz_min'],vmax=synthetic_gz['gz_max'])
plt.contourf(yi.reshape(shape),xi.reshape(shape),dobs_up.reshape(shape),
             22,cmap='jet',vmin=synthetic_gz['gz_min'],vmax=synthetic_gz['gz_max'])
plt.plot(x_p,y_p,color="k", linewidth=1)
plt.plot(x_p2,y_p2,color="k", linewidth=1)
plt.plot(y, x, color="k", linewidth=1)
cb = plt.colorbar(shrink=1)
#plt.axis('scaled')
cb.set_label('Gravity data (mGal)', rotation=90, fontsize=font_labels)
cb.ax.tick_params(labelsize=font_ticks)

plt.xlim(np.min(yi),np.max(yi))
plt.ylim(np.min(xi),np.max(xi))
plt.xticks(fontsize=font_ticks)
plt.yticks(fontsize=font_ticks)
#plt.xlabel('Easting coordinate y (km)', fontsize=14)
plt.ylabel('Northing coordinate x (m)', fontsize=font_labels)
mpl.m2km()

plt.subplot(222)
plt.title('(b)', y=0.95, x=-0.18, fontsize=font_title)
#plt.tricontourf(yi,xi,delta_gz_bccb_up,22,cmap='jet', vmin = scale_min, vmax = scale_max)
plt.contourf(yi.reshape(shape),xi.reshape(shape),delta_gz_bccb_up.reshape(shape),
             22,cmap='jet',vmin=scale_min,vmax=scale_max)
plt.plot(x_p,y_p,color="k", linewidth=1)
plt.plot(x_p2,y_p2,color="k", linewidth=1)
plt.plot(y, x, color="k", linewidth=1)

#define colorbar
cbar = plt.cm.ScalarMappable(cmap=cm.jet)
cbar.set_array(delta_gz_bccb_up)
cbar.set_clim(scale_min, scale_max)
cb = plt.colorbar(cbar, shrink=1, boundaries=colorbar_ranges)
cb.set_label('Residuals (mGal)', rotation=90, fontsize=font_labels)
cb.ax.tick_params(labelsize=font_ticks)

plt.xlim(np.min(yi),np.max(yi))
plt.ylim(np.min(xi),np.max(xi))
plt.xticks(fontsize=font_ticks)
plt.yticks(fontsize=font_ticks)
#plt.xlabel('Easting coordinate y (km)', fontsize=14)
#plt.ylabel('Northing coordinate x (m)', fontsize=14)
mpl.m2km()

plt.subplot(223)
plt.title('(c)', y=0.95, x=-0.18, fontsize=font_title)
#plt.tricontourf(yi,xi,delta_gz_up,22,cmap='jet', vmin = scale_min, vmax = scale_max)
plt.contourf(yi.reshape(shape),xi.reshape(shape),delta_gz_up.reshape(shape),
             22,cmap='jet',vmin=scale_min,vmax=scale_max)
plt.plot(x_p,y_p,color="k", linewidth=1)
plt.plot(x_p2,y_p2,color="k", linewidth=1)
plt.plot(y, x, color="k", linewidth=1)

#define colorbar
cbar = plt.cm.ScalarMappable(cmap=cm.jet)
cbar.set_array(delta_gz_up)
cbar.set_clim(scale_min, scale_max)
cb = plt.colorbar(cbar, shrink=1, boundaries=colorbar_ranges)
cb.set_label('Residuals (mGal)', rotation=90, fontsize=font_labels)
cb.ax.tick_params(labelsize=font_ticks)

plt.xlim(np.min(yi),np.max(yi))
plt.ylim(np.min(xi),np.max(xi))
plt.xticks(fontsize=font_ticks)
plt.yticks(fontsize=font_ticks)
plt.xlabel('Easting coordinate y (km)', fontsize=font_labels)
plt.ylabel('Northing coordinate x (m)', fontsize=font_labels)
mpl.m2km()

plt.subplot(224)
plt.title('(d)', y=0.95, x=-0.18, fontsize=font_title)
#plt.tricontourf(yi,xi,delta_gz_fourier_up,22,cmap='jet', vmin = scale_min, vmax = scale_max)
plt.contourf(yi.reshape(shape),xi.reshape(shape),delta_gz_fourier_up.reshape(shape),
             22,cmap='jet',vmin=scale_min,vmax=scale_max)
plt.plot(x_p,y_p,color="k", linewidth=1)
plt.plot(x_p2,y_p2,color="k", linewidth=1)
plt.plot(y, x, color="k", linewidth=1)

