import numpy as np
from scipy.constants import mu_0
from scipy.interpolate import interp1d
from scipy.constants import pi
from SimPEG import Utils
[docs]def EvalDigitalFilt(base, weight, fun, r):
"""
Evaluating Digital filtering based on given base and weight
"""
return np.dot(fun(base/r), weight)/r
[docs]def setFrequency(time):
wt = np.array([7.214369775966785e-20, 5.997984537445829e-20, 1.383536819510307e-20, 6.127201193993877e-20, 2.735622069700930e-20, 6.567948836420383e-20, 4.144963335850363e-20, 7.316414067200350e-20, 5.682375914662966e-20, 8.391977074915078e-20, 7.418756524583309e-20, 9.829637687190485e-20, 9.430643800653847e-20, 1.168146262188112e-19, 1.180370735968097e-19, 1.401723019040171e-19, 1.463726071463266e-19, 1.692722072070252e-19, 1.804796158499069e-19, 2.052560499147526e-19, 2.217507732438609e-19, 2.495469564846162e-19, 2.718603842873614e-19, 3.039069705922034e-19, 3.328334008394297e-19, 3.705052796297763e-19, 4.071277819975917e-19, 4.520053409594589e-19, 4.977334107366132e-19, 5.516707191291291e-19, 6.082931168675559e-19, 6.734956703766505e-19, 7.432489554623685e-19, 8.223651399147256e-19, 9.080210233648037e-19, 1.004250388267800e-18, 1.109225156214032e-18, 1.226448534750949e-18, 1.354938655056596e-18, 1.497875155579711e-18, 1.655024636692164e-18, 1.829422009902478e-18, 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ab = 0.7866057737580476e0
#------- Compute Frequency components reqired for transform -------#
# This is for Digital filtering and here we evalute frequency domain responses
# ritght at this bases.
# a. Generate time basedse
n = np.ceil(-10*np.log(time.min()/time.max()))
tbase = time.max()*np.exp(-0.1*np.arange(0, n+1))
# b. Determine required frequencies
omega_int = (ab/tbase[0])*np.exp(0.1*(np.r_[1:786+tbase.size:(786+tbase.size)*1j]-425))
return wt, tbase, omega_int
[docs]def transFilt(hz, wt, tbase, omega_int, t, tol=1e-12):
"""
Compute Step-off responses by Fast Hankel Transform (FHT) with cosine filters
"""
# Define the filter coeffs
# Generate time base
# Determine required frequencies
# Calculate the frequency domain data
hziw = Utils.mkvc(hz.imag)/omega_int
# Clean the low frequency results
idKeep = [idx for idx in range(len(hz)) if abs(hz.imag)[idx] > tol]
idKeep = np.array(idKeep)
idRemove = [idx for idx in range(len(hz)) if abs(hz.imag)[idx] < tol]
idRemove = np.array(idRemove)
hziwc = hziw.copy()
# if idRemove.size != 0:
# lastKeep = idKeep.max()
# idRemove[idRemove > lastKeep] = 0
# lastRemove = idRemove.max()
# hziwc[:lastRemove] = hziw[lastRemove+1]
# Apply filter
dt_filt = np.zeros_like(tbase)
for i in np.arange(tbase.size):
F = np.r_[np.zeros(i), 2*wt/(pi*tbase[i]), np.zeros(tbase.size-i-1)]
dt_filt[i] = -np.dot(F, hziwc)
# Interpolate result
fhz = interp1d(tbase[::-1], dt_filt[::-1])
hz_out = fhz(t)
return hz_out, np.r_[tbase[-1], dt_filt[-1]]
[docs]def transFiltInterp(hz, wt, tbase, omega, omega_int, t, tol=1e-12):
"""
Compute Step-off responses by Fast Hankel Transform (FHT) with cosine filters
"""
# Define the filter coeffs
# Generate time base
# Determine required frequencies
# Calculate the frequency domain data
hziw = Utils.mkvc(hz.imag)/omega
# Clean the low frequency results
idKeep = [idx for idx in range(len(hz)) if abs(hz.imag)[idx] > tol]
idKeep = np.array(idKeep)
idRemove = [idx for idx in range(len(hz)) if abs(hz.imag)[idx] < tol]
idRemove = np.array(idRemove)
hziwint = interp1d(omega, hziw)
hziwc = np.zeros(omega_int.shape)
ind = (omega_int > omega.min()) & (omega_int < omega.max())
