def calculate_znb(z_object=None, z_array=None, periods=None):
"""
Determine an array of Z_nb (depth dependent Niblett-Bostick transformed Z)
from the 1D and 2D parts of an impedance tensor array Z.
input:
- Z (object or array)
- periods (mandatory, if Z is just array)
output:
- Z_nb
The calculation of the Z_nb needs 6 steps:
1) Determine the dimensionality of the Z(T), discard all 3D parts
2) Rotate all Z(T) to TE/TM setup (T_parallel/T_ortho)
3) Transform every component individually by Niblett-Bostick
4) collect the respective 2 components each for equal/similar depths
5) interprete them as TE_nb/TM_nb
6) set up Z_nb(depth)
If 1D layers occur inbetween 2D layers, the strike angle is undefined therein.
We take an - arbitrarily chosen - linear interpolation of strike angle for
these layers, with the values varying between the angles of the bounding
upper and lower 2D layers (linearly w.r.t. the periods).
Use the output for instance for the determination of
NB-transformed phase tensors.
Note:
No propagation of errors implemented yet!
"""
#deal with inputs
#if zobject:
#z = z_object.z
#periods = 1./z_object.freq
#else:
z = z_array
periods = periods
dimensions = MTge.dimensionality(z)
angles = MTge.strike_angle(z)
#reduce actual Z by the 3D layers:
z2 = z[np.where(dimensions != 3)[0]]
angles2 = angles[np.where(dimensions != 3)[0]]
periods2 = periods[np.where(dimensions != 3)[0]]
angles_incl1D = interpolate_strike_angles(angles2[:, 0], periods2)
z3 = MTz.rotate_z(z2, -angles_incl1D)[0]
#at this point we assume that the two modes are the off-diagonal elements!!
#TE is element (1,2), TM at (2,1)
lo_nb_max = []
lo_nb_min = []
app_res = MTz.z2resphi(z3, periods2)[0]
phase = MTz.z2resphi(z3, periods2)[1]
for i, per in enumerate(periods):
te_rho, te_depth = rhophi2rhodepth(app_res[i][0, 1], phase[i][0, 1],
per)
tm_rho, tm_depth = rhophi2rhodepth(app_res[i][1, 0], phase[i][1, 0],
per)
if te_rho > tm_rho:
lo_nb_max.append([te_depth, te_rho])
lo_nb_min.append([tm_depth, tm_rho])
else:
lo_nb_min.append([te_depth, te_rho])
lo_nb_max.append([tm_depth, tm_rho])
return np.array(lo_nb_max), np.array(lo_nb_min)
def calculate_rho_minmax(z_object=None, z_array=None, periods=None):
"""
Determine 2 arrays of Niblett-Bostick transformed aparent resistivities:
minumum and maximum values for respective periods.
Values are calculated from the 1D and 2D parts of an impedance tensor array Z.
input:
- Z (object or array)
- periods (mandatory, if Z is just array)
output:
- n x 3 array, depth/rho_nb/angle for rho_nb max
- n x 3 array, depth/rho_nb/angle for rho_nb min
The calculation is carried out by :
1) Determine the dimensionality of the Z(T), discard all 3D parts
2) loop over periods
* rotate Z and calculate app_res_NB for off-diagonal elements
* find maximum and minimum values
* write out respective depths and rho values
Note:
No propagation of errors implemented yet!
