BaseMag.py

from SimPEG import Maps, Survey, Utils
import numpy as np
import scipy.sparse as sp
from scipy.constants import mu_0


class BaseMagSurvey(Survey.BaseSurvey):
    """Base Magnetics Survey"""

    rxLoc = None   #: receiver locations
    rx_type = None   #: receiver type

    def __init__(self, **kwargs):
        Survey.BaseSurvey.__init__(self, **kwargs)

    def setBackgroundField(self, Inc, Dec, Btot):

        Bx = Btot * np.cos(Inc / 180. * np.pi) * np.sin(Dec / 180. * np.pi)
        By = Btot * np.cos(Inc / 180. * np.pi) * np.cos(Dec / 180. * np.pi)
        Bz = -Btot * np.sin(Inc / 180. * np.pi)

        self.B0 = np.r_[Bx, By, Bz]

    @property
    def Qfx(self):
        if getattr(self, '_Qfx', None) is None:
            self._Qfx = self.prob.mesh.getInterpolationMat(self.rxLoc, 'Fx')
        return self._Qfx

    @property
    def Qfy(self):
        if getattr(self, '_Qfy', None) is None:
            self._Qfy = self.prob.mesh.getInterpolationMat(self.rxLoc, 'Fy')
        return self._Qfy

    @property
    def Qfz(self):
        if getattr(self, '_Qfz', None) is None:
            self._Qfz = self.prob.mesh.getInterpolationMat(self.rxLoc, 'Fz')
        return self._Qfz

    def projectFields(self, u):
        """
            This function projects the fields onto the data space.

            Especially, here for we use total magnetic intensity (TMI) data,
            which is common in practice.

            First we project our B on to data location

            .. math::

                \mathbf{B}_{rec} = \mathbf{P} \mathbf{B}

            then we take the dot product between B and b_0

            .. math ::

                \\text{TMI} = \\vec{B}_s \cdot \hat{B}_0

        """
        # TODO: There can be some different tyes of data like |B| or B

        bfx = self.Qfx * u['B']
        bfy = self.Qfy * u['B']
        bfz = self.Qfz * u['B']

        # Generate unit vector
        B0 = self.prob.survey.B0
        Bot = np.sqrt(B0[0]**2 + B0[1]**2 + B0[2]**2)
        box = B0[0] / Bot
        boy = B0[1] / Bot
        boz = B0[2] / Bot

        # return bfx*box + bfx*boy + bfx*boz
        return bfx * box + bfy * boy + bfz * boz

    @Utils.count
    def projectFieldsDeriv(self, B):
        """
            This function projects the fields onto the data space.

            .. math::

                \\frac{\partial d_\\text{pred}}{\partial \mathbf{B}} = \mathbf{P}

            Especially, this function is for TMI data type

        """
        # Generate unit vector
        B0 = self.prob.survey.B0
        Bot = np.sqrt(B0[0]**2 + B0[1]**2 + B0[2]**2)
        box = B0[0] / Bot
        boy = B0[1] / Bot
        boz = B0[2] / Bot

        return self.Qfx * box + self.Qfy * boy + self.Qfz * boz

    def projectFieldsAsVector(self, B):

        bfx = self.Qfx * B
        bfy = self.Qfy * B
        bfz = self.Qfz * B

        return np.r_[bfx, bfy, bfz]


class LinearSurvey(Survey.BaseSurvey):
    """Base Magnetics Survey"""

    rx_type = None  #: receiver type

    def __init__(self, srcField, **kwargs):
        self.srcField = srcField
        Survey.BaseSurvey.__init__(self, **kwargs)

    def eval(self, u):
        return u

    @property
    def nD(self):
        return len(self.rxLoc)

    @property
    def nRx(self):
        return self.srcField.rxList[0].locs.shape[0]

    @property
    def rxLoc(self):
        return self.srcField.rxList[0].locs


class SrcField(Survey.BaseSrc):
    """ Define the inducing field """

    param = None  #: Inducing field param (Amp, Incl, Decl)

    def __init__(self, rxList, **kwargs):
        super(SrcField, self).__init__(rxList, **kwargs)


class RxObs(Survey.BaseRx):
    """A station location must have be located in 3-D"""

    def __init__(self, locsXYZ, **kwargs):
        locs = locsXYZ
        assert locsXYZ.shape[1] == 3, 'locs must in 3-D (x,y,z).'
        super(RxObs, self).__init__(locs, 'tmi',
                                    storeProjections=False, **kwargs)

    @property
    def nD(self):
        """Number of data in the receiver."""
        return self.locs[0].shape[0]


class MagSurveyBx(object):
    """docstring for MagSurveyBx"""

    def __init__(self, **kwargs):
        Survey.BaseData.__init__(self, **kwargs)

    def projectFields(self, B):
        bfx = self.Qfx * B
        return bfx


class BaseMagMap(Maps.IdentityMap):
    """BaseMagMap"""

    def __init__(self, mesh, **kwargs):
        Maps.IdentityMap.__init__(self, mesh)

    def _transform(self, m):

        return mu_0 * (1 + m)

    def deriv(self, m):

        return mu_0 * sp.identity(self.nP)


class WeightMap(Maps.IdentityMap):
    """Weighted Map for distributed parameters"""

    def __init__(self, nP, weight, **kwargs):
        Maps.IdentityMap.__init__(self, nP)
        self.mesh = None
        self.weight = weight

    def _transform(self, m):
        return m * self.weight

    def deriv(self, m):
        return Utils.sdiag(self.weight)