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Implementation of Love surface waves. More...
#include <Love.h>
Public Member Functions | |
| double | ellipticity () |
| Love (const Seismic1DModel *model) | |
| const Seismic1DModel * | model () const |
| void | setOmega (double o) |
| double | y (double slowness) |
Implementation of Love surface waves.
It is a layered model able to calculate the roots corresponding to the theoretical Love dispersion curve.
| QGpCoreWave::Love::Love | ( | const Seismic1DModel * | model | ) | [inline] |
{_model=model;}
| double QGpCoreWave::Love::ellipticity | ( | ) | [inline] |
Useless for Love case
{return 0;}
| const Seismic1DModel* QGpCoreWave::Love::model | ( | ) | const [inline] |
{return _model;}
| void QGpCoreWave::Love::setOmega | ( | double | o | ) | [inline] |
Referenced by QGpCoreWave::ModalCurve::determinantMisfit(), DispersionReader::parse(), and QGpCoreWave::LoveFunction::value().
{_omega=o;}
| double QGpCoreWave::Love::y | ( | double | slowness | ) |
Computation of the Love function whose roots are located at the Love dispersion curves.
References QGpCoreTools::cos(), QGpCoreTools::exp(), QGpCoreWave::Seismic1DModel::h(), QGpCoreWave::Seismic1DModel::layerCount(), QGpCoreWave::Seismic1DModel::mu(), QGpCoreWave::Seismic1DModel::rho(), QGpCoreTools::sin(), QGpCoreWave::Seismic1DModel::slowS(), QGpCoreTools::sqrt(), and TRACE.
Referenced by QGpCoreWave::ModalCurve::determinantMisfit(), DispersionReader::parse(), and QGpCoreWave::LoveFunction::value().
{
TRACE;
register int i=_model->layerCount()-1;
// slowness is the inverse of V_L, the Love velocity
double k=_omega*slowness;
// inverse of V_s
double slowS=_model->slowS(i);
// Wave number for S waves
double ks=_omega*slowS;
double nu=sqrt(fabs(k*k-ks*ks));
double l21=_model->rho(i)*nu;
double l22=slowS*slowS;
double g11, sinq, g12, g21, q, mui, numui;
for(i--;i>=0;i--) {
slowS=_model->slowS(i);
ks=_omega*slowS;
nu=sqrt(fabs(k*k-ks*ks));
q=_model->h(i)*nu; // Q is always positive
mui=_model->mu(i);
numui=nu*mui;
if(k<ks) {
g11=cos(q); //=g22
sinq=sin(q);
g12=sinq/numui;
g21=-numui*sinq; // minus sign comes from i*i=-1
}
else if(k==ks) {
g11=1; //=g22
g12=_model->h(i)/mui;
g21=0;
}
else {
double fac=0;
if(q<21.2) fac=exp(-2.0*q); /* min significative number is 1e-19
19/2 *ln(10)=21.2, 0.0<fac<1.0 */
g11=(1.0+fac)*0.5; //=g22 0.5<g11<2
sinq=(1.0-fac)*0.5; // 0<sinq<0.5
g12=sinq/numui; // 0<g12<0.5/numui
g21=numui*sinq; // 0<g21<numui*0.5
}
/* Normalization (we can multiply both elements by any constant factor,
the root will be unchanged) to avoid possible overflow. */
double l21n=l21*g11+l22*g21;
double l22n=l21*g12+l22*g11;
double maxL=fabs(l21n);
if(fabs(l22n)>maxL) maxL=fabs(l22n);
if(maxL>1.0e5) {
maxL=1.0e5/maxL;
l21=l21n*maxL;
l22=l22n*maxL;
}
else {
l21=l21n;
l22=l22n;
}
}
return l21;
}
