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prem_util.c
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prem_util.c
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/*
routines to deal with PREM earth model by Dziewonki & Anderson (1981)
$Id: prem_util.c,v 1.1 2005/10/19 22:52:57 becker Exp $
*/
#include "prem.h"
#include <math.h>
#include <stdlib.h>
/*
given a radius in ruinits and n layers at radii, find the layer index
ilayer (0...n-1) and assigns x[0...3], where
output:
x[0] = 1, x[1] = r/r_unit (nondim radius), x[2]=x[1]^2, x[3]=x[1]^3
pass r and rb in the same units, and r_unit as r0 if units are [m], else as 1
*/
int prem_find_layer_x(double r, double r_unit,double *rb,
int n,int np, double *x)
{
int i,ilayer,nm1;
//
// find layer
//
ilayer = 0;nm1=n-1;
while((rb[ilayer] < r) && (ilayer < nm1))
ilayer ++;
//
// get radii and radii to some power
//
x[0] = 1.0;
x[1] = r/r_unit;// non dimensionalize r
for(i=2;i < np;i++)
x[i] = x[i-1]*x[1]; //r^i
return ilayer;
}
/*
compute the polynomial expansion of x at y[0,...np-1] and scale by
fac. y[0] = 1, y[1]=r', y[2]=r'^2
val =
fac * (par[0]*y[0] + par[1]*y[1] + par[2]*y[2] + .. par[np-1]*y[np-1])
=
fac * (par[0]*1+ par[1]*r + par[2]*r^2 + .. par[np-1]*r^(np-1))
*/
double prem_compute_pval(double *y, double *par, int np,
double fac)
{
int i;
double val;
val = par[0];
for(i=1;i < np;i++)
val += par[i] * y[i];
val *= fac;
return val;
}
/*
compute the derivative with respect to y (r)
fac * (par[1]+ par[2]*r^1 + .. par[np-1]*r^(np-2))
*/
double prem_compute_dpval(double *y, double *par,
int np, double fac)
{
int i;
double val;
val = 0.0;
for(i=1;i < np;i++)
val += par[i] * y[i-1];
val *= fac;
return val;
}
/*
calculate the mean S velocity from the Voigt shear modulus, see eg. Dahlen and
Tromp:
\mu = 1/15(A+C-2F+5N+6L) with
\eta = F/(A-2L)
and N, L, A, C corresponding to vsh, vsv, vph, and vpv respectively
according to, e.g, A = vph^2 \rho
then
vs=sqrt(1/15((1-2\eta)vph^2 + vpv^2 +5vsh^2+(6+4\eta)vsv^2))
a simplified version without information about P and eta
vs = sqrt(1/3 * vsh^2 + 2/3 * vsv^2);
*/
double prem_vs_voigt(double vsh, double vsv, double vph, double vpv,
double eta)
{
double v;
v = sqrt((1./15.) * ( (1.0-2.0*eta) * vph*vph + vpv*vpv +
5.0*vsh*vsh +
(6.0+4.0*eta)*vsv*vsv));
return v;
}
/*
compute density and drho/dr ([kg/m^3] and [kg/m^4], resp.)
