sandbox/okada.h

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
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
/* Implementation of the formulae of Okada, 1985, "Surface deformation
   due to shear and tensile faults in a half-space", Bulletin of the
   Seismological Society of America, 75:4, 1135-1154, */

/* formulae (25)-(30) */
static void rectangular_source (const double U[3], double cosd, double sind,
				double mulambda, double d,
				double psi, double eta, double q,
				double u[3])
{
  double R = sqrt (psi*psi + eta*eta + q*q);
  double X = sqrt (psi*psi + q*q);
  double dtilde = eta*sind - q*cosd;
  double ytilde = eta*cosd + q*sind;
  double atanp = fabs (q) > 1e-6 ? atan (psi*eta/(q*R)) : 0.;

  mulambda = mulambda/(1. + mulambda);
  double logReta = R + eta > 1e-6 ? log (R + eta) : - log (R - eta);
  double Reta = fabs (R + eta) > 1e-6 ? R + eta : 1e30;
  double I1, I2, I3, I4, I5;
  if (fabs (cosd) > 1e-6) {
    /* formula (28) */
    I5 = fabs (psi) < 1e-6 ? 0. :
      mulambda*2./cosd*atan ((eta*(X + q*cosd) + 
			      X*(R + X)*sind)/(psi*(R + X)*cosd));
    I4 = mulambda/cosd*(log (R + dtilde) - sind*logReta);
    I3 = mulambda*(1./cosd*ytilde/(R + dtilde) - logReta) + sind/cosd*I4;
    I2 = mulambda*(- logReta) - I3;
    I1 = mulambda*(-1./cosd*psi/(R + dtilde)) - sind/cosd*I5;
  }
  else {
    /* formula (29) */
    double R1 = R + dtilde;
    I1 = - mulambda/2.*psi*q/(R1*R1);
    I3 = mulambda/2.*(eta/R1 + ytilde*q/(R1*R1) - logReta);
    I2 = mulambda*(- logReta) - I3;
    I4 = - mulambda*q/R1;
    I5 = - mulambda*psi*sind/R1;
  }
    
  /* strike-slip, formula (25) */  
  if (U[0] != 0.) {
    double U1pi = U[0]/(2.*M_PI);
    u[0] -= U1pi*(psi*q/(R*Reta) + atanp + I1*sind);
    u[1] -= U1pi*(ytilde*q/(R*Reta) + q*cosd/Reta + I2*sind);
    u[2] -= U1pi*(dtilde*q/(R*Reta) + q*sind/Reta + I4*sind);
  }

  /* dip-slip, formula (26) */  
  if (U[1] != 0.) {
    double U2pi = U[1]/(2.*M_PI);
    u[0] -= U2pi*(q/R - I3*sind*cosd);
    u[1] -= U2pi*(ytilde*q/(R*(R + psi)) + cosd*atanp - I1*sind*cosd);
    u[2] -= U2pi*(dtilde*q/(R*(R + psi)) + sind*atanp - I5*sind*cosd);
  }

  /* tensile, formula (27) */  
  if (U[2] != 0.) {
    double U3pi = U[2]/(2.*M_PI);
    u[0] += U3pi*(q*q/(R*Reta) - I3*sind*sind);
    u[1] += U3pi*(-dtilde*q/(R*(R + psi)) - 
		  sind*(psi*q/(R*Reta) - atanp) - I1*sind*sind);
    u[2] += U3pi*(ytilde*q/(R*(R + psi)) + 
		  cosd*(psi*q/(R*Reta) - atanp) - I5*sind*sind);
  }
}

/* formula (24) */
static void okada_rectangular_source (const double U[3], 
				      double L, double W, double d, 
				      double delta, double mulambda,
				      double x, double y,
				      double u[3])
{
  double cosd = cos (delta), sind = sin (delta);
  double p = y*cosd + d*sind;
  double q = y*sind - d*cosd;

  u[0] = u[1] = u[2] = 0.;
  rectangular_source (U, cosd, sind, mulambda, d,
		      x, p, q,
		      u);
  rectangular_source (U, cosd, sind, mulambda, d,
		      x - L, p - W, q,
		      u);

  double u1[3] = {0., 0., 0.};
  rectangular_source (U, cosd, sind, mulambda, d,
		      x, p - W, q,
		      u1);
  rectangular_source (U, cosd, sind, mulambda, d,
		      x - L, p, q,
		      u1);
  u[0] -= u1[0];
  u[1] -= u1[1];
  u[2] -= u1[2];
}

static double dtheta (double theta1, double theta2)
{
  double d = theta1 - theta2;
  if (d > 180.) d -= 360.;
  if (d < -180.) d += 360.;
  return d;
}

struct Okada {
  scalar d;
  double x, y, depth;
  double strike, dip, rake;
  double mu, lambda;
  double length, width, vU[3], U;
  double R;
  int (* iterate) (void);
  bool flat;
};

void okada (struct Okada p)
{
  // default settings
  if (p.mu == 0.)     p.mu = 1.;
  if (p.lambda == 0.) p.lambda = 1.;
  if (p.R == 0.)      p.R = 6371220.; /* Earth radius (metres) */

  double dtr = pi/180.;
  if (p.rake != nodata) {
    p.vU[0] = p.U*cos (p.rake*dtr);
    p.vU[1] = p.U*sin (p.rake*dtr);
  }
  double sina = sin ((90. - p.strike)*dtr);
  double cosa = cos ((90. - p.strike)*dtr);
  double sind = sin (p.dip*dtr);
  /* depth of the bottom edge */
  double depth = sind > 0. ? p.depth + p.width*sind : p.depth;
  /* origin to the centroid */
  double x0 = p.length/2., y0 = p.width/2.*cos (p.dip*dtr);
  
  foreach() {
    if ( p.flat ) {
      x -= p.x;
      y -= p.y;
    }
    else {
      x = p.R*cos(y*dtr)*dtheta(x, p.x)*dtr;
      y = p.R*dtheta(y, p.y)*dtr;
    }
    double x1 =   cosa*x + sina*y;
    double y1 = - sina*x + cosa*y;
    double oka[3];
    okada_rectangular_source (p.vU, p.length, p.width, depth, 
			      p.dip*dtr,
			      p.mu/p.lambda,
			      x0 + x1, y0 + y1,
			      oka);
    val(p.d,0,0) = oka[2];
  }
}

void fault (struct Okada p)
{
  scalar hold[];
  // save the initial water depth
  scalar_clone (hold, h);
  foreach()
    hold[] = h[];
  boundary ({hold});

  p.d = h;
  do {
    okada (p);
    // h[] now contains the Okada vertical displacement
    foreach() {
      // deformation is added to hold[] (water depth) only in wet areas
      h[] = hold[] > dry ? max (0., hold[] + h[]) : hold[];
      eta[] = zb[] + h[];
    }
  } while (p.iterate && p.iterate());
}