hziwc[ind] = hziwint(omega_int[ind])
# if idRemove.size != 0:
# lastKeep = idKeep.max()
# idRemove[idRemove > lastKeep] = 0
# lastRemove = idRemove.max()
# hziwc[:lastRemove] = hziw[lastRemove+1]
# Apply filter
dt_filt = np.zeros_like(tbase)
for i in np.arange(tbase.size):
F = np.r_[np.zeros(i), 2*wt/(pi*tbase[i]), np.zeros(tbase.size-i-1)]
dt_filt[i] = -np.dot(F, hziwc)
# Interpolate result
fhz = interp1d(tbase[::-1], dt_filt[::-1])
hz_out = fhz(t)
return hz_out, np.r_[tbase[-1], dt_filt[-1]]
[docs]def transFiltImpulse(hz, wt, tbase, omega_int, t, tol=1e-12):
"""
Compute Impulse responses by Fast Hankel Transform (FHT) with cosine filters
"""
# Define the filter coeffs
# Generate time base
# Determine required frequencies
# Calculate the frequency domain data
hzr = -Utils.mkvc(hz.real)
# Clean the low frequency results
idKeep = [idx for idx in range(len(hz)) if abs(hz.imag)[idx] > tol]
idKeep = np.array(idKeep)
idRemove = [idx for idx in range(len(hz)) if abs(hz.imag)[idx] < tol]
idRemove = np.array(idRemove)
hzrc = hzr.copy()
# if idRemove.size != 0:
# lastKeep = idKeep.max()
# idRemove[idRemove > lastKeep] = 0
# lastRemove = idRemove.max()
# hzrc[:lastRemove] = hzr[lastRemove+1]
# Apply filter
dt_filt = np.zeros_like(tbase)
for i in np.arange(tbase.size):
F = np.r_[np.zeros(i), 2*wt/(pi*tbase[i]), np.zeros(tbase.size-i-1)]
dt_filt[i] = -np.dot(F, hzrc)
# Interpolate result
fhz = interp1d(tbase[::-1], dt_filt[::-1])
hz_out = fhz(t)
return hz_out
[docs]def transFiltImpulseInterp(hz, wt, tbase, omega, omega_int, t, tol=1e-12):
"""
Compute Impulse responses by Fast Hankel Transform (FHT) with cosine filters
"""
# Define the filter coeffs
# Generate time base
# Determine required frequencies
# Calculate the frequency domain data
hzr = -Utils.mkvc(hz.real)
# Clean the low frequency results
# idKeep = [idx for idx in range(len(hz)) if abs(hz.imag)[idx] > tol]
# idKeep = np.array(idKeep)
# idRemove = [idx for idx in range(len(hz)) if abs(hz.imag)[idx] < tol]
# idRemove = np.array(idRemove)
hzrint = interp1d(omega, hzr, kind = 'quadratic')
hzrc = np.zeros(omega_int.shape)
ind = (omega_int > omega.min()) & (omega_int < omega.max())
hzrc[ind] = hzrint(omega_int[ind])
# if idRemove.size != 0:
# lastKeep = idKeep.max()
# idRemove[idRemove > lastKeep] = 0
# lastRemove = idRemove.max()
# hzrc[:lastRemove] = hzr[lastRemove+1]
# Apply filter
dt_filt = np.zeros_like(tbase)
for i in np.arange(tbase.size):
F = np.r_[np.zeros(i), 2*wt/(pi*tbase[i]), np.zeros(tbase.size-i-1)]
dt_filt[i] = -np.dot(F, hzrc)
# Interpolate result
fhz = interp1d(tbase[::-1], dt_filt[::-1])
hz_out = fhz(t)
return hz_out
[docs]def LoadWeights():
"""
"""
YBASE=np.array([
8.9170998013274418e-14,
9.8549193740052245e-14,
1.0891370292130841e-13,
1.2036825704856076e-13,
1.3302749714952345e-13,
1.4701812115404443e-13,
1.6248015192957209e-13,
1.7956833867707590e-13,
1.9845370571306282e-13,
2.1932526413842005e-13,
2.4239190352504162e-13,
2.6788448255287407e-13,
2.9605813952117967e-13,
3.2719484585839035e-13,
3.6160622818693727e-13,
3.9963668718722961e-13,
4.4166684447542096e-13,
4.8811735199247527e-13,
5.3945310203017795e-13,
5.9618788002944785e-13,
6.5888950671771899e-13,
7.2818552104963217e-13,
8.0476946082781583e-13,
8.8940780386232124e-13,
9.8294763913816720e-13,
1.0863251447666186e-12,
1.2005749575703847e-12,
1.3268405280766938e-12,
1.4663855645544968e-12,
1.6206066806315702e-12,
1.7910473730731204e-12,
1.9794134696161976e-12,
2.1875902014670364e-12,
2.4176610713286156e-12,
