distributed data that are inside a given area. It doesn't matter whether or
not the points are on a regular grid.
"""
from fatiando import gridder
import matplotlib.pyplot as plt
import numpy as np
# Generate some synthetic data
area = (-100, 100, -60, 60)
x, y = gridder.scatter(area, 1000, seed=0)
data = np.sin(0.1*x)*np.cos(0.1*y)
# Select the data that fall inside "section"
section = [-40, 40, -25, 25]
# Tip: you pass more than one data array as input. Use this to cut multiple
# data sources (e.g., gravity + height + topography).
x_sub, y_sub, [data_sub] = gridder.cut(x, y, [data], section)
# Plot the original data besides the cut section
plt.figure(figsize=(8, 6))
plt.subplot(1, 2, 1)
plt.axis('scaled')
plt.title("Whole data")
plt.tricontourf(y, x, data, 30, cmap='RdBu_r')
plt.plot(y, x, 'xk')
x1, x2, y1, y2 = section
plt.plot([y1, y2, y2, y1, y1], [x1, x1, x2, x2, x1], '-k', linewidth=3)
plt.xlim(area[2:])
plt.ylim(area[:2])
plt.subplot(1, 2, 2)
"""
Gridding: Cut a section from a grid
"""
from fatiando import gridder, utils
from fatiando.vis import mpl
# Generate some synthetic data on a regular grid
x, y = gridder.regular((-10, 10, -10, 10), (100,100))
# Using a 2D Gaussian
z = utils.gaussian2d(x, y, 1, 1)
subarea = [-2, 2, -3, 3]
subx, suby, subscalar = gridder.cut(x, y, [z], subarea)
mpl.figure(figsize=(12, 5))
mpl.subplot(1, 2, 1)
mpl.title("Whole grid")
mpl.axis('scaled')
mpl.pcolor(x, y, z, (100,100))
mpl.square(subarea, 'k', linewidth=2, label='Cut this region')
mpl.legend(loc='lower left')
mpl.subplot(1, 2, 2)
mpl.title("Cut grid")
mpl.axis('scaled')
mpl.pcolor(subx, suby, subscalar[0], (40,60), interp=True)
mpl.show()
def center_of_mass(x,
y,
z,
eigvec1,
windows=1,
wcenter=None,
wmin=None,
wmax=None):
"""
Estimates the center of mass of a source using the method of Beiki and
Pedersen (2010).
Uses an expanding window to get the best estimate and deal with multiple
sources.
Parameters:
* x, y, z : arrays
The x, y, and z coordinates of the observation points
* eigvec1 : array (shape = (N, 3) where N is the number of observations)
The first eigenvector of the gravity gradient tensor at each observation
point
* windows : int
The number of expanding windows to use
* wcenter : list = [x, y]
The [x, y] coordinates of the center of the expanding windows. Will
default to the middle of the data area if None
* wmin, wmax : float
Minimum and maximum size of the expanding windows. Will default to
10% data area and 100% data area, respectively, if None
Returns:
* [xo, yo, zo], sigma : float
xo, yo, zo are the coordinates of the estimated center of mass. sigma is
the estimated standard deviation of the distances between the estimated
center of mass and the lines passing through the observation point in
the direction of the eigenvector
Example::
>>> import fatiando as ft
>>> # Generate synthetic data using a prism
>>> prism = ft.mesher.Prism(-200,0,-100,100,0,200,{'density':1000})
>>> x, y, z = ft.gridder.regular((-500,500,-500,500), (20,20), z=-100)
>>> tensor = [ft.gravmag.prism.gxx(x, y, z, [prism]),
... ft.gravmag.prism.gxy(x, y, z, [prism]),
... ft.gravmag.prism.gxz(x, y, z, [prism]),