#define colorbar
cbar = plt.cm.ScalarMappable(cmap=cm.jet)
cbar.set_array(delta_gz_fourier_up)
cbar.set_clim(scale_min, scale_max)
cb = plt.colorbar(cbar, shrink=1, boundaries=colorbar_ranges)
cb.set_label('Residuals (mGal)', rotation=90, fontsize=font_labels)
cb.ax.tick_params(labelsize=font_ticks)

plt.xlim(np.min(yi),np.max(yi))
plt.ylim(np.min(xi),np.max(xi))
plt.xticks(fontsize=font_ticks)
plt.yticks(fontsize=font_ticks)
plt.xlabel('Easting coordinate y (km)', fontsize=font_labels)
#plt.ylabel('Northing coordinate x (m)', fontsize=4)
mpl.m2km()

plt.tight_layout(True)
#plt.savefig('../manuscript/Fig/upward_fourier_med.png', dpi=300)
plt.savefig('../manuscript/Fig/Figure7.png', dpi=1200)

In [17]:

print np.std(delta_gz_bccb_up)
print np.std(delta_gz_up)
print np.mean(delta_gz_fourier_up)
print np.std(delta_gz_fourier_up)

0.03444145923923814
0.03444145923923826
-0.029923731936085017
0.26232817198362085

Comparison Downward - BCCB vs. Fast vs. Fourier¶

In [18]:

gzp_fourier_down = fc_c.upcontinue(xi, yi, dobs, shape, -50)

fourier_continuation.py:57: UserWarning: Using 'height' <= 0 means downward continuation, which is known to be unstable.
  "which is known to be unstable.")

In [19]:

# define the scale for residuals
delta_gz_fourier_down = dobs_down-np.ravel(gzp_fourier_down)
scale_max = np.max([delta_gz_bccb_down, delta_gz_down, delta_gz_fourier_down])
scale_min = np.min([delta_gz_bccb_down, delta_gz_down, delta_gz_fourier_down])

print scale_min, scale_max

-4.117539688908588 4.121771949535535

In [20]:

colorbar_ranges = np.arange(-4.4, 4.41, 0.4)

In [21]:

colorbar_ranges

Out[21]:

array([-4.40000000e+00, -4.00000000e+00, -3.60000000e+00, -3.20000000e+00,
       -2.80000000e+00, -2.40000000e+00, -2.00000000e+00, -1.60000000e+00,
       -1.20000000e+00, -8.00000000e-01, -4.00000000e-01,  3.55271368e-15,
        4.00000000e-01,  8.00000000e-01,  1.20000000e+00,  1.60000000e+00,
        2.00000000e+00,  2.40000000e+00,  2.80000000e+00,  3.20000000e+00,
        3.60000000e+00,  4.00000000e+00,  4.40000000e+00])

In [24]:

font_title = 8
font_ticks = 5
font_labels = 6

height=9.
width = 10.
height_per_width = height/width
#plt.figure(figsize=(10,9))
plt.figure(figsize=(4.33,4.33*height_per_width))

plt.subplot(221)
plt.title('(a)', y=0.95, x=-0.18, fontsize=font_title)
#plt.tricontourf(yi,xi,dobs_down,22,cmap='jet',
#                vmin=synthetic_gz['gz_min'],vmax=synthetic_gz['gz_max'])
plt.contourf(yi.reshape(shape),xi.reshape(shape),dobs_down.reshape(shape),
             22,cmap='jet',vmin=synthetic_gz['gz_min'],vmax=synthetic_gz['gz_max'])
plt.plot(x_p,y_p,color="k", linewidth=1)
plt.plot(x_p2,y_p2,color="k", linewidth=1)
plt.plot(y, x, color="k", linewidth=1)
cb = plt.colorbar(shrink=1)
#plt.axis('scaled')
cb.set_label('Gravity data (mGal)', rotation=90, fontsize=font_labels)
cb.ax.tick_params(labelsize=font_ticks)

plt.xlim(np.min(yi),np.max(yi))
plt.ylim(np.min(xi),np.max(xi))
plt.xticks(fontsize=font_ticks)
plt.yticks(fontsize=font_ticks)
#plt.xlabel('Easting coordinate y (km)', fontsize=14)
plt.ylabel('Northing coordinate x (m)', fontsize=font_labels)
mpl.m2km()

plt.subplot(222)
plt.title('(b)', y=0.95, x=-0.18, fontsize=font_title)
#plt.tricontourf(yi,xi,delta_gz_bccb_down,22,cmap='jet', vmin = scale_min, vmax = scale_max)
plt.contourf(yi.reshape(shape),xi.reshape(shape),delta_gz_bccb_down.reshape(shape),
             22,cmap='jet',vmin=scale_min,vmax=scale_max)
plt.plot(x_p,y_p,color="k", linewidth=1)
plt.plot(x_p2,y_p2,color="k", linewidth=1)
plt.plot(y, x, color="k", linewidth=1)

