# # Use this function to fit sound velocity data as function of # sound propagation direction, indicated by its angle against the # z-axis of an hexagonal symmetry coordinate system # # Adjustable parameters: # # c33, c11, c13, c44 elastic moduli - materials constants # phi0 angle offset # # HBB 970522: factored out common factor 1e9 from c?? into the # function, to improve the fit convergence. Fit parameters were # just too grossly different before. rho = 1000.0 # density in kg/m3 phi(x) = (x - phi0)/360.0*2.0*pi main(x) = c11*sin(phi(x))**2 + c33*cos(phi(x))**2 + c44 mixed(x) = sqrt( ((c11-c44)*sin(phi(x))**2 \ +(c44-c33)*cos(phi(x))**2)**2 \ +(2.0*(c13+c44)*sin(phi(x))*cos(phi(x)))**2 ) vlong(x) = sqrt(1.0/2.0/rho*1e9*(main(x) + mixed(x))) vtrans(x) = sqrt(1.0/2.0/rho*1e9*(main(x) - mixed(x))) # When we read the file in, we set y=index, and we use # y in this (pseudo) 3d fit to choose an x function f(x,y) = y==1 ? vlong(x) : vtrans(x)