rnd is the non-dimensionalized radius
*/
void prem_get_rhodrho(double *rho, double *drhodr,
double rnd, struct prem_model *prem)
{
int ilayer,os;
double *x;
if(!prem->init){
fprintf(stderr,"prem_get_rhodrho: error, struc not init \n");
exit(-1);
}
x=(double *)
malloc(sizeof(double)*prem->np);
if(!x){fprintf(stderr,"prem_get_rhodrho:mem error\n");exit(-1);}
ilayer = prem_find_layer_x(rnd,1.0,prem->r,prem->n,prem->np,x);
os = ilayer * prem->np;
*rho = prem_compute_pval(x,(prem->crho+os),prem->np,1e3);
*drhodr = prem_compute_dpval(x,(prem->crho+os),prem->np,1e3);
free(x);
}
/*
get density in SI units [kg/m^3] at non-dim radius rnd
*/
void prem_get_rho(double *rho,double rnd,
struct prem_model *prem)
{
int ilayer,os;
double *x;
if(!prem->init){
fprintf(stderr,"prem_get_rho: error, struc not init \n");
exit(-1);
}
x=(double *)malloc(sizeof(double)*prem->np);
if(!x){
fprintf(stderr,"prem_get_rhodrho: mem error\n");
exit(-1);
}
ilayer = prem_find_layer_x(rnd,1.0,prem->r,prem->n,prem->np,x);
os = ilayer * prem->np;
*rho = prem_compute_pval(x,(prem->crho+os),prem->np,1e3);
free(x);
}
//
//
// compute several values from PREM at radius r [m]
// output of densities in kg/m^3 and velocities m/s
//
void prem_get_values(double *rho, double *vs, double *vsv, double *vsh,
double *vp, double *vpv, double *vph, double *eta,
double *qmu, double *qkappa,
double r, struct prem_model *prem)
{
int ilayer,os;
double *x;
if(!prem->init){
fprintf(stderr,"prem_get_values: error, struc not init \n");
exit(-1);
}
x=(double *)malloc(sizeof(double)*prem->np);
if(!x){fprintf(stderr,"prem_get_values:mem error\n");exit(-1);}
ilayer = prem_find_layer_x(r,prem->r0,prem->rb,prem->n,prem->np,x);
/* velocities and densities */
os = ilayer * prem->np;
/* density */
*rho = prem_compute_pval(x, (prem->crho+os),prem->np,1e3);
/* velocities */
*vp = prem_compute_pval(x,(prem->cvp+os), prem->np,1e3);
*vs = prem_compute_pval(x,(prem->cvs+os), prem->np,1e3);
*vpv = prem_compute_pval(x,(prem->cvpv+os),prem->np,1e3);
*vph = prem_compute_pval(x,(prem->cvph+os),prem->np,1e3);
*vsv = prem_compute_pval(x,(prem->cvsv+os),prem->np,1e3);
*vsh = prem_compute_pval(x,(prem->cvsh+os),prem->np,1e3);
/* anisotropy ellipticity factor */
*eta = prem_compute_pval(x,(prem->ceta+os),prem->np,1.0);
/* q factors */
*qmu = prem_compute_pval(x, (prem->cqmu +ilayer),1,1.0);
*qkappa = prem_compute_pval(x,(prem->cqkappa+ilayer),1,1.0);
free(x);
}
/*
read in a PREM type model of Earth structure for velocities and densities
for format, see example below and comments. n= number of layers,
most parameters p1, p2 ... have three coefficients, the last two
(q factors) only one
returns error code
*/
int prem_read_model(char *filename,struct prem_model *prem,
hc_boolean verbose)
{
int i,rcnt;
FILE *in;
rcnt = 0;
sprintf(prem->model_filename,"%s",filename);
in=fopen(filename,"r");
if(!in){
fprintf(stderr,"prem_read_model: error: can't open model file %s\n",filename);
return 1;
}
rcnt += fscanf(in,"%i",&prem->n);// nr layers
