def test_surface2ind_topo(self):
file_url = "https://storage.googleapis.com/simpeg/tests/utils/vancouver_topo.xyz"
file2load = download(file_url)
vancouver_topo = np.loadtxt(file2load)
mesh_topo = Mesh.TensorMesh([
[(500., 24)],
[(500., 20)],
[(10., 30)]
],
x0='CCC')
indtopoCC = surface2ind_topo(mesh_topo, vancouver_topo, gridLoc='CC', method='nearest')
indtopoN = surface2ind_topo(mesh_topo, vancouver_topo, gridLoc='N', method='nearest')
assert len(np.where(indtopoCC)[0]) == 8729
assert len(np.where(indtopoN)[0]) == 8212
def run(plotIt=True, nx=5, ny=5):
"""
Utils: surface2ind_topo
=======================
Here we show how to use :code:`Utils.surface2ind_topo` to identify cells below
a topographic surface.
"""
mesh = Mesh.TensorMesh([nx,ny], x0='CC') # 2D mesh
xtopo = np.linspace(mesh.gridN[:,0].min(), mesh.gridN[:,0].max())
topo = 0.4*np.sin(xtopo*5) # define a topographic surface
Topo = np.hstack([Utils.mkvc(xtopo,2), Utils.mkvc(topo,2)]) #make it an array
indcc = surface2ind_topo(mesh, Topo, 'CC')
if plotIt:
from matplotlib.pylab import plt
from scipy.interpolate import interp1d
fig, ax = plt.subplots(1,1, figsize=(6,6))
mesh.plotGrid(ax=ax, nodes=True, centers=True)
ax.plot(xtopo,topo,'k',linewidth=1)
ax.plot(mesh.vectorCCx, interp1d(xtopo,topo)(mesh.vectorCCx),'--k',linewidth=3)
aveN2CC = Utils.sdiag(mesh.aveN2CC.T.sum(1))*mesh.aveN2CC.T
a = aveN2CC * indcc
a[a > 0] = 1.
a[a < 0.25] = np.nan
a = a.reshape(mesh.vnN, order='F')
masked_array = np.ma.array(a, mask=np.isnan(a))
ax.pcolor(mesh.vectorNx,mesh.vectorNy,masked_array.T, cmap=plt.cm.gray, alpha=0.2)
plt.show()
def run(plotIt=True, nx=5, ny=5):
# 2D mesh
mesh = Mesh.TensorMesh([nx, ny], x0='CC')
xtopo = np.linspace(mesh.gridN[:, 0].min(), mesh.gridN[:, 0].max())
# define a topographic surface
topo = 0.4 * np.sin(xtopo * 5)
# make it an array
Topo = np.hstack([Utils.mkvc(xtopo, 2), Utils.mkvc(topo, 2)])
indcc = surface2ind_topo(mesh, Topo, 'CC')
if plotIt:
fig, ax = plt.subplots(1, 1, figsize=(6, 6))
mesh.plotGrid(ax=ax, nodes=True, centers=True)
ax.plot(xtopo, topo, 'k', linewidth=1)
ax.plot(mesh.vectorCCx,
interp1d(xtopo, topo)(mesh.vectorCCx),
'--k',
linewidth=3)
aveN2CC = Utils.sdiag(mesh.aveN2CC.T.sum(1)) * mesh.aveN2CC.T
a = aveN2CC * indcc
a[a > 0] = 1.