... ft.gravmag.prism.gyy(x, y, z, [prism]),
... ft.gravmag.prism.gyz(x, y, z, [prism]),
... ft.gravmag.prism.gzz(x, y, z, [prism])]
>>> # Get the eigenvector
>>> eigenvals, eigenvecs = ft.gravmag.tensor.eigen(tensor)
>>> # Now estimate the center of mass
>>> cm, sigma = ft.gravmag.tensor.center_of_mass(x, y, z, eigenvecs[0])
>>> xo, yo, zo = cm
>>> print "%.2lf, %.2lf, %.2lf" % (xo, yo, zo)
-100.05, 0.00, 99.86
"""
if wmin is None:
wmin = 0.1 * numpy.mean([x.max() - x.min(), y.max() - y.min()])
if wmax is None:
wmax = numpy.mean([x.max() - x.min(), y.max() - y.min()])
# To ensure that if there is only one window, it will use the largest
# possible
if windows == 1:
wmin = wmax
if wcenter is None:
wcenter = [0.5 * (x.min() + x.max()), 0.5 * (y.min() + y.max())]
xc, yc = wcenter
best = None
for size in numpy.linspace(wmin, wmax, windows):
area = [
xc - 0.5 * size, xc + 0.5 * size, yc - 0.5 * size, yc + 0.5 * size
]
wx, wy, scalars = gridder.cut(x, y, [z, eigvec1], area)
wz, weigvec1 = scalars
# Estimate the center of mass for the data in this window
vx, vy, vz = numpy.transpose(weigvec1)
m11 = numpy.sum(1 - vx**2)
m12 = numpy.sum(-vx * vy)
m13 = numpy.sum(-vx * vz)
m22 = numpy.sum(1 - vy**2)
m23 = numpy.sum(-vy * vz)
m33 = numpy.sum(1 - vz**2)
matrix = numpy.array([[m11, m12, m13], [m12, m22, m23],
[m13, m23, m33]])
vector = numpy.array([
numpy.sum((1 - vx**2) * wx - vx * vy * wy - vx * vz * wz),
numpy.sum(-vx * vy * wx + (1 - vy**2) * wy - vy * vz * wz),
numpy.sum(-vx * vz * wx - vy * vz * wy + (1 - vz**2) * wz)
])
cm = numpy.linalg.solve(matrix, vector)
xo, yo, zo = cm
dists = ((xo - wx)**2 + (yo - wy)**2 + (zo - wz)**2 -
((xo - wx) * vx + (yo - wy) * vy + (zo - wz) * vz)**2)
sigma = numpy.sqrt(numpy.sum(dists) / len(wx))
if best is None or sigma < best[1]:
best = [cm, sigma]
return best
import numpy
from matplotlib import pyplot
from fatiando import vis, gridder, logger
log = logger.tofile(logger.get(), 'fetchdata.log')
log.info(logger.header())
data = numpy.loadtxt('/home/leo/dat/boa6/ftg/rawdata/BOA6_FTG.XYZ', unpack=True)
# Remove the coordinates from the raw data
data[0] -= data[0].min()
data[1] -= data[1].min()
area1 = [7970, 12877, 10650, 17270]
y, x, scalars = gridder.cut(data[0], data[1], data[2:], area1)
# The x and y components are switched because the coordinates are mixed up
# (my x is their y)
height, z, gyy, gxy, gyz, gxx, gxz, gzz = scalars
# Remove the coordinates from the cut data
x -= x.min()
y -= y.min()
# Convert altitude into z coordinates
z *= -1
# Save things to a file
fields = ['x', 'y', 'height', 'alt', 'gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz']
data = [x, y, height, z, gxx, gxy, gxz, gyy, gyz, gzz]
with open('data.xyz', 'w') as f:
f.write(logger.header(comment='#'))
f.write("\n# Column structure\n# ")
f.write(' '.join(fields))
f.write('\n')
numpy.savetxt(f, numpy.transpose(data), fmt="%.4f")
# Plot
def center_of_mass(x, y, z, eigvec1, windows=1, wcenter=None, wmin=None,
wmax=None):
"""
Estimates the center of mass of a source using the method of Beiki and
Pedersen (2010).
Uses an expanding window to get the best estimate and deal with multiple
sources.