rcnt += fscanf(in,"%i",&prem->np);// nr of coeff for most parameters
if(prem->n > PREM_N){
fprintf(stderr,"prem_read_model: error: read %i layers from file %s but max is %i\n",
prem->n,filename,PREM_N);
fprintf(stderr,"prem_read_model: increase PREM_N\n");
return 2;
}
if(prem->np > PREM_NP){
fprintf(stderr,"prem_read_model: error: read %i parameters from file %s but max is %i\n",
prem->np,filename,PREM_NP);
fprintf(stderr,"prem_read_model: increase PREM_NP\n");
return 3;
}
rcnt += fscanf(in,PREM_F_STRING,&prem->r0); // read top level
/*
upper layer boundary radii in [m]
*/
rcnt += prem_read_para_set(prem->rb,prem->n,1,in);
for(i=0;i < prem->n;i++) /* non dim version */
prem->r[i] = prem->rb[i]/prem->r0;
if(rcnt != 3+prem->n){
fprintf(stderr,"prem_read_model: read error: after layer input\n");
return 4;
}
/* for each parameter, read in four polynomial coefficients for each
layer */
/*
we expect the velocities to be in km/s and the densities in
g/cm^3
*/
rcnt += prem_read_para_set(prem->crho,prem->n,prem->np,in);
rcnt += prem_read_para_set(prem->cvp,prem->n,prem->np,in);
rcnt += prem_read_para_set(prem->cvs,prem->n,prem->np,in);
if(rcnt != 3+prem->n+3*prem->np*prem->n){
fprintf(stderr,"prem_read_model: read error: after vp/vs/rho: %i\n",
rcnt);
return 5;
}
rcnt += prem_read_para_set(prem->cvpv,prem->n,prem->np,in);
rcnt += prem_read_para_set(prem->cvph,prem->n,prem->np,in);
rcnt += prem_read_para_set(prem->cvsv,prem->n,prem->np,in);
rcnt += prem_read_para_set(prem->cvsh,prem->n,prem->np,in);
rcnt += prem_read_para_set(prem->ceta,prem->n,prem->np,in);
if(rcnt != 3+prem->n+8*prem->np*prem->n){
fprintf(stderr,"prem_read_model: read error: after anisotropic parameters\n");
exit(-1);
}
/*
Q factors only are constant, only one parameter
*/
for(i=0;i< prem->n;i++){// Q_mu
rcnt += fscanf(in,PREM_F_STRING,&prem->cqmu[i]);
if(fabs(prem->cqmu[i] - 1e10) < 1e-3){ /* == 1e10 */
#ifdef DBL_MAX
prem->cqmu[i] = DBL_MAX;
#else
prem->cqmu[i] = 3.40282347E+38;
#endif
}
}
rcnt += prem_read_para_set(prem->cqkappa,prem->n,1,in);
fclose(in);
if(rcnt != 3 + prem->n+ 8*prem->np*prem->n + 2 * prem->n){
fprintf(stderr,"prem_read_model: read error: after Q factors\n");
return 6;
}
prem->init = TRUE;
if(verbose)
fprintf(stderr,"prem_read_model: initialized PREM model from file %s\n",
filename);
return 0;
}
/*
read in a set of np parameters for n layers
*/
int prem_read_para_set(double *par, int n, int np,FILE *in)
{
int i,j,rc,os;
rc=0;
for(i=os=0;i<n;i++,os+=np)
for(j=0;j<np;j++)
rc += fscanf(in,PREM_F_STRING,(par+os+j));
return rc;
}
/*
the following comment block holds the prem.dat file, for clarification
note that radii are given in [m]
this is the transversely isotropic version of PREM with the ocean
layer
*/
/*
13 4
6371000.
1221500. 3480000. 3630000. 5600000. 5701000. 5771000.
5971000. 6151000. 6291000. 6346600. 6356000. 6368000.
6371000.
13.0885 0.0000 -8.8381 0.0000
12.5815 -1.2638 -3.6426 -5.5281
7.9565 -6.4761 5.5283 -3.0807
7.9565 -6.4761 5.5283 -3.0807
7.9565 -6.4761 5.5283 -3.0807
5.3197 -1.4836 0.0000 0.0000
