% *****************************************************************
% *** Depth estimation of dike-like magnetic bodies             ***
% *** Coded by Yunus Levent Ekinci June 2016                    ***
% *** Tested using Matlab R2012b under Windows 8.1              ***
% *** Method of Abdelrahman and Abo-Ezz (2001)                  ***
% *** Geophysics, 66 (1), 205-212                               ***
% *****************************************************************
% *** ylekinci@beu.edu.tr                                       ***
% *** ylekinci@yahoo.com                                        ***
% *** http://pbs.beu.edu.tr/ylekinci                            ***
% *** Bitlis Eren University                                    ***
% *****************************************************************
% Inputs;                                                       ***
% e     ; two-column data set                                   ***
% x     ; horizontal distances of the observation points        ***
% Tt    ; magnetic anomaly                                      ***
% unit  ; sampling interval (default:1)                         ***
% smax  ; maximum number of the graticule spacings (default:5)  ***
% *****************************************************************
% Outputs;                                                      ***
% results.out : A text file showing the computed depths         ***
% *****************************************************************

close all;
clear all;
clc;
[filename,pathname] = uigetfile({'*.dat','Select the data file'});
e=[pathname filename];
data=load(e);
x=data(:,1);
Tt=data(:,2);
prompt = {'Enter the sampling interval in meter:',...
    'Enter the maximum number of the graticule spacing:'};
dlg_title = 'Input values';
num_lines=1;
def={'1','5'};
answer = inputdlg(prompt,dlg_title,num_lines,def);
unit=str2double(answer(1));
smax=str2double(answer(2));
subplot(221),plot(data(:,1),data(:,2),'-o',...
    'MarkerEdgeColor','r',...
    'MarkerFaceColor','r',...
    'MarkerSize',3);
xlim([min(x) max(x)]);
ylim('manual');
hold on
xlabel('x in units');
ylabel(texlabel('nT'));
str2 = datestr(now,'HH:MM:SS');
s=[2:smax];
err=1e-5;

% Second-Order Horizontal Derivatives Computation Using Graticule Spacings

for j=1:1:length(s)
    T2=[];
    if j==1; col=[0 0 0];elseif j==2; col=[0 0 1];
    elseif j==3; col=[1 0 0];elseif j==4; col=[0 0.5 0];
    elseif j==5; col=[0.75 0 0.75];end
    for i=1+2*s(j):1:length(Tt)-2*s(j)
        T2a=Tt(i+(2*s(j)));
        T2b=2*Tt(i);
        T2c=Tt(i-(2*s(j)));
        T2(:,i)=(T2a-T2b+T2c)./(4*(s(j)^2));
    end
    ax=-((length(T2(find(T2~=0)))-1)/2):((length(T2(find(T2~=0)))-1)/2);
    subplot(222)
    plot(ax,(T2(find(T2~=0))),'Color',[col]);
    xlim([min(x) max(x)]);
    hold on
    xlabel('x in units');
    ylabel(texlabel('nT / unit ^2'));
    z=0.1;
    iter_min=0;
    iter_max=50;
    
    % Computing Depths via Nonlinear Equations
    
    while iter_min<iter_max
        iter_min=iter_min+1;
        FF=((length(T2(find(T2~=0))))+1)/2;
        A=(T2(find(T2~=0)));
        F=(A(FF-s(j))+A(FF+s(j)))/A(FF);
        up1=F*(9*(s(j)^2)+(z^2));
        up2=(s(j)^2)+(z^2);
        up3=z^3;
        up4=z*(4*(s(j).^2)+(z^2));
        down1=(4*(s(j)^2))+(z^2);
        down2=(s(j)^2)+(z^2);
        down3=z;
        down4=(9*(s(j)^2))+(z^2);
        down5=z;
        za=up1*up2*(up3-up4);
        zb=down1*((down2*down3)-(down4*down5));
        zz=sqrt(za/zb);
        n_iter2(j)=iter_min;
        if (zz-z)<err
            iter_min=iter_max;
        end
        z=zz;
    end
    z2(j)=z;
end

