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Lindsey
566 lines
25 KiB
Python
566 lines
25 KiB
Python
from SimPEG import Survey, Utils, Problem, Maps, np, sp, mkvc
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from simpegEM.FDEM.SurveyFDEM import SrcFDEM
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from simpegEM.Utils.EMUtils import omega
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from scipy.constants import mu_0
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import sys
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from numpy.lib import recfunctions as recFunc
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from DataMT import DataMT
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from simpegMT.Sources import homo1DModelSource
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#################
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### Receivers ###
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#################
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class RxMT(Survey.BaseRx):
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knownRxTypes = {
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# 3D impedance
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'zxxr':['Z3D', 'real'],
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'zxyr':['Z3D', 'real'],
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'zyxr':['Z3D', 'real'],
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'zyyr':['Z3D', 'real'],
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'zxxi':['Z3D', 'imag'],
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'zxyi':['Z3D', 'imag'],
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'zyxi':['Z3D', 'imag'],
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'zyyi':['Z3D', 'imag'],
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# 2D impedance
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# TODO:
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# 1D impedance
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'z1dr':['Z1D', 'real'],
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'z1di':['Z1D', 'imag'],
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# Tipper
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'tzxr':['T3D','real'],
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'tzxi':['T3D','imag'],
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'tzyr':['T3D','real'],
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'tzyi':['T3D','imag']
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}
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# TODO: Have locs as single or double coordinates for both or numerator and denominator separately, respectively.
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def __init__(self, locs, rxType):
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Survey.BaseRx.__init__(self, locs, rxType)
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@property
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def projField(self):
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"""
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Field Type projection (e.g. e b ...)
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:param str fracPos: Position of the field in the data ratio
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"""
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if 'numerator' in fracPos:
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return self.knownRxTypes[self.rxType][0][0]
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elif 'denominator' in fracPos:
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return self.knownRxTypes[self.rxType][1][0]
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else:
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raise Exception('{s} is an unknown option. Use numerator or denominator.')
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@property
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def projGLoc(self):
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"""
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Grid Location projection (e.g. Ex Fy ...)
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:param str fracPos: Position of the field in the data ratio
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"""
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if 'numerator' in fracPos:
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return self.knownRxTypes[self.rxType][0][1]
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elif 'denominator' in fracPos:
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return self.knownRxTypes[self.rxType][0][1]
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else:
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raise Exception('{s} is an unknown option. Use numerator or denominator.')
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@property
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def projType(self):
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"""
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Receiver type for projection.
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"""
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return self.knownRxTypes[self.rxType][0]
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@property
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def projComp(self):
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"""Component projection (real/imag)"""
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return self.knownRxTypes[self.rxType][1]
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def projectFields(self, src, mesh, f):
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'''
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Project the fields and return the correct data.
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'''
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if self.projType is 'Z1D':
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Pex = mesh.getInterpolationMat(self.locs[:,-1],'Fx')
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Pbx = mesh.getInterpolationMat(self.locs[:,-1],'Ex')
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ex = Pex*mkvc(f[src,'e_1d'],2)
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bx = Pbx*mkvc(f[src,'b_1d'],2)/mu_0
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# Note: Has a minus sign in front, to comply with quadrant calculations.
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# Can be derived from zyx case for the 3D case.
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f_part_complex = -ex/bx
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# elif self.projType is 'Z2D':
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elif self.projType is 'Z3D':
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if self.locs.ndim == 3:
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eFLocs = self.locs[:,:,0]
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bFLocs = self.locs[:,:,1]
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else:
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eFLocs = self.locs
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bFLocs = self.locs
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# Get the projection
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Pex = mesh.getInterpolationMat(eFLocs,'Ex')
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Pey = mesh.getInterpolationMat(eFLocs,'Ey')
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Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
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Pby = mesh.getInterpolationMat(bFLocs,'Fy')
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# Get the fields at location
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# px: x-polaration and py: y-polaration.
