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dc3d.py
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dc3d.py
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import numpy as np
import math
from math import sin, cos, tan, atan, radians
from math import sqrt, log
PI = math.pi
PI2 = PI*2
class C0_t:
__slots__ = ['alp1', 'alp2', 'alp3', 'alp4', 'alp5', 'sd', 'cd', 'sdsd',
'cdcd', 'sdcd', 's2d', 'c2d']
def __init__(self, *args):
for i, attr in enumerate(self.__slots__):
setattr(self, attr, args[i])
class C1_t:
__slots__ = ['p', 'q', 's', 't', 'xy', 'x2', 'y2', 'd2', 'r', 'r2', 'r3',
'r5', 'qr', 'qrx', 'a3', 'a5', 'b3', 'c3', 'uy', 'vy', 'wy',
'uz', 'vz', 'wz']
def __init__(self, *args):
for i, attr in enumerate(self.__slots__):
setattr(self, attr, args[i])
class C2_t:
__slots__ = ['xi2', 'et2', 'q2', 'r', 'r2', 'r3', 'r5', 'y', 'd', 'tt',
'alx', 'ale', 'x11', 'y11', 'x32', 'y32', 'ey', 'ez', 'fy', 'fz',
'gy', 'gz', 'hy', 'hz']
def __init__(self, *args):
for i, attr in enumerate(self.__slots__):
setattr(self, attr, args[i])
def isclose(a, b, atol=1e-5, rtol=1e-8):
if abs(a-b) <= (atol + rtol*abs(b)):
return True
else:
return False
def nearlyzero(a):
return isclose(a, 0.0)
def dc3d0(alpha,x,y,z,depth,dip,pot1,pot2,pot3,pot4):
# c 00060000
# c******************************************************************** 00070000
# c***** ***** 00080000
# c***** displacement and strain at depth ***** 00090000
# c***** due to buried point source in a semiinfinite medium ***** 00100000
# c***** coded by y.okada ... sep.1991 ***** 00110002
# c***** revised y.okada ... nov.1991 ***** 00120002
# c***** ***** 00130000
# c******************************************************************** 00140000
# c 00150000
# c***** input 00160000
# c***** alpha : medium constant (lambda+myu)/(lambda+2*myu) 00170000
# c***** x,y,z : coordinate of observing point 00180000
# c***** depth : source depth 00190000
# c***** dip : dip-angle (degree) 00200000
# c***** pot1-pot4 : strike-, dip-, tensile- and inflate-potency 00210000
# c***** potency=( moment of double-couple )/myu for pot1,2 00220000
# c***** potency=(intensity of isotropic part)/lambda for pot3 00230000
# c***** potency=(intensity of linear dipole )/myu for pot4 00240000
# c 00250000
# c***** output 00260000
# c***** ux, uy, uz : displacement ( unit=(unit of potency) / 00270000
# c***** : (unit of x,y,z,depth)**2 ) 00280000
# c***** uxx,uyx,uzx : x-derivative ( unit= unit of potency) / 00290000
# c***** uxy,uyy,uzy : y-derivative (unit of x,y,z,depth)**3 ) 00300000
# c***** uxz,uyz,uzz : z-derivative 00310000
# c***** iret : return code ( =0....normal, =1....singular ) 00320002
# c 00330000
u = np.zeros((12))
dua = np.zeros((12))
dub = np.zeros((12))
duc = np.zeros((12))
if z > 0.:
print('0** positive z was given in sub-dc3d0')
aalpha=alpha
ddip=dip
C0 = dccon0(aalpha,ddip)
#c====================================== 00480000
#c===== real-source contribution ===== 00490000
#c====================================== 00500000
xx=x
yy=y
zz=z
dd=depth+z
C1 = dccon1(xx,yy,dd,C0)
#c======================================= 00960000
#c===== in case of singular (r=0) ===== 00970000
#c======================================= 00980000
r = C1.r
if r == 0.:
return 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1.