#define colorbar
cbar = plt.cm.ScalarMappable(cmap=cm.jet)
cbar.set_array(delta_gz_bccb_down)
cbar.set_clim(scale_min, scale_max)
cb = plt.colorbar(cbar, shrink=1, boundaries=colorbar_ranges)
cb.set_label('Residuals (mGal)', rotation=90, fontsize=font_labels)
cb.ax.tick_params(labelsize=font_ticks)

plt.xlim(np.min(yi),np.max(yi))
plt.ylim(np.min(xi),np.max(xi))
plt.xticks(fontsize=font_ticks)
plt.yticks(fontsize=font_ticks)
#plt.xlabel('Easting coordinate y (km)', fontsize=14)
#plt.ylabel('Northing coordinate x (m)', fontsize=14)
mpl.m2km()

plt.subplot(223)
plt.title('(c)', y=0.95, x=-0.18, fontsize=font_title)
#plt.tricontourf(yi,xi,delta_gz_down,22,cmap='jet', vmin = scale_min, vmax = scale_max)
plt.contourf(yi.reshape(shape),xi.reshape(shape),delta_gz_down.reshape(shape),
             22,cmap='jet',vmin=scale_min,vmax=scale_max)
plt.plot(x_p,y_p,color="k", linewidth=1)
plt.plot(x_p2,y_p2,color="k", linewidth=1)
plt.plot(y, x, color="k", linewidth=1)

#define colorbar
cbar = plt.cm.ScalarMappable(cmap=cm.jet)
cbar.set_array(delta_gz_down)
cbar.set_clim(scale_min, scale_max)
cb = plt.colorbar(cbar, shrink=1, boundaries=colorbar_ranges)
cb.set_label('Residuals (mGal)', rotation=90, fontsize=font_labels)
cb.ax.tick_params(labelsize=font_ticks)

plt.xlim(np.min(yi),np.max(yi))
plt.ylim(np.min(xi),np.max(xi))
plt.xticks(fontsize=font_ticks)
plt.yticks(fontsize=font_ticks)
plt.xlabel('Easting coordinate y (km)', fontsize=font_labels)
plt.ylabel('Northing coordinate x (m)', fontsize=font_labels)
mpl.m2km()

plt.subplot(224)
plt.title('(d)', y=0.95, x=-0.18, fontsize=font_title)
#plt.tricontourf(yi,xi,delta_gz_fourier_down,22,cmap='jet', vmin = scale_min, vmax = scale_max)
plt.contourf(yi.reshape(shape),xi.reshape(shape),delta_gz_fourier_down.reshape(shape),
             22,cmap='jet',vmin=scale_min,vmax=scale_max)
plt.plot(x_p,y_p,color="k", linewidth=1)
plt.plot(x_p2,y_p2,color="k", linewidth=1)
plt.plot(y, x, color="k", linewidth=1)

#define colorbar
cbar = plt.cm.ScalarMappable(cmap=cm.jet)
cbar.set_array(delta_gz_fourier_down)
cbar.set_clim(scale_min, scale_max)
cb = plt.colorbar(cbar, shrink=1, boundaries=colorbar_ranges)
cb.set_label('Residuals (mGal)', rotation=90, fontsize=font_labels)
cb.ax.tick_params(labelsize=font_ticks)

plt.xlim(np.min(yi),np.max(yi))
plt.ylim(np.min(xi),np.max(xi))
plt.xticks(fontsize=font_ticks)
plt.yticks(fontsize=font_ticks)
plt.xlabel('Easting coordinate y (km)', fontsize=font_labels)
#plt.ylabel('Northing coordinate x (m)', fontsize=14)
mpl.m2km()

plt.tight_layout(True)
#plt.savefig('../manuscript/Fig/downward_fourier_med.png', dpi=300)
plt.savefig('../manuscript/Fig/Figure8.png', dpi=1200)

In [25]:

print np.std(delta_gz_bccb_down)
print np.std(delta_gz_down)
print np.mean(delta_gz_fourier_down)
print np.std(delta_gz_fourier_down)

0.038312022338772185
0.03831202233877217
0.007934556980489862
0.5816240951130157

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