a[a < 0.25] = np.nan
a = a.reshape(mesh.vnN, order='F')
masked_array = np.ma.array(a, mask=np.isnan(a))
ax.pcolor(mesh.vectorNx,
mesh.vectorNy,
masked_array.T,
cmap=plt.cm.gray,
alpha=0.2)
def run(plotIt=True, nx=5, ny=5):
# 2D mesh
mesh = Mesh.TensorMesh([nx, ny], x0='CC')
xtopo = mesh.vectorNx
# define a topographic surface
topo = 0.4*np.sin(xtopo*5)
# make it an array
Topo = np.hstack([Utils.mkvc(xtopo, 2), Utils.mkvc(topo, 2)])
# Compare the different options
indtopoCC_near = surface2ind_topo(mesh, Topo, gridLoc='CC', method='nearest')
indtopoN_near = surface2ind_topo(mesh, Topo, gridLoc='N', method='nearest')
indtopoCC_linear = surface2ind_topo(mesh, Topo, gridLoc='CC', method='linear')
indtopoN_linear = surface2ind_topo(mesh, Topo, gridLoc='N', method='linear')
indtopoCC_cubic = surface2ind_topo(mesh, Topo, gridLoc='CC', method='cubic')
indtopoN_cubic = surface2ind_topo(mesh, Topo, gridLoc='N', method='cubic')
if plotIt:
fig, ax = plt.subplots(2, 3, figsize=(9, 6))
ax = mkvc(ax)
xinterpolate = np.linspace(mesh.gridN[:, 0].min(), mesh.gridN[:, 0].max(),100)
listindex = [indtopoCC_near,indtopoN_near,indtopoCC_linear,indtopoN_linear,indtopoCC_cubic,indtopoN_cubic]
listmethod = ['nearest','nearest', 'linear', 'linear', 'cubic', 'cubic']
for i in range(6):
mesh.plotGrid(ax=ax[i], nodes=True, centers=True)
mesh.plotImage(listindex[i], ax=ax[i], pcolorOpts = {"alpha":0.5, "cmap":plt.cm.gray})
ax[i].scatter(Topo[:,0], Topo[:,1], color = 'black', marker = 'o',s = 50)
ax[i].plot(
xinterpolate,
interp1d(Topo[:, 0], Topo[:, 1], kind=listmethod[i])(xinterpolate),
'--k',
linewidth=3
)
ax[i].xaxis.set_ticklabels([])
ax[i].yaxis.set_ticklabels([])
ax[i].set_aspect('equal')
ax[i].set_xlabel('')
ax[i].set_ylabel('')
ax[0].set_xlabel('Nearest Interpolation', fontsize=16)
ax[2].set_xlabel('Linear Interpolation', fontsize=16)
ax[4].set_xlabel('Cubic Interpolation', fontsize=16)
ax[0].set_ylabel('Cells Center \n based selection', fontsize=16)
ax[1].set_ylabel('Nodes \n based selection', fontsize=16)
plt.tight_layout()
def run(plotIt=True, nx=5, ny=5):
"""
Utils: surface2ind_topo
=======================
Here we show how to use :code:`Utils.surface2ind_topo` to identify cells below
a topographic surface.
"""
mesh = Mesh.TensorMesh([nx, ny], x0='CC') # 2D mesh
xtopo = np.linspace(mesh.gridN[:, 0].min(), mesh.gridN[:, 0].max())
topo = 0.4 * np.sin(xtopo * 5) # define a topographic surface
Topo = np.hstack([Utils.mkvc(xtopo, 2),
Utils.mkvc(topo, 2)]) #make it an array
indcc = surface2ind_topo(mesh, Topo, 'CC')
if plotIt:
from matplotlib.pylab import plt
from scipy.interpolate import interp1d
fig, ax = plt.subplots(1, 1, figsize=(6, 6))
mesh.plotGrid(ax=ax, nodes=True, centers=True)
ax.plot(xtopo, topo, 'k', linewidth=1)
ax.plot(mesh.vectorCCx,
interp1d(xtopo, topo)(mesh.vectorCCx),
'--k',
linewidth=3)
aveN2CC = Utils.sdiag(mesh.aveN2CC.T.sum(1)) * mesh.aveN2CC.T
a = aveN2CC * indcc
a[a > 0] = 1.
