1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
|
#!/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 * 3.0 / 4.0 * 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))
|