"""
#deal with inputs
#if zobject:
#z = z_object.z
#periods = 1./z_object.freq
#else:
z = z_array
periods = periods
dimensions = MTge.dimensionality(z)
angles = MTge.strike_angle(z)
#reduce actual Z by the 3D layers:
z2 = z[np.where(dimensions != 3)[0]]
angles2 = angles[np.where(dimensions != 3)[0]]
periods2 = periods[np.where(dimensions != 3)[0]]
lo_nb_max = []
lo_nb_min = []
rotsteps = 360
rotangles = np.arange(rotsteps) * 180. / rotsteps
for i, per in enumerate(periods2):
z_curr = z2[i]
temp_vals = np.zeros((rotsteps, 4))
for j, d in enumerate(rotangles):
new_z = MTcc.rotatematrix_incl_errors(z_curr, d)[0]
#print i,per,j,d
res = MTz.z2resphi(new_z, per)[0]
phs = MTz.z2resphi(new_z, per)[1]
te_rho, te_depth = rhophi2rhodepth(res[0, 1], phs[0, 1], per)
tm_rho, tm_depth = rhophi2rhodepth(res[1, 0], phs[1, 0], per)
temp_vals[j, 0] = te_depth
temp_vals[j, 1] = te_rho
temp_vals[j, 2] = tm_depth
temp_vals[j, 3] = tm_rho
column = (np.argmax([np.max(temp_vals[:, 1]),
np.max(temp_vals[:, 3])])) * 2 + 1
maxidx = np.argmax(temp_vals[:, column])
max_rho = temp_vals[maxidx, column]
max_depth = temp_vals[maxidx, column - 1]
max_ang = rotangles[maxidx]
#alternative 1
min_column = (np.argmin(
[np.max(temp_vals[:, 1]),
np.max(temp_vals[:, 3])])) * 2 + 1
if max_ang <= 90:
min_ang = max_ang + 90
else:
min_ang = max_ang - 90
minidx = np.argmin(np.abs(rotangles - min_ang))
min_rho = temp_vals[minidx, min_column]
min_depth = temp_vals[minidx, min_column - 1]
lo_nb_max.append([max_depth, max_rho, max_ang])
lo_nb_min.append([min_depth, min_rho])
return np.array(lo_nb_max), np.array(lo_nb_min)
def calculate_rho_minmax(z_object = None, z_array = None, periods = None):
"""
Determine 2 arrays of Niblett-Bostick transformed aparent resistivities:
minumum and maximum values for respective periods.
Values are calculated from the 1D and 2D parts of an impedance tensor array Z.
input:
- Z (object or array)
- periods (mandatory, if Z is just array)
output:
- n x 3 array, depth/rho_nb/angle for rho_nb max
- n x 3 array, depth/rho_nb/angle for rho_nb min
The calculation is carried out by :
1) Determine the dimensionality of the Z(T), discard all 3D parts
2) loop over periods
* rotate Z and calculate app_res_NB for off-diagonal elements
* find maximum and minimum values
* write out respective depths and rho values
Note:
No propagation of errors implemented yet!
"""
#deal with inputs
#if zobject:
#z = z_object.z
#periods = 1./z_object.freq
#else:
z = z_array
periods = periods
dimensions = MTge.dimensionality(z)
angles = MTge.strike_angle(z)
#reduce actual Z by the 3D layers:
z2 = z[np.where(dimensions != 3)[0]]
angles2 = angles[np.where(dimensions != 3)[0]]
periods2 = periods[np.where(dimensions != 3)[0]]
lo_nb_max = []
lo_nb_min = []
rotsteps = 360
rotangles = np.arange(rotsteps)*180./rotsteps
for i,per in enumerate(periods2):
z_curr = z2[i]
temp_vals = np.zeros((rotsteps,4))
for jj,d in enumerate(rotangles):
new_z = MTcc.rotatematrix_incl_errors(z_curr, d)[0]
#print i,per,jj,d
res = MTz.z2resphi(new_z,per)[0]
phs = MTz.z2resphi(new_z,per)[1]
te_rho, te_depth = rhophi2rhodepth(res[0,1], phs[0,1], per)
tm_rho, tm_depth = rhophi2rhodepth(res[1,0], phs[1,0], per)
temp_vals[jj,0] = te_depth
temp_vals[jj,1] = te_rho
temp_vals[jj,2] = tm_depth
temp_vals[jj,3] = tm_rho
column = (np.argmax([ np.max(temp_vals[:,1]),
np.max(temp_vals[:,3])]))*2 + 1