pp1=pot1
pp2=pot2
pp3=pot3
pp4=pot4
dua = ua0(xx,yy,dd,pp1,pp2,pp3,pp4, C0, C1)
#c----- 00620000
u[:9] -= dua[:9]
u[9:] += dua[9:]
#c======================================= 00670000
#c===== image-source contribution ===== 00680000
#c======================================= 00690000
dd=depth-z
C1 = dccon1(xx,yy,dd, C0)
dua = ua0(xx,yy,dd,pp1,pp2,pp3,pp4, C0, C1)
dub = ub0(xx,yy,dd,zz,pp1,pp2,pp3,pp4, C0, C1)
duc = uc0(xx,yy,dd,zz,pp1,pp2,pp3,pp4, C0, C1)
#c----- 00750000
du = dua + dub + zz*duc
du[9:] += duc[:3]
u += du
#c===== 00810000
ux=u[0]
uy=u[1]
uz=u[2]
uxx=u[3]
uyx=u[4]
uzx=u[5]
uxy=u[6]
uyy=u[7]
uzy=u[8]
uxz=u[9]
uyz=u[10]
uzz=u[11]
iret=0
return ux, uy, uz, uxx, uyx, uzx, uxy, uyy, uzy, uxz, uyz, uzz, iret
def dc3d(alpha, x, y, z, depth, dip, al1, al2, aw1, aw2, disl1, disl2, disl3):
#C 04670005
#C******************************************************************** 04680005
#C***** ***** 04690005
#C***** DISPLACEMENT AND STRAIN AT DEPTH ***** 04700005
#C***** DUE TO BURIED FINITE FAULT IN A SEMIINFINITE MEDIUM ***** 04710005
#C***** CODED BY Y.OKADA ... SEP.1991 ***** 04720005
#C***** REVISED ... NOV.1991, APR.1992, MAY.1993, ***** 04730005
#C***** JUL.1993 ***** 04740005
#C******************************************************************** 04750005
#C 04760005
#C***** INPUT 04770005
#C***** ALPHA : MEDIUM CONSTANT (LAMBDA+MYU)/(LAMBDA+2*MYU) 04780005
#C***** X,Y,Z : COORDINATE OF OBSERVING POINT 04790005
#C***** DEPTH : DEPTH OF REFERENCE POINT 04800005
#C***** DIP : DIP-ANGLE (DEGREE) 04810005
#C***** AL1,AL2 : FAULT LENGTH RANGE 04820005
#C***** AW1,AW2 : FAULT WIDTH RANGE 04830005
#C***** DISL1-DISL3 : STRIKE-, DIP-, TENSILE-DISLOCATIONS 04840005
#C 04850005
#C***** OUTPUT 04860005
#C***** UX, UY, UZ : DISPLACEMENT ( UNIT=(UNIT OF DISL) 04870005
#C***** UXX,UYX,UZX : X-DERIVATIVE ( UNIT=(UNIT OF DISL) / 04880005
#C***** UXY,UYY,UZY : Y-DERIVATIVE (UNIT OF X,Y,Z,DEPTH,AL,AW) )04890005
#C***** UXZ,UYZ,UZZ : Z-DERIVATIVE 04900005
#C***** IRET : RETURN CODE ( =0....NORMAL, =1....SINGULAR ) 04910005
#C
if z > 0.:
print('( ** POSITIVE Z WAS GIVEN IN SUB-DC3D)')
xi = np.zeros((2))
et = np.zeros((2))
kxi = np.zeros((2))
ket = np.zeros((2))
u = np.zeros((12))
du = np.zeros((12))
dua = np.zeros((12))
dub = np.zeros((12))
duc = np.zeros((12))
aalpha = alpha
ddip = dip
C0 = dccon0(aalpha, ddip)
sd, cd = C0.sd, C0.cd
zz = z
dd1 = disl1
dd2 = disl2
dd3 = disl3
xi[0] = x - al1
xi[1] = x - al2
if nearlyzero(xi[0]):
xi[0] = 0.0
if nearlyzero(xi[1]):
xi[1] = 0.0
#======================================
#===== REAL-SOURCE CONTRIBUTION =====
#======================================
d = depth + z
p = y*cd + d*sd
q = y*sd - d*cd
et[0] = p - aw1
et[1] = p - aw2
if nearlyzero(et[0]):
et[0] = 0.0
if nearlyzero(et[1]):
et[1] = 0.0
#--------------------------------
#----- REJECT SINGULAR CASE -----
#--------------------------------
#C----- ON FAULT EDGE
if q == 0.0 and \
((xi[0]*xi[1] <= 0.0 and et[0]*et[1] == 0.0) or \
(et[0]*et[1] <= 0.0 and xi[0]*xi[1] == 0.0)):
#* GO TO 99 05350005
return None # -> modified later, return 0s
#C----- ON NEGATIVE EXTENSION OF FAULT EDGE 05360014
r12 = sqrt(xi[0]*xi[0] + et[1]*et[1] + q*q)
r21 = sqrt(xi[1]*xi[1] + et[0]*et[0] + q*q)
r22 = sqrt(xi[1]*xi[1] + et[1]*et[1] + q*q)
