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dcgsafwd.m
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function [result] = dcgsafwd(varargin)
% [result] = dcgsafwd(config, layers, cparams);
%
% dcgsafwd.m is part of the CR1Dmod forward modeling package, and contains
% the code used to calculate the DC response of electrode arrays on the surface
% of a 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:
% result: structure containing the calculated responses as well
% as information on the configuration, such as the
% geometric factor.
%
%
% Example of usage:
%
% Calculate the response from a Vertical Electrical Sounding of the
% Schlumberger type. The ground is two-layer model with the
% parameters rho_1 = 100 Ohm.m, h1 = 10 m, rho_2 = 30 Ohm.m.
% Electrode separations (OA) are logspace(0,2,21), MN distance is 0.2 m.
%
% % Setup input structures:
%
% config.type = 'Schlumberger'; % Electrode configuration
% config.OA = logspace(0,2,21); % Current electrode spacings
% config.OM = 0.1; % Half potential electrode spacing
%
% layers(1).depth_to_top = 0; % Layer 1 depth-to-top of layer
% layers(1).thickness = 10; % Layer 1 thickness
% layers(1).rho = 100; % Layer 1 resistivity
% layers(2).depth_to_top = 10; % Layer 2 depth-to-top of layer
% layers(2).thickness = Inf; % Layer 2 thickness (use Inf for bottom layer)
% layers(2).rho = 30; % Layer 1 resistivity
%
% cparams.domain = 'DC'; % Toggles DC calculation
% cparams.hank_type = 'FHT'; % Choose Fast Hankel Transform using
% % digital filters, 'NHT' chooses
% % numerical integration scheme
% cparams.FHT_err = 1.0000e-008; % Tolerance of Fast Hankel Transform.
%
% % Only needed for Numerical Hankel Transform integration:
%
% cparams.Seg_tol = 1e-6; % Tolerance on each segment of the integration
% cparams.NHT_tol = 1e-5; % Tolerance on the sum of the series
% cparams.Max_seg = 100; % Maximum number of segments to sum
%
% % Run forward calculation:
%
% result = dcgsafwd(config,layers,cparams);
% loglog([result.OA],[result.Z].*[result.G_factor]);
% ylim([10,100])
%
%
%
%
% Updated 2010-12-09 to handle an array of config structure parameters
% ( config(1:x) ) for the General Surface Array. This change is not tested yet.
%
% Written by:
% Thomas Ingeman-Nielsen
% The Arctic Technology Center, BYG
% Technical University of Denmark
% Email: [email protected]
cpu_t=cputime;
disp('Routine: DCgsafwd');
if nargin < 3
disp('Not enough input parameters');
return
else
config = varargin{1};
layers = varargin{2};
cparams = varargin{3};
end
h = [layers.thickness]; h(end) = [];
config.r = [];
% setup config structure
switch config.type
case {'Dipole-Dipole'}
for k = 1:length(config(1,1).Aspac)
for m = 1:length(config(1,1).Nspac)
config(k,m) = config(1,1);
config(k,m) = config(1,1);
config(k,m).C1 = [-config(k,m).Aspac(k)-...
0.5*config(k,m).Aspac(k)*config(k,m).Nspac(m) 0 0]; % transmitter dipole C1 a C2 P1 a P2
config(k,m).C2 = [config(k,m).C1(1)+...
config(k,m).Aspac(1) 0 0]; % transmitter dipole o------o o------o
config(k,m).P1 = [config(k,m).C2(1)+... % receiver dipole Tx n*a Rx
config(k,m).Nspac(m)*config(k,m).Aspac(k) 0 0];
config(k,m).P2 = [config(k,m).P1(1)+... % receiver dipole
config(k,m).Aspac(k) 0 0];
result(k,m).Aspac = config(k,m).Aspac(k);
result(k,m).Nspac = config(k,m).Nspac(m);
if result(k,m).Aspac == 0 || result(k,m).Nspac == 0
result(k,m).skip = 1;
else
result(k,m).skip = 0;
config(k,m).r = sqrt(sum(([ ... % calculate distance between electrodes
config(k,m).P2-config(k,m).C2; ...
config(k,m).P2-config(k,m).C1; ...
config(k,m).P1-config(k,m).C2; ...
config(k,m).P1-config(k,m).C1]).^2,2));
result(k,m).G_factor = 2*pi*(1/config(k,m).r(1)- ...
1/config(k,m).r(2)-1/config(k,m).r(3)+ ...
