simpeg.maps.Surject2Dto3D#

class simpeg.maps.Surject2Dto3D(mesh, normal='y', **kwargs)[source]#

Bases: IdentityMap

Map 2D tensor model to 3D tensor mesh.

Let \(m\) define the parameters for a 2D tensor model. Surject2Dto3D constructs a surjective mapping that projects the 2D tensor model to a 3D tensor mesh.

Mathematically, the mapping \(\mathbf{u}(\mathbf{m})\) can be represented by a projection matrix:

\[\mathbf{u}(\mathbf{m}) = \mathbf{Pm}\]

Parameters:

meshdiscretize.TensorMesh: A 3D tensor mesh
normal{‘y’, ‘x’, ‘z’}: Define the projection axis.

Attributes

`is_linear`	Determine whether or not this mapping is a linear operation.
`mesh`	The mesh used for the mapping
`nP`	Number of model properties.
`normal`	The projection axis.
`shape`	Dimensions of the mapping operator

Methods

`deriv`(m[, v])	Derivative of the mapping with respect to the model paramters.
`dot`(map1)	Multiply two mappings to create a `simpeg.maps.ComboMap`.
`inverse`(D)	The transform inverse is not implemented.
`test`([m, num, random_seed])	Derivative test for the mapping.

Examples

Here we project a 3 layered Earth model defined on a 2D tensor mesh to a 3D tensor mesh. We assume that at for some y-location, we have a 2D tensor model which defines the physical property distribution as a function of the x and z location. Using Surject2Dto3D, we project the model along the y-axis to obtain a 3D distribution for the physical property (i.e. a 3D tensor model).

>>> from simpeg.maps import Surject2Dto3D
>>> from discretize import TensorMesh
>>> import numpy as np
>>> import matplotlib as mpl
>>> import matplotlib.pyplot as plt

>>> dh = np.ones(20)
>>> mesh2D = TensorMesh([dh, dh], 'CC')
>>> mesh3D = TensorMesh([dh, dh, dh], 'CCC')

Here, we define the 2D tensor model.

>>> m = np.zeros(mesh2D.nC)
>>> m[mesh2D.cell_centers[:, 1] < 0] = 10.
>>> m[mesh2D.cell_centers[:, 1] < -5] = 5.

We then plot the 2D tensor model; which is defined along the x and z axes.

>>> fig1 = plt.figure(figsize=(6, 5))
>>> ax11 = fig1.add_axes([0.1, 0.15, 0.7, 0.8])
>>> mesh2D.plot_image(m, ax=ax11, grid=True)
>>> ax11.set_ylabel('z')
>>> ax11.set_title('2D Tensor Model')
>>> ax12 = fig1.add_axes([0.83, 0.15, 0.05, 0.8])
>>> norm1 = mpl.colors.Normalize(vmin=np.min(m), vmax=np.max(m))
>>> cbar1 = mpl.colorbar.ColorbarBase(ax12, norm=norm1, orientation="vertical")

By setting normal = ‘Y’ we are projecting along the y-axis.

>>> mapping = Surject2Dto3D(mesh3D, normal='Y')
>>> u = mapping * m

Finally we plot a slice of the resulting 3D tensor model.

>>> fig2 = plt.figure(figsize=(6, 5))
>>> ax21 = fig2.add_axes([0.1, 0.15, 0.7, 0.8])
>>> mesh3D.plot_slice(u, ax=ax21, ind=10, normal='Y', grid=True)
>>> ax21.set_ylabel('z')
>>> ax21.set_title('Projected to 3D Mesh (y=0)')
>>> ax22 = fig2.add_axes([0.83, 0.15, 0.05, 0.8])
>>> norm2 = mpl.colors.Normalize(vmin=np.min(m), vmax=np.max(m))
>>> cbar2 = mpl.colorbar.ColorbarBase(ax22, norm=norm2, orientation="vertical")