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FDEMfwd.m
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function out = FDEMfwd(varargin)
% out = FDEMfwd(config, layers, cparams);
%
% FDEMfwd.m is part of the CR1Dmod forward modeling package, and contains
% the code used to calculate the response of a HCP configuration over
% 1D layered half space.
%
% Input:
% config : structure defining the configuation (generated by cr1dmod)
% layers : structure defining layer-parameters (generated by cr1dmod)
% cparams: structure defining calculation options (generated by compute)
%
% Output:
% out: structure containing the model result in terms of
% H: Total measured field
% H_prim: Primary field
%
% Written by:
% Thomas Ingeman-Nielsen
% The Arctic Technology Center, BYG
% Technical University of Denmark
% Email: [email protected]
cpu_t=cputime;
disp('Routine: FDEMfwd');
if ( nargin < 3 )
disp('A call to fdemfwd must provide three input arguments!');
return
end
% Set up structures of parameters...
ok = 0;
if ( isstruct(varargin{1}) )
config = varargin{1};
if ( isstruct(varargin{2}) )
layers = varargin{2};
if ( isstruct(varargin{3}) )
cparams = varargin{3};
ok = 1;
end % if
end % if
end % if
if ~ok
disp('Input must be structures!');
return
end % if
switch config.type
case {'HCP FDEM (HLEM)'}
out = Zdip_Hz(config, layers, cparams); % Hz field of Z directed magnetic dipole
case {'VCP'}
% not implemented yet
case {'VCA'}
% not implemented yet
end % switch
disp(['Time spent: ' num2str(cputime-cpu_t) ' s']);
% *************************************************************************
% * Code for Hz from a z-directed magnetic dipole *
% *************************************************************************
function [result] = Zdip_Hz(config, layers, cparams)
% [Hz] = Zdip_Hz(config, layers, cparams);
% Calculates the Hz from a z-directed magnetic dipole
omega = cparams.freq.*2.*pi;
mu0 = 4.*pi.*1e-7;
eps0 = 8.85418782.*1e-12;
if ~all([layers.m]==0)
sigma = 1./Z_CR(omega, [layers.rho].', [layers.tau].', ...
[layers.c].', [layers.m].');
else
sigma = 1./[layers.rho].'*ones(size(omega));
end
for r = 1:length(config.Rspac)
% Allocate memory for Hz
result(r).H = zeros(size(omega));
result(r).H_prim = zeros(size(omega));
if strcmpi(cparams.calc_type,'Quasi')
% Quasi static Halfspace response assumes also nonmagnetic first layer
% Here calculated using analytic expression
% disp('quasi+nonmag')
%z0 = i.*omega.*mu0;
%y0 = 0;
k0_sq = 0;
layers(1).mu = 0; % ensures non-magnetic first layer
y = sigma; % Permittivity of subsurface is neglected
z = i.*mu0.*([layers.mu]+1).'*omega;
k_sq = -z.*y;
FDEM_handle = @Zdip_Hz_kernel_quasi;
for k=1:max(size(omega))
result(r).H(k) = 1/(2.*pi.*k_sq(1,k).*config.Rspac(r).^5).* ...
(9 -(9 + 9.*i.*k_sq(1,k).^0.5.*config.Rspac(r) - ...
4.*k_sq(1,k).*config.Rspac(r).^2- ...
i.*k_sq(1,k).^1.5.*config.Rspac(r).^3) ...
.*exp(-i.*k_sq(1,k).^0.5.*config.Rspac(r)));
end % k
elseif layers(1).mu == 0
% Halfspace response non-magnetic first layer
% Here calculated using analytic expression
%disp('nonmag')
z0 = i.*omega.*mu0;
y0 = i.*omega.*eps0;
k0_sq = -z0.*y0;
y = sigma + i.*eps0.*[layers.eps_r].'*omega;
z = i.*mu0.*([layers.mu]+1).'*omega;
k_sq = -z.*y;
FDEM_handle = @Zdip_Hz_kernel_nonmag;
for k=1:max(size(omega))
result(r).H(k) = 1/(2.*pi.*(k_sq(1,k)-k0_sq(k)).*config.Rspac(r).^5) ...