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ex_px = Pex*f[src,'e_px']
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ey_px = Pey*f[src,'e_px']
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ex_py = Pex*f[src,'e_py']
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ey_py = Pey*f[src,'e_py']
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hx_px = Pbx*f[src,'b_px']/mu_0
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hy_px = Pby*f[src,'b_px']/mu_0
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hx_py = Pbx*f[src,'b_py']/mu_0
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hy_py = Pby*f[src,'b_py']/mu_0
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# Make the complex data
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if 'zxx' in self.rxType:
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f_part_complex = ( ex_px*hy_py - ex_py*hy_px)/(hx_px*hy_py - hx_py*hy_px)
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elif 'zxy' in self.rxType:
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f_part_complex = (-ex_px*hx_py + ex_py*hx_px)/(hx_px*hy_py - hx_py*hy_px)
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elif 'zyx' in self.rxType:
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f_part_complex = ( ey_px*hy_py - ey_py*hy_px)/(hx_px*hy_py - hx_py*hy_px)
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elif 'zyy' in self.rxType:
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f_part_complex = (-ey_px*hx_py + ey_py*hx_px)/(hx_px*hy_py - hx_py*hy_px)
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elif self.projType is 'T3D':
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if self.locs.ndim == 3:
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horLoc = self.locs[:,:,0]
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vertLoc = self.locs[:,:,1]
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else:
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horLoc = self.locs
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vertLoc = self.locs
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Pbx = mesh.getInterpolationMat(horLoc,'Fx')
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Pby = mesh.getInterpolationMat(horLoc,'Fy')
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Pbz = mesh.getInterpolationMat(vertLoc,'Fz')
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bx_px = Pbx*f[src,'b_px']
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by_px = Pby*f[src,'b_px']
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bz_px = Pbz*f[src,'b_px']
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bx_py = Pbx*f[src,'b_py']
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by_py = Pby*f[src,'b_py']
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bz_py = Pbz*f[src,'b_py']
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if 'tzx' in self.rxType:
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f_part_complex = (- by_px*bz_py + by_py*bz_px)/(bx_px*by_py - bx_py*by_px)
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if 'tzy' in self.rxType:
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f_part_complex = ( bx_px*bz_py - bx_py*bz_px)/(bx_px*by_py - bx_py*by_px)
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else:
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NotImplementedError('Projection of {:s} receiver type is not implemented.'.format(self.rxType))
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# Get the real or imag component
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real_or_imag = self.projComp
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f_part = getattr(f_part_complex, real_or_imag)
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# print f_part
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return f_part
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def projectFieldsDeriv(self, src, mesh, f, v, adjoint=False):
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"""
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The derivative of the projection wrt u
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:param MTsrc src: MT source
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:param TensorMesh mesh: Mesh defining the topology of the problem
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:param MTfields f: MT fields object of the source
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:param numpy.ndarray v: Random vector of size
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"""
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real_or_imag = self.projComp
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if not adjoint:
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if self.projType is 'Z1D':
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Pex = mesh.getInterpolationMat(self.locs[:,-1],'Fx')
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Pbx = mesh.getInterpolationMat(self.locs[:,-1],'Ex')
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# ex = Pex*mkvc(f[src,'e_1d'],2)
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# bx = Pbx*mkvc(f[src,'b_1d'],2)/mu_0
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dP_de = -mkvc(Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0))*(Pex*v),2)
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dP_db = mkvc( Utils.sdiag(Pex*mkvc(f[src,'e_1d'],2))*(Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0)).T*Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0)))*(Pbx*f._bDeriv_u(src,v)/mu_0),2)
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PDeriv_complex = np.sum(np.hstack((dP_de,dP_db)),1)
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elif self.projType is 'Z2D':
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raise NotImplementedError('Has not been implement for 2D impedance tensor')
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elif self.projType is 'Z3D':
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if self.locs.ndim == 3:
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eFLocs = self.locs[:,:,0]
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bFLocs = self.locs[:,:,1]
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else:
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eFLocs = self.locs
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bFLocs = self.locs
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# Get the projection
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Pex = mesh.getInterpolationMat(eFLocs,'Ex')
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Pey = mesh.getInterpolationMat(eFLocs,'Ey')
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Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
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Pby = mesh.getInterpolationMat(bFLocs,'Fy')
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# Get the fields at location
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# px: x-polaration and py: y-polaration.
