function velocity = multi_layer(vs)
% Input file for example 1 without thickness estimation (NumExample1_Vs.m),
% and rayleigh.m. In this Example experimental phase velocities are 
% inverted to estimate only shear wave velocities.
%
% Authors: Morteza Zarrabi and Shahram Pezeshk
% Department of Civil Engineering 
% The University of Memphis
% Spring 2004 
%
% This program is associated with the Following publications: 
% Pezeshk, S., and M. Zarrabi (2005). A new inversion procedure for 
% spectral analysis of surface waves using agenetic algorithm, Bull. Seism. 
% Soc. Am. 95(5), 1801-1808.; and Morteza Zarrabi (2006). Ph.D. 
% Dissertation, the University of Memphis.
% For more information please visit http://umdrive.memphis.edu/mzarrabi/www
%
% In this example a soft layer is sandwiched between two stiffer layers!
%
% Vectors of layer thickness, mass densities, compression wave 
% velocities, and frequencies.
  thk = [5 10 10]; %For 3 Layers in meters
  dns = [1.8 1.8 1.8 1.8];
% vs_sim = [500 400 500 600]; %The simulated shear wave velocities

  vp = 2.0*vs;

% Vector of frequencies (in Hz)
  freq = linspace(5,100,50);

% Vector of offsets from the source
  offsets = linspace(5,100,20);

% Amplitude and orientation (in radians) of the source 
  Fx = 0; Fy = 0; Fz = 1;
  Phi = 0;

% Depth of the source and receivers
  s_depth = 0;
  r_depth = 0;

% Call rayleigh.m to solve the eigenvalue problem and calculate phase
% velocities, displacement-stress functions, and surface wave displacements
  [vr] = rayleigh(thk,dns,vp,vs,freq);
  velocity = vr(:,1);