simpeg.maps.SurjectVertical1D#

class simpeg.maps.SurjectVertical1D(mesh, **kwargs)[source]#

Bases: IdentityMap

Map 1D layered Earth model to 2D or 3D tensor mesh.

Let \(m\) be a 1D model that defines the property values along the last dimension of a tensor mesh; i.e. the y-direction for 2D meshes and the z-direction for 3D meshes. SurjectVertical1D construct a surjective mapping from the 1D model to all voxel cells in the 2D or 3D tensor mesh provided.

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

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

Parameters:

meshdiscretize.TensorMesh: A 2D or 3D tensor mesh

Attributes

`is_linear`	Determine whether or not this mapping is a linear operation.
`mesh`	The mesh used for the mapping
`nP`	Number of parameters the mapping acts on.
`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 define a 1D layered Earth model comprised of 3 layers on a 1D tensor mesh. We then use SurjectVertical1D to construct a mapping which projects the 1D model onto a 2D tensor mesh.

>>> from simpeg.maps import SurjectVertical1D
>>> from simpeg.utils import plot_1d_layer_model
>>> from discretize import TensorMesh
>>> import numpy as np
>>> import matplotlib as mpl
>>> import matplotlib.pyplot as plt

>>> dh = np.ones(20)
>>> mesh1D = TensorMesh([dh], 'C')
>>> mesh2D = TensorMesh([dh, dh], 'CC')

>>> m = np.zeros(mesh1D.nC)
>>> m[mesh1D.cell_centers < 0] = 10.
>>> m[mesh1D.cell_centers < -5] = 5.

>>> fig1 = plt.figure(figsize=(5,5))
>>> ax1 = fig1.add_subplot(111)
>>> plot_1d_layer_model(
>>>     mesh1D.h[0], np.flip(m), ax=ax1, z0=0,
>>>     scale='linear', show_layers=True, plot_elevation=True
>>> )
>>> ax1.set_xlim([-0.1, 11])
>>> ax1.set_title('1D Model')

>>> mapping = SurjectVertical1D(mesh2D)
>>> u = mapping * m

>>> fig2 = plt.figure(figsize=(6, 5))
>>> ax2a = fig2.add_axes([0.1, 0.15, 0.7, 0.8])
>>> mesh2D.plot_image(u, ax=ax2a, grid=True)
>>> ax2a.set_title('Projected to 2D Mesh')
>>> ax2b = fig2.add_axes([0.83, 0.15, 0.05, 0.8])
>>> norm = mpl.colors.Normalize(vmin=np.min(m), vmax=np.max(m))
>>> cbar = mpl.colorbar.ColorbarBase(ax2b, norm=norm, orientation="vertical")