if xi[0] < 0.0 and r21+xi[1] < 1.e-6:
kxi[0] = 1
if xi[0] < 0.0 and r22+xi[1] < 1.e-6:
kxi[1] = 1
if et[0] < 0.0 and r12+et[1] < 1.e-6:
ket[0] = 1
if et[0] < 0.0 and r22+et[1] < 1.e-6:
ket[1] = 1
for k in range(2):
for j in range(2):
C2 = dccon2(xi[j], et[k], q, sd, cd, kxi[k], ket[j])
dua = ua(xi[j], et[k], q, dd1, dd2, dd3, C0, C2)
for i in [0, 3, 6, 9]:
du[i] = -dua[i]
du[i+1] = -dua[i+1]*cd + dua[i+2]*sd
du[i+2] = -dua[i+1]*sd - dua[i+2]*cd
if i < 9:
continue
du[i] = -du[i]
du[i+1] = -du[i+1]
du[i+2] = -du[i+2]
for i in range(12):
#if j+k /= 3:
if j+k != 1:
u[i] += du[i]
#if j+k == 3:
if j+k == 1:
u[i] -= du[i]
# C======================================= 05700005
# C===== IMAGE-SOURCE CONTRIBUTION ===== 05710005
# C======================================= 05720005
d = depth - z
p = y*cd + d*sd
q = y*sd - d*cd
et[0] = p - aw1
et[1] = p - aw2
if nearlyzero(q):
q = 0.0
if nearlyzero(et[0]):
et[0] = 0.0
if nearlyzero(et[1]):
et[1] = 0.0
# c-------------------------------- 05810005
# c----- reject singular case ----- 05820005
# c-------------------------------- 05830005
# c----- on fault edge 05840015
if q == 0.0 and \
( (xi[0]*xi[1] <= 0.0 and et[0]*et[1] == 0.0) \
or (et[0]*et[1] <= 0.0 and xi[0]*xi[1] == 0.0) ):
# * go to 99 05880015
return None # -> modified later, return 0s
## c----- on negative extension of fault edge 05890015
kxi[:] = 0 # init flag
ket[:] = 0
r12 = sqrt(xi[0]*xi[0]+et[1]*et[1]+q*q)
r21 = sqrt(xi[1]*xi[1]+et[0]*et[0]+q*q)
r22 = sqrt(xi[1]*xi[1]+et[1]*et[1]+q*q)
if xi[0] < 0.0 and r21+xi[1] < 1.e-6:
kxi[0] = 1
if xi[0] < 0.0 and r22+xi[1] < 1.e-6:
kxi[1] = 1
if et[0] < 0.0 and r12+et[1] < 1.e-6:
ket[0] = 1
if et[0] < 0.0 and r22+et[1] < 1.e-6:
ket[1] = 1
for k in range(2):
for j in range(2):
C2 = dccon2(xi[j],et[k],q,sd,cd,kxi[k],ket[j])
dua = ua(xi[j],et[k],q,dd1,dd2,dd3,C0, C2)
dub = ub(xi[j],et[k],q,dd1,dd2,dd3,C0, C2)
duc = uc(xi[j],et[k],q,zz,dd1,dd2,dd3,C0, C2)
for i in [0, 3, 6, 9]:
du[i] = dua[i] + dub[i] +z*duc[i]
du[i+1] = (dua[i+1]+dub[i+1]+z*duc[i+1])*cd \
-(dua[i+2]+dub[i+2]+z*duc[i+2])*sd
du[i+2] = (dua[i+1]+dub[i+1]-z*duc[i+1])*sd \
+(dua[i+2]+dub[i+2]-z*duc[i+2])*cd
if i < 9:
continue
du[i] += duc[0]
du[i+1] += duc[1]*cd-duc[2]*sd
du[i+2] += -duc[1]*sd-duc[2]*cd
for i in range(12):
if j+k != 1:
u[i] += du[i]
if j+k == 1:
u[i] -= du[i]
###
ux = u[0]
uy = u[1]
uz = u[2]
uxx = u[3]
uyx = u[4]
uzx = u[5]
uxy = u[6]
uyy = u[7]
uzy = u[8]
uxz = u[9]
uyz = u[10]
uzz = u[11]
iret = 0
return ux, uy, uz, uxx, uyx, uzx, uxy, uyy, uzy, uxz, uyz, uzz, iret
def dccon0(alpha, dip):
'''
Calculate medium constants and fault-dip constants
INPUT:
alpha : medium constant (lambda+mu)/(lambda+2*mu)
dip : dip angle (degree)
RETURN:
alp1, alp2, alp3, alp4, alp5,
sd, cd, sdsd, cdcd, sdcd, s2d, c2d
### CAUTION ###
if cos(dip) is sufficiently small, it is set to zero.
'''
alp1 = (1.0 - alpha)/2.0
alp2 = alpha/2.0
alp3 = (1.0 - alpha)/alpha
alp4 = 1.0 - alpha
alp5 = alpha
sd = sin(radians(dip))
cd = cos(radians(dip))
if nearlyzero(cd):
cd = 0.0
if sd > 0.:
sd = 1.0
elif sd < 0.:
sd = -1.0
sdsd = sd*sd
cdcd = cd*cd
sdcd = sd*cd
s2d = 2.0*sdcd
c2d = cdcd - sdsd
return C0_t(alp1, alp2, alp3, alp4, alp5, sd, cd, sdsd, cdcd, sdcd, s2d, c2d)
def dccon1(x, y, d, C0):
'''calculate station geometry constants for point source.