1/config(k,m).r(4))^(-1);
end % if
end % m
end % k
case {'Wenner'}
for k = 1:length(config(1,1).Aspac)
config(k) = config(1);
config(k).C1 = [-1.5.*config(k).Aspac(k) 0 0]; % transmitter electrode C1 P1 P2 C2
config(k).C2 = [1.5.*config(k).Aspac(k) 0 0]; % transmitter electrode o------o------o------o
config(k).P1 = [-0.5.*config(k).Aspac(k) 0 0]; % receiver electrode a a a
config(k).P2 = [0.5.*config(k).Aspac(k) 0 0]; % receiver electrode
result(k).Aspac = config(k).Aspac(k);
if result(k).Aspac == 0
result(k).skip = 1;
else
result(k).skip = 0;
config(k).r = sqrt(sum(([ ... % calculate distance between electrodes
config(k).P2-config(k).C2; ...
config(k).P2-config(k).C1; ...
config(k).P1-config(k).C2; ...
config(k).P1-config(k).C1]).^2,2));
result(k).G_factor = 2*pi*(1/config(k).r(1)- ...
1/config(k).r(2)-1/config(k).r(3)+ ...
1/config(k).r(4))^(-1);
end % if
end % k
case {'Schlumberger'}
for k = 1:length(config(1,1).OA)
for m = 1:length(config(1,1).OM)
config(k,m) = config(1,1);
config(k,m).C1 = [-config(k,m).OA(k) 0 0]; % transmitter electrode C1 P1 P2 C2
config(k,m).C2 = [config(k,m).OA(k) 0 0]; % transmitter electrode o--------o---o--------o
config(k,m).P1 = [-config(k,m).OM(m) 0 0]; % receiver electrode | OA |
config(k,m).P2 = [config(k,m).OM(m) 0 0]; % receiver electrode OM| |
result(k,m).OA = config(k,m).OA(k);
result(k,m).OM = config(k,m).OM(m);
if result(k,m).OA == result(k,m).OM
result(k,m).skip = 1;
else
result(k,m).skip = 0;
config(k,m).r = sqrt(sum(([ ... % calculate distance between electrodes
config(k,m).P2-config(k,m).C2; ...
config(k,m).P2-config(k,m).C1; ...
config(k,m).P1-config(k,m).C2; ...
config(k,m).P1-config(k,m).C1]).^2,2));
result(k,m).G_factor = 2*pi*(1/config(k,m).r(1)- ...
1/config(k,m).r(2)-1/config(k,m).r(3)+ ...
1/config(k,m).r(4))^(-1);
end % if
end % m
end % k
otherwise
for k=1:length(config)
config(k).r = sqrt(sum(([ ... % calculate distance between electrodes
config(k).P2-config(k).C2; ...
config(k).P2-config(k).C1; ...
config(k).P1-config(k).C2; ...
config(k).P1-config(k).C1]).^2,2));
if any(config(k).r) == 0
result(k).skip = 1;
else
result(k).skip = 0;
result(k).G_factor = 2*pi*(1/config(k).r(1)- ...
1/config(k).r(2)-1/config(k).r(3)+ ...
1/config(k).r(4))^(-1);
result(k).Z = [];
end
end % k
end
r = unique([config.r]);
if isfinite(layers(1).thickness)
% Do the calculations
Q = Q_DC(r, [layers.rho], h, cparams);
% Distribute results
for k = 1:prod(size(config))
if ~result(k).skip
result(k).Z = Q(r==config(k).r(1)) - ...
Q(r==config(k).r(2)) - ...
Q(r==config(k).r(3)) + ...
Q(r==config(k).r(4));
else
result(k).Z = NaN;
result(k).G_factor = 1;
end % if
end % k
else
% Distribute results
for k = 1:prod(size(config))
if ~result(k).skip
result(k).Z = layers(1).rho./result(k).G_factor;
else
result(k).Z = NaN;
result(k).G_factor = 1;
end % if
end % k
end % if
if length(config) == 1
disp(['Resistivity: ' num2str(result.Z.*result.G_factor) ' Ohmm']);
end
disp(['Time spent: ' num2str(cputime-cpu_t) ' s']);
% ******************************************************
% * Subfunctions *
% ******************************************************
% ------------------------------------------------------
function Q = Q_DC(r, rho, h, cparams)
K = zeros(size(r));
for k = 1:length(r)
if strcmpi(cparams.hank_type,'NHT')
K(k) = NJCST('J0', @K_DC, r(k), cparams.Seg_tol, cparams.NHT_tol,...
cparams.Max_seg, 1./rho, h);
else
K(k) = FJCST('J02', r(k), -1, 0, 1, cparams.FHT_err, @K_DC, ...
1./rho, h);
end % if
end % k
%Q = rho(1)./(2.*pi).*(1./r.' + K);
Q = rho(1)./(2.*pi).*(1./r + K);
% ------------------------------------------------------
function Out = K_DC(lambda, sigma, d)
K = ones(size(d,2)+1,length(lambda));
for k = length(d):-1:1
K(k,:) = (K(k+1,:)+sigma(k+1)/sigma(k).*tanh(lambda.*d(k)))./ ...
(sigma(k+1)/sigma(k)+K(k+1,:).*tanh(lambda.*d(k)));
end
Out = K(1,:)-1;