11.2494 -8.0298 0.0000 0.0000
7.1089 -3.8045 0.0000 0.0000
2.6910 0.6924 0.0000 0.0000
2.6910 0.6924 0.0000 0.0000
2.9000 0.0000 0.0000 0.0000
2.6000 0.0000 0.0000 0.0000
1.0200 0.0000 0.0000 0.0000
11.2622 0.0000 -6.3640 0.0000
11.0487 -4.0362 4.8023 -13.5732
15.3891 -5.3181 5.5242 -2.5514
24.9520 -40.4673 51.4832 -26.6419
29.2766 -23.6027 5.5242 -2.5514
19.0957 -9.8672 0.0000 0.0000
39.7027 -32.6166 0.0000 0.0000
20.3926 -12.2569 0.0000 0.0000
4.1875 3.9382 0.0000 0.0000
4.1875 3.9382 0.0000 0.0000
6.8000 0.0000 0.0000 0.0000
5.8000 0.0000 0.0000 0.0000
1.4500 0.0000 0.0000 0.0000
3.6678 0.0000 -4.4475 0.0000
0.0000 0.0000 0.0000 0.0000
6.9254 1.4672 -2.0834 0.9783
11.1671 -13.7818 17.4575 -9.2777
22.3459 -17.2473 -2.0834 0.9783
9.9839 -4.9324 0.0000 0.0000
22.3512 -18.5856 0.0000 0.0000
8.9496 -4.4597 0.0000 0.0000
2.1519 2.3481 0.0000 0.0000
2.1519 2.3481 0.0000 0.0000
3.9000 0.0000 0.0000 0.0000
3.2000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
11.2622 0.0000 -6.3640 0.0000
11.0487 -4.0362 4.8023 -13.5732
15.3891 -5.3181 5.5242 -2.5514
24.9520 -40.4673 51.4832 -26.6419
29.2766 -23.6027 5.5242 -2.5514
19.0957 -9.8672 0.0000 0.0000
39.7027 -32.6166 0.0000 0.0000
20.3926 -12.2569 0.0000 0.0000
0.8317 7.2180 0.0000 0.0000
0.8317 7.2180 0.0000 0.0000
6.8000 0.0000 0.0000 0.0000
5.8000 0.0000 0.0000 0.0000
1.4500 0.0000 0.0000 0.0000
11.2622 0.0000 -6.3640 0.0000
11.0487 -4.0362 4.8023 -13.5732
15.3891 -5.3181 5.5242 -2.5514
24.9520 -40.4673 51.4832 -26.6419
29.2766 -23.6027 5.5242 -2.5514
19.0957 -9.8672 0.0000 0.0000
39.7027 -32.6166 0.0000 0.0000
20.3926 -12.2569 0.0000 0.0000
3.5908 4.6172 0.0000 0.0000
3.5908 4.6172 0.0000 0.0000
6.8000 0.0000 0.0000 0.0000
5.8000 0.0000 0.0000 0.0000
1.4500 0.0000 0.0000 0.0000
3.6678 0.0000 -4.4475 0.0000
0.0000 0.0000 0.0000 0.0000
6.9254 1.4672 -2.0834 0.9783
11.1671 -13.7818 17.4575 -9.2777
22.3459 -17.2473 -2.0834 0.9783
9.9839 -4.9324 0.0000 0.0000
22.3512 -18.5856 0.0000 0.0000
8.9496 -4.4597 0.0000 0.0000
5.8582 -1.4678 0.0000 0.0000
5.8582 -1.4678 0.0000 0.0000
3.9000 0.0000 0.0000 0.0000
3.2000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
3.6678 0.0000 -4.4475 0.0000
0.0000 0.0000 0.0000 0.0000
6.9254 1.4672 -2.0834 0.9783
11.1671 -13.7818 17.4575 -9.2777
22.3459 -17.2473 -2.0834 0.9783
9.9839 -4.9324 0.0000 0.0000
22.3512 -18.5856 0.0000 0.0000
8.9496 -4.4597 0.0000 0.0000
-1.0839 5.7176 0.0000 0.0000
-1.0839 5.7176 0.0000 0.0000
3.9000 0.0000 0.0000 0.0000
3.2000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
1.0000 0.0000 0.0000 0.0000
1.0000 0.0000 0.0000 0.0000
1.0000 0.0000 0.0000 0.0000
1.0000 0.0000 0.0000 0.0000
1.0000 0.0000 0.0000 0.0000
1.0000 0.0000 0.0000 0.0000
1.0000 0.0000 0.0000 0.0000
1.0000 0.0000 0.0000 0.0000
3.3687 -2.4778 0.0000 0.0000
3.3687 -2.4778 0.0000 0.0000
1.0000 0.0000 0.0000 0.0000
1.0000 0.0000 0.0000 0.0000
1.0000 0.0000 0.0000 0.0000
84.6
1e10
312
312
312
143
143
143
80
600
600
600
1e10
1327.7
57823
57823
57823
57823
57823
57823
57823
57823
57823
57823
57823
57823
*/