INPUT:
x,y,d : station coordinates in fault system
'''
sd = C0.sd
cd = C0.cd
sdsd = C0.sdsd
cdcd = C0.cdcd
sdcd = C0.sdcd
s2d = C0.s2d
c2d = C0.c2d
if nearlyzero(x):
x = 0.0
if nearlyzero(y):
y = 0.0
if nearlyzero(d):
d = 0.0
p=y*cd+d*sd
q=y*sd-d*cd
s=p*sd+q*cd
t=p*cd-q*sd
xy=x*y
x2=x*x
y2=y*y
d2=d*d
r2=x2+y2+d2
r =sqrt(r2)
if r == 0.:
return
r3=r *r2
r5=r3*r2
r7=r5*r2
#c----- 10390005
a3=1.-3.*x2/r2
a5=1.-5.*x2/r2
b3=1.-3.*y2/r2
c3=1.-3.*d2/r2
#c----- 10440005
qr=3.*q/r5
qrx=5.*qr*x/r2
#c----- 10470005
uy=sd-5.*y*q/r2
uz=cd+5.*d*q/r2
vy=s -5.*y*p*q/r2
vz=t +5.*d*p*q/r2
wy=uy+sd
wz=uz+cd
return C1_t(p, q, s, t, xy, x2, y2, d2, r, r2, r3, r5, qr, qrx, a3, a5, b3,
c3, uy, vy, wy, uz, vz, wz)
def dccon2(xi, et, q, sd, cd, kxi, ket):
'''
Calculate station geometry constants for finite source
INPUT:
xi, et, q : station coordinates in fault system
sd, cd : sin, cos of dip-angel
kxi, ket : kxi=1, ket=1 means r+xi<eps, r+et<eps, respectively.
### CAUTION ###
if xi, et, q are sufficiently small, they are set to zero.
'''
if nearlyzero(xi):
xi = 0.0
if nearlyzero(et):
et = 0.0
if nearlyzero(q):
q = 0.0
xi2 = xi*xi
et2 = et*et
q2 = q*q
r2 = xi2 + et2 + q2
r = sqrt(r2)
if nearlyzero(r):
return
r3 = r*r2
r5 = r3*r2
y = et*cd + q*sd
d = et*sd - q*cd
if q == 0.0:
tt = 0.0
else:
tt = atan(xi*et/(q*r))
if kxi == 1:
alx = -log(r-xi)
x11 = 0.0
x32 = 0.0
else:
rxi = r + xi
alx = log(rxi)
x11 = 1.0/(r*rxi)
x32 = (r+rxi)*x11*x11/r
if ket == 1:
ale = -log(r-et)
y11 = 0.0
y32 = 0.0
else:
ret = r + et
ale = log(ret)
y11 = 1.0/(r*ret)
y32 = (r+ret)*y11*y11/r
ey = sd/r - y*q/r3
ez = cd/r + d*q/r3
fy = d/r3 + xi2*y32*sd
fz = y/r3 + xi2*y32*cd
gy = 2.0*x11*sd - y*q*x32
gz = 2.0*x11*cd + d*q*x32
hy = d*q*x32 + xi*q*y32*sd
hz = y*q*x32 + xi*q*y32*cd
return C2_t(xi2, et2, q2, r, r2, r3, r5, y, d, tt, alx, ale, x11, y11, x32,
y32, ey, ez, fy, fz, gy, gz, hy, hz)
def ua0(x,y,d,pot1,pot2,pot3,pot4, C0, C1):
''' displacement and strain at depth (part-a)
due to buried point source in a semiinfinite medium.
INPUT:
x,y,d : station coordinates in fault system
pot1-pot4 : strike-, dip-, tensile- and inflate-potency
OUTPUT:
u(12) : displacement and their derivatives
'''
u = np.zeros((12))
du = np.zeros((12))
alp1 = C0.alp1
alp2 = C0.alp2
sd = C0.sd
cd = C0.cd
s2d = C0.s2d
c2d = C0.c2d
p = C1.p
q = C1.q
s = C1.s
t = C1.t
xy = C1.xy
x2 = C1.x2
r3 = C1.r3
r5 = C1.r5
qr = C1.qr
qrx = C1.qrx
a3 = C1.a3
a5 = C1.a5
b3 = C1.b3
c3 = C1.c3
uy = C1.uy
vy = C1.vy
wy = C1.wy
uz = C1.uz
vz = C1.vz
wz = C1.wz
#c====================================== 01370000
#c===== strike-slip contribution ===== 01380000
#c====================================== 01390000
if pot1 != 0.:
du[ 0]= alp1*q/r3 +alp2*x2*qr
du[ 1]= alp1*x/r3*sd +alp2*xy*qr
du[ 2]=-alp1*x/r3*cd +alp2*x*d*qr
du[ 3]= x*qr*(-alp1 +alp2*(1.+a5) )
du[ 4]= alp1*a3/r3*sd +alp2*y*qr*a5
du[ 5]=-alp1*a3/r3*cd +alp2*d*qr*a5
du[ 6]= alp1*(sd/r3-y*qr) +alp2*3.*x2/r5*uy
du[ 7]= 3.*x/r5*(-alp1*y*sd +alp2*(y*uy+q) )
du[ 8]= 3.*x/r5*( alp1*y*cd +alp2*d*uy )
