def test_gy_derivatives(): "gravmag.transform FFT 1st derivatives of gy against analytical solutions" model = [Prism(-1000, 1000, -500, 500, 0, 2000, {'density': 100})] shape = (300, 300) x, y, z = gridder.regular([-10000, 10000, -10000, 10000], shape, z=-100) derivatives = 'x y z'.split() grav = utils.mgal2si(prism.gy(x, y, z, model)) for deriv in derivatives: if deriv == 'x': func = getattr(prism, 'g{}y'.format(deriv)) else: func = getattr(prism, 'gy{}'.format(deriv)) analytical = func(x, y, z, model) calculated = utils.si2eotvos( getattr(transform, 'deriv' + deriv)(x, y, grav, shape, method='fft')) diff = _trim(np.abs(analytical - calculated), shape) assert np.all(diff <= 0.005*np.abs(analytical).max()), \ "Failed for gy{}".format(deriv)
def test_around(): "gravmag.prism gravitational results are consistent around the prism" funcs = ['potential', 'gx', 'gy', 'gz', 'gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz'] model = [Prism(-300, 300, -300, 300, -300, 300, {'density': 1000})] # Make the computation points surround the prism shape = (101, 101) area = [-600, 600, -600, 600] distance = 310 grids = [gridder.regular(area, shape, z=-distance), gridder.regular(area, shape, z=distance), gridder.regular(area, shape, z=distance)[::-1], gridder.regular(area, shape, z=-distance)[::-1], np.array(gridder.regular(area, shape, z=distance))[[0, 2, 1]], np.array(gridder.regular(area, shape, z=-distance))[[0, 2, 1]]] xp, yp, zp = grids[0] # Test if each component is consistent # POTENTIAL face = [prism.potential(x, y, z, model) for x, y, z in grids] for i in range(6): for j in range(i + 1, 6): assert_almost(face[i], face[j], 10, 'Failed potential, faces %d and %d' % (i, j)) # GX top, bottom, north, south, east, west = [prism.gx(x, y, z, model) for x, y, z in grids] assert_almost(top, bottom, 10, 'Failed gx, top and bottom') assert_almost(north, -south, 10, 'Failed gx, north and south') assert_almost(east, west, 10, 'Failed gx, east and west') assert_almost(east, top, 10, 'Failed gx, east and top') assert_almost(north, -prism.gz(xp, yp, zp, model), 10, 'Failed gx, north and gz') assert_almost(south, prism.gz(xp, yp, zp, model), 10, 'Failed gx, south and gz') # GY top, bottom, north, south, east, west = [prism.gy(x, y, z, model) for x, y, z in grids] assert_almost(top, bottom, 10, 'Failed gy, top and bottom') assert_almost(north, south, 10, 'Failed gy, north and south') assert_almost(east, -west, 10, 'Failed gy, east and west') assert_almost(north, top, 10, 'Failed gy, north and top') assert_almost(east, -prism.gz(xp, yp, zp, model), 10, 'Failed gy, east and gz') assert_almost(west, prism.gz(xp, yp, zp, model), 10, 'Failed gy, west and gz') # GZ top, bottom, north, south, east, west = [prism.gz(x, y, z, model) for x, y, z in grids] assert_almost(top, -bottom, 10, 'Failed gz, top and bottom') assert_almost(north, south, 10, 'Failed gz, north and south') assert_almost(east, west, 10, 'Failed gz, east and west') assert_almost(north, prism.gx(xp, yp, zp, model), 10, 'Failed gz, north and gx') assert_almost(south, prism.gx(xp, yp, zp, model), 10, 'Failed gz, south and gx') assert_almost(east, prism.gy(xp, yp, zp, model), 10, 'Failed gz, east and gy') assert_almost(west, prism.gy(xp, yp, zp, model), 10, 'Failed gz, west and gy') # GXX top, bottom, north, south, east, west = [prism.gxx(x, y, z, model) for x, y, z in grids] assert_almost(top, bottom, 10, 'Failed gxx, top and bottom') assert_almost(north, south, 10, 'Failed gxx, north and south') assert_almost(east, west, 10, 'Failed gxx, east and west') assert_almost(east, top, 10, 'Failed gxx, east and top') assert_almost(north, prism.gzz(xp, yp, zp, model), 10, 'Failed gxx, north and gzz') assert_almost(south, prism.gzz(xp, yp, zp, model), 10, 'Failed gxx, south and gzz') # GXY top, bottom, north, south, east, west = [prism.gxy(x, y, z, model) for x, y, z in grids] assert_almost(top, bottom, 4, 'Failed gxy, top and bottom') assert_almost(north, -south, 10, 'Failed gxy, north and south') assert_almost(east, -west, 10, 'Failed gxy, east and west') assert_almost(north, -prism.gyz(xp, yp, zp, model), 10, 'Failed gxy, north and gyz') assert_almost(south, prism.gyz(xp, yp, zp, model), 10, 'Failed gxy, south and gyz') # GXZ top, bottom, north, south, east, west = [prism.gxz(x, y, z, model) for x, y, z in grids] assert_almost(top, -bottom, 10, 'Failed gxz, top and bottom') assert_almost(north, -south, 10, 'Failed gxz, north