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#!/usr/bin/env python
"""
Mogi's model of surface displacements from a point spherical source in an
elastic half space
References::
[3] Mogi, K. Relations between the eruptions of various
volcanoes and the deformations of the ground surfaces around them,
Bull. Earthquake. Res. Inst., 36, 99-134, 1958.
"""
from numpy import array, pi
def mogi(data, x0, y0, z0, dV):
"""
Computes surface displacements Ux, Uy, Uz in meters from a point spherical
pressure source in an elastic half space [3].
evaluate a single Mogi peak over a 2D (2 by N) numpy array of evalpts,
where coeffs = (x0,y0,z0,dV)
"""
dx = data[0,:] - x0
dy = data[1,:] - y0
dz = 0 - z0
c = dV * 3. / 4. * pi
# or equivalently c= (3/4) a^3 dP / rigidity
# where a = sphere radius, dP = delta Pressure
r2 = dx*dx + dy*dy + dz*dz
C = c / pow(r2, 1.5)
return array((C*dx,C*dy,C*dz))
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