# 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

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))
>>> 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")


Attributes

 nP Number of parameters the mapping acts on.

Methods

 deriv(m[, v]) Derivative of the mapping with respect to the model paramters.

## Galleries and Tutorials using SimPEG.maps.SurjectVertical1D#

Maps: ComboMaps

Maps: ComboMaps

EM: TDEM: 1D: Inversion

EM: TDEM: 1D: Inversion

EM: TDEM: 1D: Inversion with VTEM waveform

EM: TDEM: 1D: Inversion with VTEM waveform

Heagy et al., 2017 1D RESOLVE and SkyTEM Bookpurnong Inversions

Heagy et al., 2017 1D RESOLVE and SkyTEM Bookpurnong Inversions

Heagy et al., 2017 1D RESOLVE Bookpurnong Inversion

Heagy et al., 2017 1D RESOLVE Bookpurnong Inversion

Heagy et al., 2017 1D FDEM and TDEM inversions

Heagy et al., 2017 1D FDEM and TDEM inversions