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ex_px = Pex*f[src,'e_px']
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ey_px = Pey*f[src,'e_px']
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ex_py = Pex*f[src,'e_py']
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ey_py = Pey*f[src,'e_py']
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hx_px = Pbx*f[src,'b_px']/mu_0
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hy_px = Pby*f[src,'b_px']/mu_0
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hx_py = Pbx*f[src,'b_py']/mu_0
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hy_py = Pby*f[src,'b_py']/mu_0
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# Derivatives as lambda functions
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# The size of the diratives should be nD,nU
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ex_px_u = lambda vec: Pex*f._e_pxDeriv_u(src,vec)
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ey_px_u = lambda vec: Pey*f._e_pxDeriv_u(src,vec)
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ex_py_u = lambda vec: Pex*f._e_pyDeriv_u(src,vec)
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ey_py_u = lambda vec: Pey*f._e_pyDeriv_u(src,vec)
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# NOTE: Think b_p?Deriv_u should return a 2*nF size matrix
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hx_px_u = lambda vec: Pbx*f._b_pxDeriv_u(src,vec)/mu_0
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hy_px_u = lambda vec: Pby*f._b_pxDeriv_u(src,vec)/mu_0
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hx_py_u = lambda vec: Pbx*f._b_pyDeriv_u(src,vec)/mu_0
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hy_py_u = lambda vec: Pby*f._b_pyDeriv_u(src,vec)/mu_0
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# Update the input vector
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sDiag = lambda t: Utils.sdiag(mkvc(t,2))
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# Define the components of the derivative
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Hd = sDiag(1./(sDiag(hx_px)*hy_py - sDiag(hx_py)*hy_px))
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Hd_uV = sDiag(hy_py)*hx_px_u(v) + sDiag(hx_px)*hy_py_u(v) - sDiag(hx_py)*hy_px_u(v) - sDiag(hy_px)*hx_py_u(v)
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# Calculate components
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if 'zxx' in self.rxType:
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Zij = sDiag(Hd*( sDiag(ex_px)*hy_py - sDiag(ex_py)*hy_px ))
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ZijN_uV = sDiag(hy_py)*ex_px_u(v) + sDiag(ex_px)*hy_py_u(v) - sDiag(ex_py)*hy_px_u(v) - sDiag(hy_px)*ex_py_u(v)
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elif 'zxy' in self.rxType:
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Zij = sDiag(Hd*(-sDiag(ex_px)*hx_py + sDiag(ex_py)*hx_px ))
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ZijN_uV = -sDiag(hx_py)*ex_px_u(v) - sDiag(ex_px)*hx_py_u(v) + sDiag(ex_py)*hx_px_u(v) + sDiag(hx_px)*ex_py_u(v)
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elif 'zyx' in self.rxType:
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Zij = sDiag(Hd*( sDiag(ey_px)*hy_py - sDiag(ey_py)*hy_px ))
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ZijN_uV = sDiag(hy_py)*ey_px_u(v) + sDiag(ey_px)*hy_py_u(v) - sDiag(ey_py)*hy_px_u(v) - sDiag(hy_px)*ey_py_u(v)
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elif 'zyy' in self.rxType:
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Zij = sDiag(Hd*(-sDiag(ey_px)*hx_py + sDiag(ey_py)*hx_px ))
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ZijN_uV = -sDiag(hx_py)*ey_px_u(v) - sDiag(ey_px)*hx_py_u(v) + sDiag(ey_py)*hx_px_u(v) + sDiag(hx_px)*ey_py_u(v)
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# Calculate the complex derivative
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PDeriv_complex = Hd * (ZijN_uV - Zij * Hd_uV )
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# Extract the real number for the real/imag components.