.*( ...
(9 + 9.*i.*k0_sq(k).^0.5.*config.Rspac(r) - ...
4.*k0_sq(k).*config.Rspac(r).^2- ...
i.*k0_sq(k).^1.5.*config.Rspac(r).^3) ...
.*exp(-i.*k0_sq(k).^0.5.*config.Rspac(r)) ...
- ...
(9 + 9.*i.*k_sq(1,k).^0.5.*config.Rspac(r) - ...
4.*k_sq(1,k).*config.Rspac(r).^2- ...
i.*k_sq(1,k).^1.5.*config.Rspac(r).^3) ...
.*exp(-i.*k_sq(1,k).^0.5.*config.Rspac(r)) ...
);
end % k
else
%disp('full')
FDEM_handle = @Zdip_Hz_kernel_full;
end
if length(layers) > 1 || ...
~strcmpi(cparams.calc_type,'Quasi')
% If not homogeneous half-space, go through with hankel transform evaluation
switch cparams.hank_type
case 'NHT'
for k=1:max(size(omega))
result(r).H(k) = result(r).H(k) + (1./(4.*pi)).* ...
NJCST('J0', FDEM_handle, config.Rspac(r), ...
cparams.Seg_tol, cparams.NHT_tol, cparams.Max_seg, ...
omega(k), [layers.eps_r].'.*eps0, ...
([layers.mu].'+1).*4e-7.*pi, sigma(:,k), ...
[layers(1:end-1).thickness].');
end % k
case 'FHT'
for k=1:max(size(omega))
result(r).H(k) = result(r).H(k) + (1./(4.*pi)).* ...
FJCST('J04', config.Rspac(r), -1, 0, 0, ...
cparams.FHT_err, FDEM_handle, ...
omega(k), [layers.eps_r].'.*eps0, ...
([layers.mu].'+1).*4e-7.*pi, sigma(:,k), ...
[layers(1:end-1).thickness].');
end % k
end % switch
end % if
result(r).H_prim = 1./(4.*pi.*config.Rspac(r).^3).* ...
exp(-i.*k0_sq.^0.5.*config.Rspac(r)).*( ...
k0_sq.*config.Rspac(r).^2-i.*k0_sq.^0.5.*config.Rspac(r)-1);
end % r
% *************************************************************************
% * Kernel functions for Hz from a z-directed magnetic dipole *
% *************************************************************************
function kern = Zdip_Hz_kernel_full(lambda, varargin)
% kern = Zdip_Hz_kernel_full(lambda, omega, eps, mu, sigma, h)
%
% Kernelfunction: (1+R_TE).*lambda^3./u0
%
% This version is for the full solution!
omega = varargin{1};
eps = varargin{2};
mu = varargin{3};
sigma = varargin{4};
h = varargin{5};
lambda_sq = lambda.^2;
z0 = i.*omega.*4.*pi.*1e-7;
y0 = i.*omega.*8.85418782.*1e-12;
k0_sq = -z0.*y0;
u0 = sqrt(lambda_sq-k0_sq);
z = j.*omega.*mu;
y = sigma + i.*eps.*omega;
k_sq = -z.*y;
u = sqrt(repmat(lambda_sq,size(k_sq,1),1)-repmat(k_sq, 1, size(lambda_sq,2)));
Y = u./repmat(z,1,size(lambda,2));
Y0 = u0./z0;
gamma = 0;
if ~isempty(h)
expuh2 = exp(-2.*u(1:end-1,:).*repmat(h,1,length(lambda)));
phi = (Y(1:end-1,:)-Y(2:end,:))./(Y(1:end-1,:)+Y(2:end,:)); % = (Yn-Yn+1)/(Yn+Yn+1)
for m = length(h):-1:1
gamma = expuh2(m,:).*(gamma+phi(m,:))./(gamma.*phi(m,:)+1);
end
end
phi1 = (Y0-Y(1,:))./(Y0+Y(1,:)); % as needed in the numerator
phi1mod = (2./z0)./(Y0+Y(1,:)); % as needed in the denominator
kern = ((gamma+1).*phi1mod.*lambda.^3)./(gamma.*phi1+1); % = ((R_TE+1)/u0) *lambda
% -------------------------------------------------------------------------
function kern = Zdip_Hz_kernel_nonmag(lambda, varargin)
% kern = P_kernel(lambda, omega, eps, sigma, h)
%
% Kernelfunction: (1+R_TE).*lambda^3./u0-homhalf
%
% This version is for the nonmagnetic first layer case!