and south') assert_almost(east, west, 4, 'Failed gxz, east and west') assert_almost(bottom, north, 10, 'Failed gxz, bottom and north') assert_almost(top, south, 10, 'Failed gxz, top and south') assert_almost(east, prism.gxy(xp, yp, zp, model), 4, 'Failed gxz, east and gxy') assert_almost(west, prism.gxy(xp, yp, zp, model), 10, 'Failed gxz, west and gxy') # GYY top, bottom, north, south, east, west = [prism.gyy(x, y, z, model) for x, y, z in grids] assert_almost(top, bottom, 10, 'Failed gyy, top and bottom') assert_almost(north, south, 10, 'Failed gyy, north and south') assert_almost(east, west, 10, 'Failed gyy, east and west') assert_almost(top, north, 10, 'Failed gyy, top and north') assert_almost(east, prism.gzz(xp, yp, zp, model), 10, 'Failed gyy, east and gzz') assert_almost(west, prism.gzz(xp, yp, zp, model), 10, 'Failed gyy, west and gzz') # GYZ top, bottom, north, south, east, west = [prism.gyz(x, y, z, model) for x, y, z in grids] assert_almost(top, -bottom, 10, 'Failed gyz, top and bottom') assert_almost(north, south, 4, 'Failed gyz, north and south') assert_almost(east, -west, 10, 'Failed gyz, east and west') assert_almost(top, west, 10, 'Failed gyz, top and west') assert_almost(bottom, east, 10, 'Failed gyz, bottom and east') assert_almost(north, prism.gxy(xp, yp, zp, model), 4, 'Failed gyz, north and gxy') assert_almost(south, prism.gxy(xp, yp, zp, model), 10, 'Failed gyz, south and gxy') # GZZ top, bottom, north, south, east, west = [prism.gzz(x, y, z, model) for x, y, z in grids] assert_almost(top, bottom, 10, 'Failed gzz, top and bottom') assert_almost(north, south, 10, 'Failed gzz, north and south') assert_almost(east, west, 10, 'Failed gzz, east and west') assert_almost(north, prism.gxx(xp, yp, zp, model), 10, 'Failed gzz, north and gxx') assert_almost(south, prism.gxx(xp, yp, zp, model), 10, 'Failed gzz, south and gxx') assert_almost(east, prism.gyy(xp, yp, zp, model), 10, 'Failed gzz, east and gyy') assert_almost(west, prism.gyy(xp, yp, zp, model), 10, 'Failed gzz, west and gyy')
""" GravMag: Forward modeling of the gravitational potential and its derivatives using 3D model """ from fatiando import mesher, gridder from fatiando.gravmag import prism from fatiando.vis import mpl, myv model = [mesher.Prism(-4000,-3000,-4000,-3000,0,2000,{'density':1000}), mesher.Prism(-1000,1000,-1000,1000,0,2000,{'density':-900}), mesher.Prism(2000,4000,3000,4000,0,2000,{'density':1300})] shape = (100,100) xp, yp, zp = gridder.regular((-5000, 5000, -5000, 5000), shape, z=-150) fields = [prism.potential(xp, yp, zp, model), prism.gx(xp, yp, zp, model), prism.gy(xp, yp, zp, model), prism.gz(xp, yp, zp, model), prism.gxx(xp, yp, zp, model), prism.gxy(xp, yp, zp, model), prism.gxz(xp, yp, zp, model), prism.gyy(xp, yp, zp, model), prism.gyz(xp, yp, zp, model), prism.gzz(xp, yp, zp, model)] titles = ['potential', 'gx', 'gy', 'gz', 'gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz'] mpl.figure(figsize=(8, 9)) mpl.subplots_adjust(left=0.03, right=0.95, bottom=0.05, top=0.92, hspace=0.3) mpl.suptitle("Potential fields produced by a 3 prism model") for i, field in enumerate(fields): mpl.subplot(4, 3, i + 3) mpl.axis('scaled')
def test_gy(): "gravmag.prism.gy python vs cython implementation" py = _prism_numpy.gy(xp, yp, zp, model) cy = prism.gy(xp, yp, zp, model) diff = np.abs(py - cy) assert np.all(diff <= precision), 'max diff: %g' % (max(diff))
""" from fatiando import mesher, gridder from fatiando.gravmag import prism from fatiando.vis import mpl, myv model = [ mesher.Prism(-4000, -3000, -4000, -3000, 0, 2000, {'density': 1000}), mesher.Prism(-1000, 1000, -1000, 1000, 0, 2000, {'density': -900}), mesher.Prism(2000, 4000, 3000, 4000, 0, 2000, {'density': 1300}) ] shape = (100, 100) xp, yp, zp = gridder.regular((-5000, 5000, -5000, 5000), shape, z=-150) fields = [ prism.potential(xp, yp, zp, model), prism.gx(xp, yp, zp, model), prism.gy(xp, yp, zp, model), prism.gz(xp, yp, zp, model), prism.gxx(xp, yp, zp, model), prism.gxy(xp, yp, zp, model), prism.gxz(xp, yp, zp, model), prism.gyy(xp, yp, zp, model), prism.gyz(xp, yp, zp, model), prism.gzz(xp, yp, zp, model) ] titles = [ 'potential', 'gx', 'gy', 'gz', 'gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz' ] mpl.figure(figsize=(8, 9)) mpl.subplots_adjust(left=0.03, right=0.95, bottom=0.05, top=0.92, hspace=0.3) mpl.suptitle("Potential fields produced by a 3 prism model") for i, field in enumerate(fields):