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Pv = np.array(getattr(PDeriv_complex, real_or_imag))
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elif adjoint:
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# Note: The v vector is real and the return should be complex
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if self.projType is 'Z1D':
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Pex = mesh.getInterpolationMat(self.locs[:,-1],'Fx')
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Pbx = mesh.getInterpolationMat(self.locs[:,-1],'Ex')
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# ex = Pex*mkvc(f[src,'e_1d'],2)
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# bx = Pbx*mkvc(f[src,'b_1d'],2)/mu_0
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dP_deTv = -mkvc(Pex.T*Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0)).T*v,2)
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db_duv = Pbx.T/mu_0*Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0))*(Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0))).T*Utils.sdiag(Pex*mkvc(f[src,'e_1d'],2)).T*v
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dP_dbTv = mkvc(f._bDeriv_u(src,db_duv,adjoint=True),2)
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PDeriv_real = np.sum(np.hstack((dP_deTv,dP_dbTv)),1)
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elif self.projType is 'Z2D':
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raise NotImplementedError('Has not be implement for 2D impedance tensor')
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elif self.projType is 'Z3D':
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if self.locs.ndim == 3:
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eFLocs = self.locs[:,:,0]
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bFLocs = self.locs[:,:,1]
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else:
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eFLocs = self.locs
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bFLocs = self.locs
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# Get the projection
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Pex = mesh.getInterpolationMat(eFLocs,'Ex')
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Pey = mesh.getInterpolationMat(eFLocs,'Ey')
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Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
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Pby = mesh.getInterpolationMat(bFLocs,'Fy')
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# Get the fields at location
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# px: x-polaration and py: y-polaration.
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aex_px = mkvc(mkvc(f[src,'e_px'],2).T*Pex.T)
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aey_px = mkvc(mkvc(f[src,'e_px'],2).T*Pey.T)
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aex_py = mkvc(mkvc(f[src,'e_py'],2).T*Pex.T)
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aey_py = mkvc(mkvc(f[src,'e_py'],2).T*Pey.T)
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ahx_px = mkvc(mkvc(f[src,'b_px'],2).T/mu_0*Pbx.T)
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ahy_px = mkvc(mkvc(f[src,'b_px'],2).T/mu_0*Pby.T)
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ahx_py = mkvc(mkvc(f[src,'b_py'],2).T/mu_0*Pbx.T)
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ahy_py = mkvc(mkvc(f[src,'b_py'],2).T/mu_0*Pby.T)
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# Derivatives as lambda functions
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aex_px_u = lambda vec: f._e_pxDeriv_u(src,Pex.T*vec,adjoint=True)
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aey_px_u = lambda vec: f._e_pxDeriv_u(src,Pey.T*vec,adjoint=True)
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aex_py_u = lambda vec: f._e_pyDeriv_u(src,Pex.T*vec,adjoint=True)
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aey_py_u = lambda vec: f._e_pyDeriv_u(src,Pey.T*vec,adjoint=True)
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ahx_px_u = lambda vec: f._b_pxDeriv_u(src,Pbx.T*vec,adjoint=True)/mu_0
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ahy_px_u = lambda vec: f._b_pxDeriv_u(src,Pby.T*vec,adjoint=True)/mu_0
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ahx_py_u = lambda vec: f._b_pyDeriv_u(src,Pbx.T*vec,adjoint=True)/mu_0
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ahy_py_u = lambda vec: f._b_pyDeriv_u(src,Pby.T*vec,adjoint=True)/mu_0
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# Update the input vector
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# Define shortcuts
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sDiag = lambda t: Utils.sdiag(mkvc(t,2))
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sVec = lambda t: Utils.sp.csr_matrix(mkvc(t,2))
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# Define the components of the derivative
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aHd = sDiag(1./(sDiag(ahx_px)*ahy_py - sDiag(ahx_py)*ahy_px))
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aHd_uV = lambda x: ahx_px_u(sDiag(ahy_py)*x) + ahx_px_u(sDiag(ahy_py)*x) - ahy_px_u(sDiag(ahx_py)*x) - ahx_py_u(sDiag(ahy_px)*x)
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# Need to fix this to reflect the adjoint
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if 'zxx' in self.rxType:
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Zij = sDiag(aHd*( sDiag(ahy_py)*aex_px - sDiag(ahy_px)*aex_py))
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ZijN_uV = lambda x: aex_px_u(sDiag(ahy_py)*x) + ahy_py_u(sDiag(aex_px)*x) - ahy_px_u(sDiag(aex_py)*x) - aex_py_u(sDiag(ahy_px)*x)
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elif 'zxy' in self.rxType:
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Zij = sDiag(aHd*(-sDiag(ahx_py)*aex_px + sDiag(ahx_px)*aex_py))
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ZijN_uV = lambda x:-aex_px_u(sDiag(ahx_py)*x) - ahx_py_u(sDiag(aex_px)*x) + ahx_px_u(sDiag(aex_py)*x) + aex_py_u(sDiag(ahx_px)*x)
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elif 'zyx' in self.rxType:
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Zij = sDiag(aHd*( sDiag(ahy_py)*aey_px - sDiag(ahy_px)*aey_py))
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ZijN_uV = lambda x: aey_px_u(sDiag(ahy_py)*x) + ahy_py_u(sDiag(aey_px)*x) - ahy_px_u(sDiag(aey_py)*x) - aey_py_u(sDiag(ahy_px)*x)
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elif 'zyy' in self.rxType:
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Zij = sDiag(aHd*(-sDiag(ahx_py)*aey_px + sDiag(ahx_px)*aey_py))
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ZijN_uV = lambda x:-aey_px_u(sDiag(ahx_py)*x) - ahx_py_u(sDiag(aey_px)*x) + ahx_px_u(sDiag(aey_py)*x) + aey_py_u(sDiag(ahx_px)*x)
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# Calculate the complex derivative
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PDeriv_real = ZijN_uV(aHd*v) - aHd_uV(Zij.T*aHd*v)#
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# NOTE: Need to reshape the output to go from 2*nU array to a (nU,2) matrix for each polarization
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# PDeriv_real = np.hstack((mkvc(PDeriv_real[:len(PDeriv_real)/2],2),mkvc(PDeriv_real[len(PDeriv_real)/2::],2)))
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PDeriv_real = PDeriv_real.reshape((2,mesh.nE)).T
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# Extract the data
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if real_or_imag == 'imag':
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Pv = 1j*PDeriv_real
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elif real_or_imag == 'real':
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Pv = PDeriv_real.astype(complex)
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return Pv
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###############
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### Sources ###
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###############
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class srcMT(SrcFDEM): # Survey.BaseSrc):
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'''
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Sources for the MT problem.
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Use the SimPEG BaseSrc, since the source fields share properties with the transmitters.
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:param float freq: The frequency of the source
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:param list rxList: A list of receivers associated with the source
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'''
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freq = None #: Frequency (float)
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rxPair = RxMT
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def __init__(self, rxList, freq):
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self.freq = float(freq)
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Survey.BaseSrc.__init__(self, rxList)
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# 1D sources
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class srcMT_polxy_1DhomotD(srcMT):
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"""
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MT source for both polarizations (x and y) for the total Domain. It calculates fields calculated based on conditions on the boundary of the domain.
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"""
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def __init__(self, rxList, freq):
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srcMT.__init__(self, rxList, freq)
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# TODO: need to add the primary fields calc and source terms into the problem.
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# Need to implement such that it works for all dims.
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class srcMT_polxy_1Dprimary(srcMT):
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"""
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MT source for both polarizations (x and y) given a 1D primary models. It assigns fields calculated from the 1D model
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as fields in the full space of the problem.
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"""
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def __init__(self, rxList, freq):
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# assert mkvc(self.mesh.hz.shape,1) == mkvc(sigma1d.shape,1),'The number of values in the 1D background model does not match the number of vertical cells (hz).'