Parameters:
* x, y, z : arrays
The x, y, and z coordinates of the observation points
* eigvec1 : array (shape = (N, 3) where N is the number of observations)
The first eigenvector of the gravity gradient tensor at each observation
point
* windows : int
The number of expanding windows to use
* wcenter : list = [x, y]
The [x, y] coordinates of the center of the expanding windows. Will
default to the middle of the data area if None
* wmin, wmax : float
Minimum and maximum size of the expanding windows. Will default to
10% data area and 100% data area, respectively, if None
Returns:
* [xo, yo, zo], sigma : float
xo, yo, zo are the coordinates of the estimated center of mass. sigma is
the estimated standard deviation of the distances between the estimated
center of mass and the lines passing through the observation point in
the direction of the eigenvector
Example::
>>> import fatiando as ft
>>> # Generate synthetic data using a prism
>>> prism = ft.mesher.Prism(-200,0,-100,100,0,200,{'density':1000})
>>> x, y, z = ft.gridder.regular((-500,500,-500,500), (20,20), z=-100)
>>> tensor = [ft.gravmag.prism.gxx(x, y, z, [prism]),
... ft.gravmag.prism.gxy(x, y, z, [prism]),
... ft.gravmag.prism.gxz(x, y, z, [prism]),
... ft.gravmag.prism.gyy(x, y, z, [prism]),
... ft.gravmag.prism.gyz(x, y, z, [prism]),
... ft.gravmag.prism.gzz(x, y, z, [prism])]
>>> # Get the eigenvector
>>> eigenvals, eigenvecs = ft.gravmag.tensor.eigen(tensor)
>>> # Now estimate the center of mass
>>> cm, sigma = ft.gravmag.tensor.center_of_mass(x, y, z, eigenvecs[0])
>>> xo, yo, zo = cm
>>> print "%.2lf, %.2lf, %.2lf" % (xo, yo, zo)
-100.05, 0.00, 99.86
"""
if wmin is None:
wmin = 0.1*numpy.mean([x.max() - x.min(), y.max() - y.min()])
if wmax is None:
wmax = numpy.mean([x.max() - x.min(), y.max() - y.min()])
# To ensure that if there is only one window, it will use the largest
# possible
if windows == 1:
wmin = wmax
if wcenter is None:
wcenter = [0.5*(x.min() + x.max()), 0.5*(y.min() + y.max())]
xc, yc = wcenter
best = None
for size in numpy.linspace(wmin, wmax, windows):
area = [xc - 0.5*size, xc + 0.5*size, yc - 0.5*size, yc + 0.5*size]
wx, wy, scalars = gridder.cut(x, y, [z, eigvec1], area)
wz, weigvec1 = scalars
# Estimate the center of mass for the data in this window
vx, vy, vz = numpy.transpose(weigvec1)
m11 = numpy.sum(1 - vx**2)
m12 = numpy.sum(-vx*vy)
m13 = numpy.sum(-vx*vz)
m22 = numpy.sum(1 - vy**2)
m23 = numpy.sum(-vy*vz)
m33 = numpy.sum(1 - vz**2)
matrix = numpy.array(
[[m11, m12, m13],
[m12, m22, m23],
[m13, m23, m33]])
vector = numpy.array([
numpy.sum((1 - vx**2)*wx - vx*vy*wy - vx*vz*wz),
numpy.sum(-vx*vy*wx + (1 - vy**2)*wy - vy*vz*wz),
numpy.sum(-vx*vz*wx - vy*vz*wy + (1 - vz**2)*wz)])
cm = numpy.linalg.solve(matrix, vector)
xo, yo, zo = cm
dists = ((xo - wx)**2 + (yo - wy)**2 + (zo - wz)**2 -
((xo - wx)*vx + (yo - wy)*vy + (zo - wz)*vz)**2)
sigma = numpy.sqrt(numpy.sum(dists)/len(wx))
if best is None or sigma < best[1]:
best = [cm, sigma]
return best
"""
Gridding: Cut a section from a grid
"""
from fatiando import gridder, utils
from fatiando.vis import mpl
# Generate some synthetic data on a regular grid
x, y = gridder.regular((-10, 10, -10, 10), (100, 100))
# Using a 2D Gaussian
z = utils.gaussian2d(x, y, 1, 1)
subarea = [-2, 2, -3, 3]
subx, suby, subscalar = gridder.cut(x, y, [z], subarea)
mpl.figure(figsize=(12, 5))
mpl.subplot(1, 2, 1)
mpl.title("Whole grid")
mpl.axis('scaled')
mpl.pcolor(x, y, z, (100, 100))
mpl.square(subarea, 'k', linewidth=2, label='Cut this region')
mpl.legend(loc='lower left')
mpl.subplot(1, 2, 2)
mpl.title("Cut grid")
mpl.axis('scaled')
mpl.pcolor(subx, suby, subscalar[0], (40, 60), interp=True)
mpl.show()