du[ 9]= alp1*(cd/r3+d*qr) +alp2*3.*x2/r5*uz
du[10]= 3.*x/r5*( alp1*d*sd +alp2*y*uz )
du[11]= 3.*x/r5*(-alp1*d*cd +alp2*(d*uz-q) )
u += pot1/PI2*du
#c=================================== 01560000
#c===== dip-slip contribution ===== 01570000
#c=================================== 01580000
if pot2 != 0.:
du[ 0]= alp2*x*p*qr
du[ 1]= alp1*s/r3 +alp2*y*p*qr
du[ 2]=-alp1*t/r3 +alp2*d*p*qr
du[ 3]= alp2*p*qr*a5
du[ 4]=-alp1*3.*x*s/r5 -alp2*y*p*qrx
du[ 5]= alp1*3.*x*t/r5 -alp2*d*p*qrx
du[ 6]= alp2*3.*x/r5*vy
du[ 7]= alp1*(s2d/r3-3.*y*s/r5) +alp2*(3.*y/r5*vy+p*qr)
du[ 8]=-alp1*(c2d/r3-3.*y*t/r5) +alp2*3.*d/r5*vy
du[ 9]= alp2*3.*x/r5*vz
du[10]= alp1*(c2d/r3+3.*d*s/r5) +alp2*3.*y/r5*vz
du[11]= alp1*(s2d/r3-3.*d*t/r5) +alp2*(3.*d/r5*vz-p*qr)
u += pot2/PI2*du
#c======================================== 01750000
#c===== tensile-fault contribution ===== 01760000
#c======================================== 01770000
if pot3 != 0.:
du[ 0]= alp1*x/r3 -alp2*x*q*qr
du[ 1]= alp1*t/r3 -alp2*y*q*qr
du[ 2]= alp1*s/r3 -alp2*d*q*qr
du[ 3]= alp1*a3/r3 -alp2*q*qr*a5
du[ 4]=-alp1*3.*x*t/r5 +alp2*y*q*qrx
du[ 5]=-alp1*3.*x*s/r5 +alp2*d*q*qrx
du[ 6]=-alp1*3.*xy/r5 -alp2*x*qr*wy
du[ 7]= alp1*(c2d/r3-3.*y*t/r5) -alp2*(y*wy+q)*qr
du[ 8]= alp1*(s2d/r3-3.*y*s/r5) -alp2*d*qr*wy
du[ 9]= alp1*3.*x*d/r5 -alp2*x*qr*wz
du[10]=-alp1*(s2d/r3-3.*d*t/r5) -alp2*y*qr*wz
du[11]= alp1*(c2d/r3+3.*d*s/r5) -alp2*(d*wz-q)*qr
u += pot3/PI2*du
#c========================================= 01940000
#c===== inflate source contribution ===== 01950000
#c========================================= 01960000
if pot4 != 0.:
du[ 0]=-alp1*x/r3
du[ 1]=-alp1*y/r3
du[ 2]=-alp1*d/r3
du[ 3]=-alp1*a3/r3
du[ 4]= alp1*3.*xy/r5
du[ 5]= alp1*3.*x*d/r5
du[ 6]= du[4]
du[ 7]=-alp1*b3/r3
du[ 8]= alp1*3.*y*d/r5
du[ 9]=-du[5]
du[10]=-du[8]
du[11]= alp1*c3/r3
u += pot4/PI2*du
return u
def ub0(x,y,d,z,pot1,pot2,pot3,pot4,C0, C1):
'''displacement and strain at depth (part-b)
due to buried point source in a semiinfinite medium
INPUT:
x,y,d,z : station coordinates in fault system
pot1-pot4 : strike-, dip-, tensile- and inflate-potency
OUTPUT:
u(12) : displacement and their derivatives
'''
u = np.zeros((12))
du = np.zeros((12))
alp3 = C0.alp3
sd = C0.sd
sdsd = C0.sdsd
sdcd = C0.sdcd
p = C1.p
q = C1.q
xy = C1.xy
x2 = C1.x2
y2 = C1.y2
d2 = C1.d2
r = C1.r
r2 = C1.r2
r3 = C1.r3
r5 = C1.r5
qr = C1.qr
qrx = C1.qrx
a3 = C1.a3
a5 = C1.a5
b3 = C1.b3
c3 = C1.c3
uy = C1.uy
vy = C1.vy
wy = C1.wy
uz = C1.uz
vz = C1.vz
wz = C1.wz
c=d+z
rd=r+d
d12=1./(r*rd*rd)
d32=d12*(2.*r+d)/r2
d33=d12*(3.*r+d)/(r2*rd)
d53=d12*(8.*r2+9.*r*d+3.*d2)/(r2*r2*rd)
d54=d12*(5.*r2+4.*r*d+d2)/r3*d12
fi1= y*(d12-x2*d33)
fi2= x*(d12-y2*d33)
fi3= x/r3-fi2
fi4=-xy*d32
fi5= 1./(r*rd)-x2*d32
fj1=-3.*xy*(d33-x2*d54)
fj2= 1./r3-3.*d12+3.*x2*y2*d54
fj3= a3/r3-fj2
fj4=-3.*xy/r5-fj1
fk1=-y*(d32-x2*d53)
fk2=-x*(d32-y2*d53)
fk3=-3.*x*d/r5-fk2
#c====================================== 02600000
#c===== strike-slip contribution ===== 02610000
#c====================================== 02620000