maxidx = np.argmax(temp_vals[:,column])
max_rho = temp_vals[maxidx,column]
max_depth = temp_vals[maxidx,column-1]
max_ang = rotangles[maxidx]
#alternative 1
min_column = (np.argmin([ np.max(temp_vals[:,1]),
np.max(temp_vals[:,3])]))*2 + 1
if max_ang <= 90:
min_ang = max_ang + 90
else:
min_ang = max_ang - 90
minidx = np.argmin(np.abs(rotangles-min_ang))
min_rho = temp_vals[minidx,min_column]
min_depth = temp_vals[minidx,min_column-1]
lo_nb_max.append([max_depth, max_rho, max_ang])
lo_nb_min.append([min_depth, min_rho])
return np.array(lo_nb_max), np.array(lo_nb_min)
def calculate_znb(z_object = None, z_array = None, periods = None): """ Determine an array of Z_nb (depth dependent Niblett-Bostick transformed Z) from the 1D and 2D parts of an impedance tensor array Z. input: - Z (object or array) - periods (mandatory, if Z is just array) output: - Z_nb The calculation of the Z_nb needs 6 steps: 1) Determine the dimensionality of the Z(T), discard all 3D parts 2) Rotate all Z(T) to TE/TM setup (T_parallel/T_ortho) 3) Transform every component individually by Niblett-Bostick 4) collect the respective 2 components each for equal/similar depths 5) interprete them as TE_nb/TM_nb 6) set up Z_nb(depth) If 1D layers occur inbetween 2D layers, the strike angle is undefined therein. We take an - arbitrarily chosen - linear interpolation of strike angle for these layers, with the values varying between the angles of the bounding upper and lower 2D layers (linearly w.r.t. the periods). Use the output for instance for the determination of NB-transformed phase tensors. Note: No propagation of errors implemented yet! """ #deal with inputs #if zobject: #z = z_object.z #periods = 1./z_object.freq #else: z = z_array periods = periods dimensions = MTge.dimensionality(z) angles = MTge.strike_angle(z) #reduce actual Z by the 3D layers: z2 = z[np.where(dimensions != 3)[0]] angles2 = angles[np.where(dimensions != 3)[0]] periods2 = periods[np.where(dimensions != 3)[0]] angles_incl1D = interpolate_strike_angles(angles2[:,0],periods2) z3 = MTz.rotate_z(z2,-angles_incl1D)[0] #at this point we assume that the two modes are the off-diagonal elements!! #TE is element (1,2), TM at (2,1) lo_nb_max = [] lo_nb_min = [] app_res = MTz.z2resphi(z3,periods2)[0] phase = MTz.z2resphi(z3,periods2)[1] for i,per in enumerate(periods): te_rho, te_depth = rhophi2rhodepth(app_res[i][0,1], phase[i][0,1], per) tm_rho, tm_depth = rhophi2rhodepth(app_res[i][1,0], phase[i][1,0], per) if te_rho > tm_rho: lo_nb_max.append([te_depth, te_rho]) lo_nb_min.append([tm_depth, tm_rho]) else: lo_nb_min.append([te_depth, te_rho]) lo_nb_max.append([tm_depth, tm_rho]) return np.array(lo_nb_max), np.array(lo_nb_min)
def calculate_depth_nb(z_object = None, z_array = None, periods = None):
"""
Determine an array of Z_nb (depth dependent Niblett-Bostick transformed Z)
from the 1D and 2D parts of an impedance tensor array Z.
The calculation of the Z_nb needs 6 steps:
1) Determine the dimensionality of the Z(T), discard all 3D parts
2) Rotate all Z(T) to TE/TM setup (T_parallel/T_ortho)
3) Transform every component individually by Niblett-Bostick
4) collect the respective 2 components each for equal/similar depths
5) interprete them as TE_nb/TM_nb
6) set up Z_nb(depth)
If 1D layers occur inbetween 2D layers, the strike angle is undefined therein.