2.6719287057960000e-12,
2.9529379008172425e-12,
3.2635010908665675e-12,
3.6067264967338821e-12,
3.9860492336431492e-12,
4.4052656910401313e-12,
4.8685715281339743e-12,
5.3806036654647833e-12,
5.9464866927629101e-12,
6.5718841575654077e-12,
7.2630552479033658e-12,
8.0269174363595134e-12,
8.8711157124588670e-12,
9.8040990962934688e-12,
1.0835205199155280e-11,
1.1974753677488471e-11,
1.3234149515479672e-11,
1.4625997169973058e-11,
1.6164226720110948e-11,
1.7864233284247930e-11,
1.9743031099469828e-11,
2.1819423805797136e-11,
2.4114192639334462e-11,
2.6650304417866294e-11,
2.9453141400488783e-11,
3.2550755321790057e-11,
3.5974148143038491e-11,
3.9757582330231206e-11,
4.3938923764369768e-11,
4.8560020715924429e-11,
5.3667122676390673e-11,
5.9311343238745088e-11,
6.5549171659463761e-11,
7.2443038221987792e-11,
8.0061939059983487e-11,
8.8482126693838504e-11,
9.7787873191515278e-11,
1.0807231359173195e-10,
1.1943837803073370e-10,
1.3199982190169224e-10,
1.4588236435691521e-10,
1.6122494654737812e-10,
1.7818112219246310e-10,
1.9692059439719362e-10,
2.1763091409794871e-10,
2.4051935713527238e-10,
2.6581499874015355e-10,
2.9377100619593265e-10,
3.2466717262156566e-10,
3.5881271723520049e-10,
3.9654938012404428e-10,
4.3825484249401899e-10,
4.8434650663021337e-10,
5.3528567339924565e-10,
5.9158215910338558e-10,
6.5379939789346253e-10,
7.2256008080722362e-10,
7.9855238787053352e-10,
8.8253687563437822e-10,
9.7535408908045947e-10,
1.0779329740778886e-09,
1.1913001745856734e-09,
1.3165903076505279e-09,
1.4550573190356333e-09,
1.6080870331313015e-09,
1.7772110227512649e-09,
1.9641219376281762e-09,
2.1706904450210516e-09,
2.3989839519819520e-09,
2.6512872966606394e-09,
2.9301256157327411e-09,
3.2382896168163261e-09,
3.5788635088117363e-09,
3.9552558697009004e-09,
4.3712337607414382e-09,
4.8309604284818817e-09,
5.3390369719324459e-09,
5.9005483919104070e-09,
6.5211144834374116e-09,
7.2069460805369272e-09,
7.9649072163486862e-09,
8.8025838206794284e-09,
9.7283596425381269e-09,
1.0751500157513941e-08,
1.1882245299770154e-08,
1.3131911946747030e-08,
1.4513007182274982e-08,
1.6039353471673310e-08,
1.7726227001629019e-08,
1.9590510569407677e-08,
2.1650862551562963e-08,
2.3927903643240499e-08,
2.6444423237025737e-08,
2.9225607506844726e-08,
3.2299291479658129e-08,
3.5696237617766722e-08,
3.9450443699873716e-08,
4.3599483082281089e-08,
4.8184880745668262e-08,
5.3252528891055793e-08,
5.8853146244378082e-08,
6.5042785666539686e-08,
7.1883395149287240e-08,
7.9443437811532343e-08,
8.7798577101256825e-08,
9.7032434060731539e-08,
1.0723742423401342e-07,
1.1851568259277232e-07,
1.3098008573741623e-07,
1.4475538160404734e-07,
1.5997943798373573e-07,
1.7680462234971138e-07,
1.9539932680224871e-07,
2.1594965339340473e-07,
2.3866127669890702e-07,
2.6376150227843728e-07,
2.9150154162607256e-07,
3.2215902637935327e-07,
3.5604078695002664e-07,
3.9348592338593700e-07,
4.3486919919827997e-07,
4.8060479212078480e-07,
5.3115043933968360e-07,
5.8701201868132178e-07,
6.4874861160747570e-07,
7.1697809869053571e-07,
7.9238334356995170e-07,
8.7571902728105488e-07,
9.6781920135651654e-07,
1.0696056352944216e-06,
1.1820970419372223e-06,
1.3064192730922673e-06,
1.4438165874351013e-06,
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#
# Next, setup the weights for 0-th order.
#
WT0=np.array([
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])
# Next, setup the weights for 1-th order.
WT1=np.array([
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])
return WT0, WT1, YBASE