if pot1 != 0.:
du[ 0]=-x2*qr -alp3*fi1*sd
du[ 1]=-xy*qr -alp3*fi2*sd
du[ 2]=-c*x*qr -alp3*fi4*sd
du[ 3]=-x*qr*(1.+a5) -alp3*fj1*sd
du[ 4]=-y*qr*a5 -alp3*fj2*sd
du[ 5]=-c*qr*a5 -alp3*fk1*sd
du[ 6]=-3.*x2/r5*uy -alp3*fj2*sd
du[ 7]=-3.*xy/r5*uy-x*qr -alp3*fj4*sd
du[ 8]=-3.*c*x/r5*uy -alp3*fk2*sd
du[ 9]=-3.*x2/r5*uz +alp3*fk1*sd
du[10]=-3.*xy/r5*uz +alp3*fk2*sd
du[11]= 3.*x/r5*(-c*uz +alp3*y*sd)
u += pot1/PI2*du
#c=================================== 02790000
#c===== dip-slip contribution ===== 02800000
#c=================================== 02810000
if pot2 != 0.:
du[ 0]=-x*p*qr +alp3*fi3*sdcd
du[ 1]=-y*p*qr +alp3*fi1*sdcd
du[ 2]=-c*p*qr +alp3*fi5*sdcd
du[ 3]=-p*qr*a5 +alp3*fj3*sdcd
du[ 4]= y*p*qrx +alp3*fj1*sdcd
du[ 5]= c*p*qrx +alp3*fk3*sdcd
du[ 6]=-3.*x/r5*vy +alp3*fj1*sdcd
du[ 7]=-3.*y/r5*vy-p*qr +alp3*fj2*sdcd
du[ 8]=-3.*c/r5*vy +alp3*fk1*sdcd
du[ 9]=-3.*x/r5*vz -alp3*fk3*sdcd
du[10]=-3.*y/r5*vz -alp3*fk1*sdcd
du[11]=-3.*c/r5*vz +alp3*a3/r3*sdcd
u += pot2/PI2*du
#c======================================== 02980000
#c===== tensile-fault contribution ===== 02990000
#c======================================== 03000000
if pot3 != 0.:
du[ 0]= x*q*qr -alp3*fi3*sdsd
du[ 1]= y*q*qr -alp3*fi1*sdsd
du[ 2]= c*q*qr -alp3*fi5*sdsd
du[ 3]= q*qr*a5 -alp3*fj3*sdsd
du[ 4]=-y*q*qrx -alp3*fj1*sdsd
du[ 5]=-c*q*qrx -alp3*fk3*sdsd
du[ 6]= x*qr*wy -alp3*fj1*sdsd
du[ 7]= qr*(y*wy+q) -alp3*fj2*sdsd
du[ 8]= c*qr*wy -alp3*fk1*sdsd
du[ 9]= x*qr*wz +alp3*fk3*sdsd
du[10]= y*qr*wz +alp3*fk1*sdsd
du[11]= c*qr*wz -alp3*a3/r3*sdsd
u += pot3/PI2*du
#c========================================= 03170000
#c===== inflate source contribution ===== 03180000
#c========================================= 03190000
if pot4 != 0.:
du[ 0]= alp3*x/r3
du[ 1]= alp3*y/r3
du[ 2]= alp3*d/r3
du[ 3]= alp3*a3/r3
du[ 4]=-alp3*3.*xy/r5
du[ 5]=-alp3*3.*x*d/r5
du[ 6]= du[4]
du[ 7]= alp3*b3/r3
du[ 8]=-alp3*3.*y*d/r5
du[ 9]=-du[5]
du[10]=-du[8]
du[11]=-alp3*c3/r3
u += pot4/PI2*du
return u
def uc0(x,y,d,z,pot1,pot2,pot3,pot4, C0, C1):
'''displacement and strain at depth (part-b)
due to buried point source in a semiinfinite medium
INPUT:
x,y,d,z : station coordinates in fault system
pot1-pot4 : strike-, dip-, tensile- and inflate-potency
OUTPUT:
u(12) : displacement and their derivatives
'''
u = np.zeros((12))
du = np.zeros((12))
alp4 = C0.alp4
alp5 = C0.alp5
sd = C0.sd
cd = C0.cd
sdsd = C0.sdsd
sdcd = C0.sdcd
s2d = C0.s2d
c2d = C0.c2d
p = C1.p
s = C1.s
t = C1.t
xy = C1.xy
x2 = C1.x2
y2 = C1.y2
d2 = C1.d2
q = C1.q
r2 = C1.r2
r3 = C1.r3
r5 = C1.r5
qr = C1.qr
qrx = C1.qrx
a3 = C1.a3
a5 = C1.a5
c3 = C1.c3
c=d+z
q2=q*q
r7=r5*r2
a7=1.-7.*x2/r2
b5=1.-5.*y2/r2
b7=1.-7.*y2/r2
c5=1.-5.*d2/r2
c7=1.-7.*d2/r2
d7=2.-7.*q2/r2
qr5=5.*q/r2
qr7=7.*q/r2
dr5=5.*d/r2
#c====================================== 03740000
#c===== strike-slip contribution ===== 03750000
#c====================================== 03760000
if pot1 != 0.:
du[ 0]=-alp4*a3/r3*cd +alp5*c*qr*a5
du[ 1]= 3.*x/r5*( alp4*y*cd +alp5*c*(sd-y*qr5) )