We take an - arbitrarily chosen - linear interpolation of strike angle for
these layers, with the values varying between the angles of the bounding
upper and lower 2D layers (linearly w.r.t. the periods).
Use the output for instance for the determination of
NB-transformed phase tensors.
Note:
No propagation of errors implemented yet!
Arguments
-------------
*z_object* : mtpy.core.z object
*z_array* : np.ndarray [num_periods, 2, 2]
*periods* : np.ndarray(num_periods)
only input if input z_array, otherwise periods are extracted
from z_object.freq
Returns
------------------
*depth_array* : np.ndarray(num_periods,
dtype=['period', 'depth_min', 'depth_max',
'rho_min', 'rho_max'])
numpy structured array with keywords.
- period --> period in s
- depth_min --> minimum depth estimated (m)
- depth_max --> maximum depth estimated (m)
- rho_min --> minimum resistivity estimated (Ohm-m)
- rho_max --> maximum resistivity estimated (Ohm-m)
Example
------------
>>> import mtpy.analysis.niblettbostick as nb
>>> depth_array = nb.calculate_znb(z_object=z1)
>>> # plot the results
>>> import matplotlib.pyplot as plt
>>> fig = plt.figure()
>>> ax = fig.add_subplot(1,1,1)
>>> ax.semilogy(depth_array['depth_min'], depth_array['period'])
>>> ax.semilogy(depth_array['depth_max'], depth_array['period'])
>>> plt.show()
"""
#deal with inputs
if z_object is not None:
z = z_object.z
periods = 1./z_object.freq
else:
z = z_array
periods = periods
dimensions = MTge.dimensionality(z_array=z)
angles = MTge.strike_angle(z_array=z)
#reduce actual Z by the 3D layers:
# z_2d = z[np.where(dimensions != 3)[0]]
angles_2d = np.nan_to_num(angles[np.where(dimensions != 3)][:, 0])
periods_2d = periods[np.where(dimensions != 3)]
# interperpolate strike angle onto all periods
# make a function for strike using only 2d angles
strike_interp = spi.interp1d(periods_2d, angles_2d,
bounds_error=False,
fill_value=0)
strike_angles = strike_interp(periods)
# rotate z to be along the interpolated strike angles
z_rot = MTz.rotate_z(z, strike_angles)[0]
# angles_incl1D = interpolate_strike_angles(angles_2d, periods_2d)
# z3 = MTz.rotate_z(z_2d, -angles_incl1D)[0]
#at this point we assume that the two modes are the off-diagonal elements!!
#TE is element (1,2), TM at (2,1)
# lo_nb_max = []
# lo_nb_min = []
depth_array = np.zeros(periods.shape[0],
dtype=[('period', np.float),
('depth_min', np.float),
('depth_max', np.float),
('rho_min', np.float),
('rho_max', np.float)])
# app_res, app_res_err, phase, phase_err = MTz.z2resphi(z3, periods_2d)
app_res, app_res_err, phase, phase_err = MTz.z2resphi(z_rot, periods)
for ii, per in enumerate(periods):
te_rho, te_depth = rhophi2rhodepth(app_res[ii, 0, 1],
phase[ii, 0, 1],
per)
tm_rho, tm_depth = rhophi2rhodepth(app_res[ii, 1, 0],
phase[ii, 1, 0],
per)
depth_array[ii]['period'] = per
depth_array[ii]['depth_min'] = min([te_depth, tm_depth])
depth_array[ii]['depth_max'] = max([te_depth, tm_depth])
depth_array[ii]['rho_min'] = min([te_rho, tm_rho])
depth_array[ii]['rho_max'] = max([te_rho, tm_rho])
return depth_array