def lineIntegralZ_WonBevis(p1, p2):
r"""TODO WRITEME.
:cite:`WonBev1987`
Returns
-------
g = -grad u =(Fx, 0.0, Fz), dFz(Fzx, Fzy, Fzz)
"""
dg = pg.RVector3(0.0, 0.0, 0.0)
dgz = pg.RVector3(0.0, 0.0, 0.0)
pg.lineIntegralZ_WonBevis(p1, p2, dg, dgz)
return np.asarray((dg[0], dg[1], dg[2])), \
np.asarray((dgz[0], dgz[1], dgz[2]))
def solveGravimetry(mesh, dDensity=None, pnts=None, complete=False):
r"""Solve gravimetric response.
2D with :py:mod:`pygimli.physics.gravimetry.lineIntegralZ_WonBevis`
3D with :py:mod:`pygimli.physics.gravimetry.gravMagBoundarySinghGup`
TOWRITE
Parameters
----------
mesh : :gimliapi:`GIMLI::Mesh`
2d or 3d mesh with or without cells.
dDensity : float | array
Density difference.
* float -- solve for positive boundary marker only.
Assuming one inhomogeneity.
* [[int, float]] -- solve for multiple positive boundaries TOIMPL
* array -- solve for one delta density value per cell
* None -- return per cell kernel matrix G TOIMPL
pnts : [[x_i, y_i]]
List of measurement positions.
complete : bool [False]
If True return whole solution or matrix for [dgx, dgy, dgz] and ...
TODO
Returns
-------
"""
if pnts is None:
pnts = [[0.0, 0.0]]
mesh.createNeighbourInfos()
Gdg = None
Gdgz = None
dg = None
dgz = None
if complete:
Gdg = np.zeros((len(pnts), mesh.cellCount(), 3))
Gdgz = np.zeros((len(pnts), mesh.cellCount(), 3))
dg = np.zeros((len(pnts), 3))
dgz = np.zeros((len(pnts), 3))
else:
dg = np.zeros(len(pnts))
Gdg = np.zeros((len(pnts), mesh.cellCount()))
dgi = None
dgzi = None
for i, p in enumerate(pnts):
mesh.translate(-pg.RVector3(p))
for b in mesh.boundaries():
if b.marker() != 0 or hasattr(dDensity, '__len__') or \
dDensity is None:
if mesh.dimension() == 2:
# tic = time.time()
if complete:
dgi, dgzi = lineIntegralZ_WonBevis(b.node(0).pos(),
b.node(1).pos())
# times.append(time.time() - tic)
dgi *= -2.0
dgzi *= -2.0
else:
dgi = pg.lineIntegralZ_WonBevis(b.node(0).pos(),
b.node(1).pos())
dgi *= -2.0 * G
else:
if complete:
dgi, dgzi = gravMagBoundarySinghGup(b)
else:
raise Exception("TOIMPL")
if complete:
dgi *= [1.0, 1.0, -1.0]
dgi *= -G
dgzi *= -G
if hasattr(dDensity, '__len__') or dDensity is None:
cl = b.leftCell()
cr = b.rightCell()
if cl:
Gdg[i][cl.id()] += dgi
if complete:
Gdgz[i][cl.id()] += dgzi
if cr:
Gdg[i][cr.id()] -= dgi
if complete:
Gdgz[i][cr.id()] -= dgzi
else:
dg[i] += dgi * dDensity
if complete:
dgz[i] += dgzi * dDensity
mesh.translate(pg.RVector3(p))
# import matplotlib.pyplot as plt
# print("times:", sum(times), np.mean(times))
# plt.plot(times)
if dDensity is None:
if complete:
return Gdg.transpose([0, 2, 1]), Gdgz.transpose([0, 2, 1])
return Gdg
elif hasattr(dDensity, '__len__'):
if complete:
dg = Gdg.transpose([0, 2, 1]).dot(dDensity)
dgz = Gdgz.transpose([0, 2, 1]).dot(dDensity)
return dg, dgz
else:
return Gdg.dot(dDensity)
if complete:
return dg, dgz
return dg
def lineIntegralZ_WonBevis(p1, p2):
"""
WonBevis1987.
Returns
-------
g = -grad u =(Fx, 0.0, Fz), dFz(Fzx, Fzy, Fzz)
"""
dg = pg.RVector3(0.0, 0.0, 0.0)
dgz = pg.RVector3(0.0, 0.0, 0.0)
pg.lineIntegralZ_WonBevis(p1, p2, dg, dgz)
return np.asarray((dg[0], dg[1], dg[2])), np.asarray(
(dgz[0], dgz[1], dgz[2]))
x1 = p1[0]
z1 = p1[1]
x2 = p2[0]
z2 = p2[1]
x21 = x2 - x1
z21 = z2 - z1
z21s = z21 * z21
x21s = x21 * x21
xz12 = x1 * z2 - x2 * z1
if x1 == 0. and z1 == 0.:
return np.asarray((0.0, 0.0, 0.0)), np.asarray((0.0, 0.0, 0.0))
if x2 == 0. and z2 == 0.:
return np.asarray((0.0, 0.0, 0.0)), np.asarray((0.0, 0.0, 0.0))
theta1 = np.arctan2(z1, x1)
theta2 = np.arctan2(z2, x2)
r1s = x1 * x1 + z1 * z1
r2s = x2 * x2 + z2 * z2
r1 = np.sqrt(r1s)
r2 = np.sqrt(r2s)
r21s = x21s + z21s
R2 = r21s
rln = np.log(r2 / r1)
p = (xz12 / r21s) * \
((x1 * x21 - z1 * z21) / r1s - (x2 * x21 - z2 * z21) / r2s)
q = (xz12 / r21s) * \
((x1 * z21 + z1 * x21) / r1s - (x2 * z21 + z2 * x21) / r2s)
Fz = 0.0
Fx = 0.0
Fzx = 0.0 # dFz/dx
Fzz = 0.0 # dFz/dz
if np.sign(z1) != np.sign(z2):
if (x1 * z2 < x2 * z1) and z2 >= 0.0:
theta1 = theta1 + 2. * np.pi
if (x1 * z2 > x2 * z1) and z1 >= 0.0:
theta2 = theta2 + 2. * np.pi
if x1 * z2 == x2 * z1:
return np.asarray((0., 0.0, 0.)), np.asarray((0., 0.0, 0.))
th12 = (theta1 - theta2)
if abs(x21) < 1e-4:
# print("case 3")
Fz = x1 * rln
Fx = 0.0
Fzz = -p
Fzx = q - z21s / r21s * rln
# print(Zz, Zx, R2, x1, z1, x2, z2)
else: # default
B = z21 / x21
A = (x21 * xz12) / R2
Fz = A * (th12 + B * rln)
Fx = A * (-th12 * B + rln)
z21dx21 = z21 / x21
# z21x21 = z21 * x21
fz = (th12 + z21dx21 * rln) / r21s
Fzz = -p + x21s * fz
Fzx = q - x21 * z21 * fz
# // check this!!!
# fx = (th12 * z21dx21 - rln)/r21s
# print(np.asarray((Fx, 0.0, Fz)), np.asarray((Fzx, 0.0, Fzz)))
return np.asarray((Fx, 0.0, Fz)), np.asarray((Fzx, 0.0, Fzz))