du[ 2]= 3.*x/r5*(-alp4*y*sd +alp5*c*(cd+d*qr5) )
du[ 3]= alp4*3.*x/r5*(2.+a5)*cd -alp5*c*qrx*(2.+a7)
du[ 4]= 3./r5*( alp4*y*a5*cd +alp5*c*(a5*sd-y*qr5*a7) )
du[ 5]= 3./r5*(-alp4*y*a5*sd +alp5*c*(a5*cd+d*qr5*a7) )
du[ 6]= du[4]
du[ 7]= 3.*x/r5*( alp4*b5*cd -alp5*5.*c/r2*(2.*y*sd+q*b7) )
du[ 8]= 3.*x/r5*(-alp4*b5*sd +alp5*5.*c/r2*(d*b7*sd-y*c7*cd) )
du[ 9]= 3./r5* (-alp4*d*a5*cd +alp5*c*(a5*cd+d*qr5*a7) )
du[10]= 15.*x/r7*( alp4*y*d*cd +alp5*c*(d*b7*sd-y*c7*cd) )
du[11]= 15.*x/r7*(-alp4*y*d*sd +alp5*c*(2.*d*cd-q*c7) )
u += pot1/PI2*du
#c=================================== 03930000
#c===== dip-slip contribution ===== 03940000
#c=================================== 03950000
if pot2 != 0.:
du[ 0]= alp4*3.*x*t/r5 -alp5*c*p*qrx
du[ 1]=-alp4/r3*(c2d-3.*y*t/r2) +alp5*3.*c/r5*(s-y*p*qr5)
du[ 2]=-alp4*a3/r3*sdcd +alp5*3.*c/r5*(t+d*p*qr5)
du[ 3]= alp4*3.*t/r5*a5 -alp5*5.*c*p*qr/r2*a7
du[ 4]= 3.*x/r5*(alp4*(c2d-5.*y*t/r2)-alp5*5.*c/r2*(s-y*p*qr7))
du[ 5]= 3.*x/r5*(alp4*(2.+a5)*sdcd -alp5*5.*c/r2*(t+d*p*qr7))
du[ 6]= du[4]
du[ 7]= 3./r5*(alp4*(2.*y*c2d+t*b5) \
+alp5*c*(s2d-10.*y*s/r2-p*qr5*b7))
du[ 8]= 3./r5*(alp4*y*a5*sdcd-alp5*c*((3.+a5)*c2d+y*p*dr5*qr7))
du[ 9]= 3.*x/r5*(-alp4*(s2d-t*dr5) -alp5*5.*c/r2*(t+d*p*qr7))
du[10]= 3./r5*(-alp4*(d*b5*c2d+y*c5*s2d) \
-alp5*c*((3.+a5)*c2d+y*p*dr5*qr7))
du[11]= 3./r5*(-alp4*d*a5*sdcd-alp5*c*(s2d-10.*d*t/r2+p*qr5*c7))
u += pot2/PI2*du
#c======================================== 04140000
#c===== tensile-fault contribution ===== 04150000
#c======================================== 04160000
if pot3 != 0.:
du[ 0]= 3.*x/r5*(-alp4*s +alp5*(c*q*qr5-z))
du[ 1]= alp4/r3*(s2d-3.*y*s/r2)+alp5*3./r5*(c*(t-y+y*q*qr5)-y*z)
du[ 2]=-alp4/r3*(1.-a3*sdsd) -alp5*3./r5*(c*(s-d+d*q*qr5)-d*z)
du[ 3]=-alp4*3.*s/r5*a5 +alp5*(c*qr*qr5*a7-3.*z/r5*a5)
du[ 4]= 3.*x/r5*(-alp4*(s2d-5.*y*s/r2) \
-alp5*5./r2*(c*(t-y+y*q*qr7)-y*z))
du[ 5]= 3.*x/r5*( alp4*(1.-(2.+a5)*sdsd) \
+alp5*5./r2*(c*(s-d+d*q*qr7)-d*z))
du[ 6]= du[4]
du[ 7]= 3./r5*(-alp4*(2.*y*s2d+s*b5) \
-alp5*(c*(2.*sdsd+10.*y*(t-y)/r2-q*qr5*b7)+z*b5))
du[ 8]= 3./r5*( alp4*y*(1.-a5*sdsd) \
+alp5*(c*(3.+a5)*s2d-y*dr5*(c*d7+z)))
du[ 9]= 3.*x/r5*(-alp4*(c2d+s*dr5) \
+alp5*(5.*c/r2*(s-d+d*q*qr7)-1.-z*dr5))
du[10]= 3./r5*( alp4*(d*b5*s2d-y*c5*c2d) \
+alp5*(c*((3.+a5)*s2d-y*dr5*d7)-y*(1.+z*dr5)))
du[11]= 3./r5*(-alp4*d*(1.-a5*sdsd) \
-alp5*(c*(c2d+10.*d*(s-d)/r2-q*qr5*c7)+z*(1.+c5)))
u += pot3/PI2*du
#c========================================= 04400000
#c===== inflate source contribution ===== 04410000
#c========================================= 04420000
if pot4 != 0.:
du[ 0]= alp4*3.*x*d/r5
du[ 1]= alp4*3.*y*d/r5
du[ 2]= alp4*c3/r3
du[ 3]= alp4*3.*d/r5*a5
du[ 4]=-alp4*15.*xy*d/r7
du[ 5]=-alp4*3.*x/r5*c5
du[ 6]= du[4]
du[ 7]= alp4*3.*d/r5*b5
du[ 8]=-alp4*3.*y/r5*c5
du[ 9]= du[5]
du[10]= du[8]
du[11]= alp4*3.*d/r5*(2.+c5)
u += pot4/PI2*du
return u
def ua(xi, et, q, disl1, disl2, disl3, C0, C2):
'''
Displacement and strain at depth (part-a)
due to buries finite fault in a semiinfinite medium.