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self.sigma1d = None
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srcMT.__init__(self, rxList, freq)
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# Hidden property of the ePrimary
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self._ePrimary = None
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def ePrimary(self,problem):
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# Get primary fields for both polarizations
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if self.sigma1d is None:
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# Set the sigma1d as the 1st column in the background model
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if len(problem._sigmaPrimary) == problem.mesh.nC:
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if problem.mesh.dim == 1:
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self.sigma1d = problem.mesh.r(problem._sigmaPrimary,'CC','CC','M')[:]
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elif problem.mesh.dim == 3:
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self.sigma1d = problem.mesh.r(problem._sigmaPrimary,'CC','CC','M')[0,0,:]
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# Or as the 1D model that matches the vertical cell number
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elif len(problem._sigmaPrimary) == problem.mesh.nCz:
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self.sigma1d = problem._sigmaPrimary
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if self._ePrimary is None:
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self._ePrimary = homo1DModelSource(problem.mesh,self.freq,self.sigma1d)
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return self._ePrimary
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def bPrimary(self,problem):
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# Project ePrimary to bPrimary
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# Satisfies the primary(background) field conditions
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if problem.mesh.dim == 1:
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C = problem.mesh.nodalGrad
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elif problem.mesh.dim == 3:
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C = problem.mesh.edgeCurl
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bBG_bp = (- C * self.ePrimary(problem) )*(1/( 1j*omega(self.freq) ))
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return bBG_bp
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def S_e(self,problem):
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"""
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Get the electrical field source
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"""
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e_p = self.ePrimary(problem)
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Map_sigma_p = Maps.Vertical1DMap(problem.mesh)
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sigma_p = Map_sigma_p._transform(self.sigma1d)
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# Make mass matrix
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# Note: M(sig) - M(sig_p) = M(sig - sig_p)
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# Need to deal with the edge/face discrepencies between 1d/2d/3d
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if problem.mesh.dim == 1:
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Mesigma = problem.mesh.getFaceInnerProduct(problem.curModel.sigma)
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Mesigma_p = problem.mesh.getFaceInnerProduct(sigma_p)
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if problem.mesh.dim == 2:
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pass
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if problem.mesh.dim == 3:
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Mesigma = problem.MeSigma
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Mesigma_p = problem.mesh.getEdgeInnerProduct(sigma_p)
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return (Mesigma - Mesigma_p) * e_p
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def S_eDeriv_m(self, problem, v, adjoint = False):
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'''
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Get the derivative of S_e wrt to sigma (m)
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'''
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# Need to deal with
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if problem.mesh.dim == 1:
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# Need to use the faceInnerProduct
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MsigmaDeriv = problem.mesh.getFaceInnerProductDeriv(problem.curModel.sigma)(self.ePrimary(problem)[:,1]) * problem.curModel.sigmaDeriv
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# MsigmaDeriv = ( MsigmaDeriv * MsigmaDeriv.T)**2
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if problem.mesh.dim == 2:
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pass
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if problem.mesh.dim == 3:
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# Need to take the derivative of both u_px and u_py
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ePri = self.ePrimary(problem)
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# MsigmaDeriv = problem.MeSigmaDeriv(ePri[:,0]) + problem.MeSigmaDeriv(ePri[:,1])
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# MsigmaDeriv = problem.MeSigmaDeriv(np.sum(ePri,axis=1))
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if adjoint:
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return sp.hstack(( problem.MeSigmaDeriv(ePri[:,0]).T, problem.MeSigmaDeriv(ePri[:,1]).T ))*v
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else:
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return np.hstack(( mkvc(problem.MeSigmaDeriv(ePri[:,0]) * v,2), mkvc(problem.MeSigmaDeriv(ePri[:,1])*v,2) ))
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if adjoint:
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#
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return MsigmaDeriv.T * v
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else:
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# v should be nC size
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return MsigmaDeriv * v
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class srcMT_polxy_3Dprimary(srcMT):
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"""
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MT source for both polarizations (x and y) given a 3D primary model. It assigns fields calculated from the 1D model
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as fields in the full space of the problem.
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"""
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def __init__(self, rxList, freq):
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# assert mkvc(self.mesh.hz.shape,1) == mkvc(sigma1d.shape,1),'The number of values in the 1D background model does not match the number of vertical cells (hz).'
