def test_laplace_equation():
"gravmag.tesseroid obeys Laplace equation"
model = [
Tesseroid(0, 1, 0, 1, 1000, -20000, {'density': 2670}),
Tesseroid(-1.5, 1.5, -1.5, -1, -1000, -20000, {'density': -1000}),
Tesseroid(0.1, 0.6, -0.8, -0.3, 10000, -20000, {'density': 2000}),
]
area = [-2, 2, -2, 2]
shape = (51, 51)
lon, lat, h = gridder.regular(area, shape, z=50000)
gxx = tesseroid.gxx(lon, lat, h, model)
gyy = tesseroid.gyy(lon, lat, h, model)
gzz = tesseroid.gzz(lon, lat, h, model)
trace = gxx + gyy + gzz
assert_array_almost_equal(
trace, np.zeros_like(lon), 9,
'Failed whole model. Max diff %.15g' % (np.abs(trace).max()))
for tess in model:
gxx = tesseroid.gxx(lon, lat, h, [tess])
gyy = tesseroid.gyy(lon, lat, h, [tess])
gzz = tesseroid.gzz(lon, lat, h, [tess])
trace = gxx + gyy + gzz
assert_array_almost_equal(
trace, np.zeros_like(lon), 9,
'Failed tesseroid %s. Max diff %.15g' %
(str(tess), np.abs(trace).max()))
def test_gyy():
"gravmag.tesseroid.gyy with optimal discretize against half a shell"
shell = half_sph_shell.gyy(heights, top, bottom, density)
lons = np.zeros_like(heights)
lats = lons
tess = tesseroid.gyy(lons, lats, heights, shellmodel)
diff = np.abs(shell - tess) / np.abs(shell)
assert np.all(diff <= 0.01), 'diff: %s' % (str(diff))
def test_laplace_equation():
"gravmag.tesseroid obeys Laplace equation"
model = [Tesseroid(0, 1, 0, 1, 1000, -20000, {'density': 2670}),
Tesseroid(-1.5, 1.5, -1.5, -1, -1000, -20000, {'density': -1000}),
Tesseroid(0.1, 0.6, -0.8, -0.3, 10000, -20000, {'density': 2000}),
]
area = [-2, 2, -2, 2]
shape = (51, 51)
lon, lat, h = gridder.regular(area, shape, z=50000)
gxx = tesseroid.gxx(lon, lat, h, model)
gyy = tesseroid.gyy(lon, lat, h, model)
gzz = tesseroid.gzz(lon, lat, h, model)
trace = gxx + gyy + gzz
assert_array_almost_equal(trace, np.zeros_like(lon), 9,
'Failed whole model. Max diff %.15g'
% (np.abs(trace).max()))
for tess in model:
gxx = tesseroid.gxx(lon, lat, h, [tess])
gyy = tesseroid.gyy(lon, lat, h, [tess])
gzz = tesseroid.gzz(lon, lat, h, [tess])
trace = gxx + gyy + gzz
assert_array_almost_equal(trace, np.zeros_like(lon), 9,
'Failed tesseroid %s. Max diff %.15g'
% (str(tess), np.abs(trace).max()))
# Create the computation grid
area = (-80, -30, -40, 10)
shape = (100, 100)
lons, lats, heights = gridder.regular(area, shape, z=250000)
start = time.time()
fields = [
tesseroid.potential(lons, lats, heights, model),
tesseroid.gx(lons, lats, heights, model),
tesseroid.gy(lons, lats, heights, model),
tesseroid.gz(lons, lats, heights, model),
tesseroid.gxx(lons, lats, heights, model),
tesseroid.gxy(lons, lats, heights, model),
tesseroid.gxz(lons, lats, heights, model),
tesseroid.gyy(lons, lats, heights, model),
tesseroid.gyz(lons, lats, heights, model),
tesseroid.gzz(lons, lats, heights, model)]
print "Time it took: %s" % (utils.sec2hms(time.time() - start))
titles = ['potential', 'gx', 'gy', 'gz',
'gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz']
bm = mpl.basemap(area, 'merc')
mpl.figure()
mpl.title(titles[0])
mpl.contourf(lons, lats, fields[0], shape, 40, basemap=bm)
bm.drawcoastlines()
mpl.colorbar()
mpl.figure()
for i, field in enumerate(fields[1:4]):
mpl.subplot(1, 3, i + 1)
# Create the computation grid
area = (-80, -30, -40, 10)
shape = (100, 100)
lons, lats, heights = gridder.regular(area, shape, z=250000)
start = time.time()
fields = [
tesseroid.potential(lons, lats, heights, model),
tesseroid.gx(lons, lats, heights, model),
tesseroid.gy(lons, lats, heights, model),
tesseroid.gz(lons, lats, heights, model),
tesseroid.gxx(lons, lats, heights, model),
tesseroid.gxy(lons, lats, heights, model),
tesseroid.gxz(lons, lats, heights, model),
tesseroid.gyy(lons, lats, heights, model),
tesseroid.gyz(lons, lats, heights, model),
tesseroid.gzz(lons, lats, heights, model)
]
print "Time it took: %s" % (utils.sec2hms(time.time() - start))
titles = [
'potential', 'gx', 'gy', 'gz', 'gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz'
]
bm = mpl.basemap(area, 'merc')
mpl.figure()
mpl.title(titles[0])
mpl.contourf(lons, lats, fields[0], shape, 40, basemap=bm)
bm.drawcoastlines()
mpl.colorbar()
mpl.figure()