INPUT:
xi, et, q : station coordintes in fault system
disl1-disl3 : strike, dip, tensile dislocations
OUTPUT:
u(12) : displacement and their derivatives
'''
u = np.zeros((12))
du = np.zeros((12))
alp1, alp2, sd, cd = C0.alp1, C0.alp2, C0.sd, C0.cd
y11 = C2.y11
x11 = C2.x11
xi2 = C2.xi2
q2 = C2.q2
r = C2.r
r3 = C2.r3
ale = C2.ale
y32 = C2.y32
fy = C2.fy
y = C2.y
d = C2.d
tt = C2.tt
alx = C2.alx
ey = C2.ey
ez = C2.ez
fz = C2.fz
gy = C2.gy
gz = C2.gz
hy = C2.hy
hz = C2.hz
xy = xi*y11
qx = q*x11
qy = q*y11
#C====================================== 06850005
#C===== STRIKE-SLIP CONTRIBUTION ===== 06860005
#C====================================== 06870005
if disl1 != 0.0:
du[0]= tt/2.0 +alp2*xi*qy
du[1]= alp2*q/r
du[2]= alp1*ale -alp2*q*qy
du[3]=-alp1*qy -alp2*xi2*q*y32
du[4]= -alp2*xi*q/r3
du[5]= alp1*xy +alp2*xi*q2*y32
du[6]= alp1*xy*sd +alp2*xi*fy+d/2.0*x11
du[7]= alp2*ey
du[8]= alp1*(cd/r+qy*sd) -alp2*q*fy
du[9]= alp1*xy*cd +alp2*xi*fz+y/2.0*x11
du[10]= alp2*ez
du[11]=-alp1*(sd/r-qy*cd) -alp2*q*fz
u[:] += disl1/PI2*du[:]
#C====================================== 07040005
#C===== DIP-SLIP CONTRIBUTION ===== 07050005
#C====================================== 07060005
if disl2 != 0.0:
du[0]= alp2*q/r
du[1]= tt/2.0 +alp2*et*qx
du[2]= alp1*alx -alp2*q*qx
du[3]= -alp2*xi*q/r3
du[4]= -qy/2.0 -alp2*et*q/r3
du[5]= alp1/r +alp2*q2/r3
du[6]= alp2*ey
du[7]= alp1*d*x11+xy/2.0*sd +alp2*et*gy
du[8]= alp1*y*x11 -alp2*q*gy
du[9]= alp2*ez
du[10]= alp1*y*x11+xy/2.0*cd +alp2*et*gz
du[11]=-alp1*d*x11 -alp2*q*gz
u[:] += disl2/PI2*du[:]
#C======================================== 07230005
#C===== TENSILE-FAULT CONTRIBUTION ===== 07240005
#C======================================== 07250005
if disl3 != 0.0:
du[0]=-alp1*ale -alp2*q*qy
du[1]=-alp1*alx -alp2*q*qx
du[2]= tt/2.0 -alp2*(et*qx+xi*qy)
du[3]=-alp1*xy +alp2*xi*q2*y32
du[4]=-alp1/r +alp2*q2/r3
du[5]=-alp1*qy -alp2*q*q2*y32
du[6]=-alp1*(cd/r+qy*sd) -alp2*q*fy
du[7]=-alp1*y*x11 -alp2*q*gy
du[8]= alp1*(d*x11+xy*sd) +alp2*q*hy
du[9]= alp1*(sd/r-qy*cd) -alp2*q*fz
du[10]= alp1*d*x11 -alp2*q*gz
du[11]= alp1*(y*x11+xy*cd) +alp2*q*hz
u[:] += disl3/PI2*du[:]
return u
def ub(xi, et, q, disl1, disl2, disl3, C0, C2):
'''
Displacement and strain at depth (part-b)
due to buried finite fault in a semiinfinite medium.