omega = varargin{1};
eps = varargin{2};
mu = varargin{3};
sigma = varargin{4};
h = varargin{5};
lambda_sq = lambda.^2;
z0 = i.*omega.*4e-7.*pi;
y0 = i.*omega.*8.85418782.*1e-12;
k0_sq = -z0.*y0;
u0 = sqrt(lambda_sq-k0_sq);
z = j.*omega.*mu;
y = sigma + i.*eps.*omega;
k_sq = -z.*y;
u = sqrt(repmat(lambda_sq,size(k_sq,1),1)-repmat(k_sq, 1, size(lambda_sq,2)));
Y = u./repmat(z,1,size(lambda,2));
%Y0 = u0./z0;
gamma = 0;
if ~isempty(h)
expuh2 = exp(-2.*u(1:end-1,:).*repmat(h,1,length(lambda)));
phi = (Y(1:end-1,:)-Y(2:end,:))./(Y(1:end-1,:)+Y(2:end,:)); % = (Yn-Yn+1)/(Yn+Yn+1)
for m = length(h):-1:1
gamma = expuh2(m,:).*(gamma+phi(m,:))./(gamma.*phi(m,:)+1);
end
end
kern = (4.*gamma.*u(1,:).*lambda.^3)./ ...
(gamma.*(k_sq(1,:)-k0_sq) + (u0+u(1,:)).^2); % = layered-homhalf
% -------------------------------------------------------------------------
function kern = Zdip_Hz_kernel_quasi(lambda, varargin)
% kern = P_kernel(lambda, omega, eps, sigma, h)
%
% Kernelfunction: (1+R_TE).*lambda^3./u0-homhalf
%
% This version is for the quasistatic nonmagnetic first layer case!
omega = varargin{1};
%eps = varargin{2};
mu = varargin{3};
sigma = varargin{4};
h = varargin{5};
lambda_sq = lambda.^2;
z0 = i.*omega.*4e-7.*pi;
% y0 = 0;
% k0_sq = -z0.*y0 = 0;
z = j.*omega.*mu;
y = sigma; % Permittivity of the ground is neglected
k_sq = -z.*y;
u = sqrt(repmat(lambda_sq,size(k_sq,1),1)-repmat(k_sq, 1, size(lambda_sq,2)));
Y = u./repmat(z,1,size(lambda,2));
%Y0 = lambda./z0;
gamma = 0;
if ~isempty(h)
expuh2 = exp(-2.*u(1:end-1,:).*repmat(h,1,length(lambda)));
phi = (Y(1:end-1,:)-Y(2:end,:))./(Y(1:end-1,:)+Y(2:end,:)); % = (Yn-Yn+1)/(Yn+Yn+1)
for m = length(h):-1:1
gamma = expuh2(m,:).*(gamma+phi(m,:))./(gamma.*phi(m,:)+1);
end
end
kern = (4.*gamma.*u(1,:).*lambda.^3)./ ...
(gamma.*k_sq(1,:) + (lambda+u(1,:)).^2); % = layered-homhalf