a[a < 0.25] = np.nan
a = a.reshape(mesh.vnN, order='F')
masked_array = np.ma.array(a, mask=np.isnan(a))
ax.pcolor(mesh.vectorNx,
mesh.vectorNy,
masked_array.T,
cmap=plt.cm.gray,
alpha=0.2)
plt.show()
def run(plotIt=True, nx=5, ny=5):
# 2D mesh
mesh = Mesh.TensorMesh([nx, ny], x0='CC')
xtopo = mesh.vectorNx
# define a topographic surface
topo = 0.4 * np.sin(xtopo * 5)
# make it an array
Topo = np.hstack([Utils.mkvc(xtopo, 2), Utils.mkvc(topo, 2)])
# Compare the different options
indtopoCC_near = surface2ind_topo(mesh,
Topo,
gridLoc='CC',
method='nearest')
indtopoN_near = surface2ind_topo(mesh, Topo, gridLoc='N', method='nearest')
indtopoCC_linear = surface2ind_topo(mesh,
Topo,
gridLoc='CC',
method='linear')
indtopoN_linear = surface2ind_topo(mesh,
Topo,
gridLoc='N',
method='linear')
indtopoCC_cubic = surface2ind_topo(mesh,
Topo,
gridLoc='CC',
method='cubic')
indtopoN_cubic = surface2ind_topo(mesh, Topo, gridLoc='N', method='cubic')
if plotIt:
fig, ax = plt.subplots(2, 3, figsize=(9, 6))
ax = mkvc(ax)
xinterpolate = np.linspace(mesh.gridN[:, 0].min(),
mesh.gridN[:, 0].max(), 100)
listindex = [
indtopoCC_near, indtopoN_near, indtopoCC_linear, indtopoN_linear,
indtopoCC_cubic, indtopoN_cubic
]
listmethod = [
'nearest', 'nearest', 'linear', 'linear', 'cubic', 'cubic'
]
for i in range(6):
mesh.plotGrid(ax=ax[i], nodes=True, centers=True)
mesh.plotImage(listindex[i],
ax=ax[i],
pcolorOpts={
"alpha": 0.5,
"cmap": plt.cm.gray
})
ax[i].scatter(Topo[:, 0],
Topo[:, 1],
color='black',
marker='o',
s=50)
ax[i].plot(xinterpolate,
interp1d(Topo[:, 0], Topo[:, 1],
kind=listmethod[i])(xinterpolate),
'--k',
linewidth=3)
ax[i].xaxis.set_ticklabels([])
ax[i].yaxis.set_ticklabels([])
ax[i].set_aspect('equal')
ax[i].set_xlabel('')
ax[i].set_ylabel('')
ax[0].set_xlabel('Nearest Interpolation', fontsize=16)
ax[2].set_xlabel('Linear Interpolation', fontsize=16)
ax[4].set_xlabel('Cubic Interpolation', fontsize=16)
ax[0].set_ylabel('Cells Center \n based selection', fontsize=16)
ax[1].set_ylabel('Nodes \n based selection', fontsize=16)
plt.tight_layout()
mesh = refine_box(mesh)
mesh.finalize()
background_value = 100.
dyke_value = 40.
block_value = 70.
# Define surface topography as an (N, 3) np.array. You could also load a file
# containing the xyz points
[xx, yy] = np.meshgrid(mesh.vectorNx, mesh.vectorNy)
zz = -3 * np.exp((xx**2 + yy**2) / 60**2) + 45.
topo = np.c_[mkvc(xx), mkvc(yy), mkvc(zz)]
# Find cells below topography and define mapping
air_value = 0.
ind_active = surface2ind_topo(mesh, topo)
model_map = Maps.InjectActiveCells(mesh, ind_active, air_value)
# Define the model on subsurface cells
model = background_value * np.ones(ind_active.sum())
ind_dyke = (mesh.gridCC[ind_active, 0] > 20.) & (mesh.gridCC[ind_active, 0] <
40.)
model[ind_dyke] = dyke_value
ind_block = ((mesh.gridCC[ind_active, 0] > -40.) &
(mesh.gridCC[ind_active, 0] < -10.) &
(mesh.gridCC[ind_active, 1] > -30.) &
(mesh.gridCC[ind_active, 1] < 30.) &
(mesh.gridCC[ind_active, 2] > -40.) &
(mesh.gridCC[ind_active, 2] < 0.))
model[ind_block] = block_value