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self.sigmaPrimary = None
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srcMT.__init__(self, rxList, freq)
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# Hidden property of the ePrimary
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self._ePrimary = None
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def ePrimary(self,problem):
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# Get primary fields for both polarizations
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self.sigmaPrimary = problem._sigmaPrimary
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if self._ePrimary is None:
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self._ePrimary = homo3DModelSource(problem.mesh,self.sigmaPrimary,self.freq)
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return self._ePrimary
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def bPrimary(self,problem):
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# Project ePrimary to bPrimary
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# Satisfies the primary(background) field conditions
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if problem.mesh.dim == 1:
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C = problem.mesh.nodalGrad
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elif problem.mesh.dim == 3:
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C = problem.mesh.edgeCurl
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bBG_bp = (- C * self.ePrimary(problem) )*(1/( 1j*omega(self.freq) ))
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return bBG_bp
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def S_e(self,problem):
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"""
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Get the electrical field source
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"""
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e_p = self.ePrimary(problem)
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Map_sigma_p = Maps.Vertical1DMap(problem.mesh)
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sigma_p = Map_sigma_p._transform(self.sigma1d)
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# Make mass matrix
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# Note: M(sig) - M(sig_p) = M(sig - sig_p)
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# Need to deal with the edge/face discrepencies between 1d/2d/3d
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if problem.mesh.dim == 1:
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Mesigma = problem.mesh.getFaceInnerProduct(problem.curModel.sigma)
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Mesigma_p = problem.mesh.getFaceInnerProduct(sigma_p)
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if problem.mesh.dim == 2:
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pass
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if problem.mesh.dim == 3:
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Mesigma = problem.MeSigma
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Mesigma_p = problem.mesh.getEdgeInnerProduct(sigma_p)
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return (Mesigma - Mesigma_p) * e_p
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def S_eDeriv_m(self, problem, v, adjoint = False):
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'''
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Get the derivative of S_e wrt to sigma (m)
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'''
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# Need to deal with
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if problem.mesh.dim == 1:
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# Need to use the faceInnerProduct
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MsigmaDeriv = problem.mesh.getFaceInnerProductDeriv(problem.curModel.sigma)(self.ePrimary(problem)[:,1]) * problem.curModel.sigmaDeriv
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# MsigmaDeriv = ( MsigmaDeriv * MsigmaDeriv.T)**2
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if problem.mesh.dim == 2:
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pass
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if problem.mesh.dim == 3:
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# Need to take the derivative of both u_px and u_py
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ePri = self.ePrimary(problem)
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# MsigmaDeriv = problem.MeSigmaDeriv(ePri[:,0]) + problem.MeSigmaDeriv(ePri[:,1])
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# MsigmaDeriv = problem.MeSigmaDeriv(np.sum(ePri,axis=1))
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if adjoint:
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return sp.hstack(( problem.MeSigmaDeriv(ePri[:,0]).T, problem.MeSigmaDeriv(ePri[:,1]).T ))*v
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else:
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return np.hstack(( mkvc(problem.MeSigmaDeriv(ePri[:,0]) * v,2), mkvc(problem.MeSigmaDeriv(ePri[:,1])*v,2) ))
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if adjoint:
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#
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return MsigmaDeriv.T * v
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else:
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# v should be nC size
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return MsigmaDeriv * v
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##############
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### Survey ###
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##############
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class SurveyMT(Survey.BaseSurvey):
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"""
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Survey class for MT. Contains all the sources associated with the survey.
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:param list srcList: List of sources associated with the survey
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"""
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srcPair = srcMT
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def __init__(self, srcList, **kwargs):
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# Sort these by frequency
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self.srcList = srcList
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Survey.BaseSurvey.__init__(self, **kwargs)
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_freqDict = {}
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for src in srcList:
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if src.freq not in _freqDict:
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_freqDict[src.freq] = []
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_freqDict[src.freq] += [src]
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self._freqDict = _freqDict
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self._freqs = sorted([f for f in self._freqDict])
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@property
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def freqs(self):
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"""Frequencies"""
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return self._freqs
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@property
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def nFreq(self):
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"""Number of frequencies"""
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return len(self._freqDict)
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# TODO: Rename to getSources
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def getSrcByFreq(self, freq):
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"""Returns the sources associated with a specific frequency."""
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assert freq in self._freqDict, "The requested frequency is not in this survey."
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return self._freqDict[freq]
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def projectFields(self, u):
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data = DataMT(self)
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for src in self.srcList:
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sys.stdout.flush()
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for rx in src.rxList:
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data[src, rx] = rx.projectFields(src, self.mesh, u)
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return data
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def projectFieldsDeriv(self, u):
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raise Exception('Use Transmitters to project fields deriv.')
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