% Third-Order Horizontal Derivatives Computation Using Graticule Spacings

for j=1:1:length(s)
    T3=[];
    if j==1; col=[0 0 0];elseif j==2; col=[0 0 1];
    elseif j==3; col=[1 0 0];elseif j==4; col=[0 0.5 0];
    elseif j==5; col=[0.75 0 0.75];end
    for i=1+3*s(j):1:length(Tt)-3*s(j)
        T3a=Tt(i+(3*s(j)));
        T3b=3*Tt(i+s(j));
        T3c=3*Tt(i-s(j));
        T3d=Tt(i-(3*s(j)));
        T3(:,i)=(T3a-T3b+T3c-T3d)./(8*(s(j)^3));
    end
    ax=-((length(T3(find(T3~=0)))-1)/2):((length(T3(find(T3~=0)))-1)/2);
    subplot(223)
    plot(ax,(T3(find(T3~=0))),'Color',[col]);
    xlim([min(x) max(x)]);
    hold on
    xlabel('x in units');
    ylabel(texlabel('nT / unit ^3'));
    z=0.1;
    iter_min=0;
    iter_max=50;
    
    % Computing Depths via Nonlinear Equations
    
    while iter_min<iter_max
        iter_min=iter_min+1;
        FF=((length(T3(find(T3~=0))))+1)/2;
        A=(T3(find(T3~=0)));
        F=(A(FF-s(j))+A(FF+s(j)))/A(FF);
        A1=3*F*(4*(s(j)^2)+(z^2));
        A2=(16*(s(j)^2)+(z^2));
        A3=4*(9*(s(j)^2)+(z^2));
        B1=(s(j)^2)+(z^2);
        B2=(9*(s(j)^2)+(z^2));
        B3=(4*(s(j)^2)+(z^2));
        B4=(16*(s(j)^2)+(z^2));
        zz1a=(A1*A2)/A3;
        zz1b=(((B1-B2)/(B3-B4)));
        zz=sqrt(zz1a*zz1b-(s(j)^2));
        n_iter3(j)=iter_min;
        if (zz-z)<err
            iter_min=iter_max;
        end
        z=zz;
    end
    z3(j)=z;
end

% Fourth-Order Horizontal Derivatives Computation Using Graticule Spacings

for j=1:1:length(s)
    T4=[];
    if j==1; col=[0 0 0];elseif j==2; col=[0 0 1];
    elseif j==3; col=[1 0 0];elseif j==4; col=[0 0.5 0];
    elseif j==5; col=[0.75 0 0.75];end
    for i=1+4*s(j):1:length(Tt)-4*s(j)
        T4a=Tt(i+(4*s(j)));
        T4b=4*Tt(i+2*s(j));
        T4c=6*Tt(i);
        T4d=4*Tt(i-2*s(j));
        T4e=Tt(i-(4*s(j)));
        T4(:,i)=(T4a-T4b+T4c-T4d+T4e)./(16*(s(j)^4));
    end
    ax=-((length(T4(find(T4~=0)))-1)/2):((length(T4(find(T4~=0)))-1)/2);
    subplot(224)
    plot(ax,(T4(find(T4~=0))),'Color',[col]);
    xlim([min(x) max(x)]);
    hold on
    xlabel('x in units');
    ylabel(texlabel('nT / unit ^4'));
    z=0.1;
    iter_min=0;
    iter_max=50;
    
    % Computing Depths via Nonlinear Equations
    
    while iter_min<iter_max
        iter_min=iter_min+1;
        W1=(z^2)*(4*(s(j)^2)+(z^2));
        W2=z;
        W3=4*(z^2)*(16*(s(j)^2)+(z^2));
        W4=z;
        W5=3*z*((16*(s(j)^2))+(z^2));
        W6=4*(s(j)^2)+(z^2);
        W7=16*(s(j)^2)+(z^2);
        W8=4*(s(j)^2)+(z^2);
        W=((W1*W2)-(W3*W4)+(W5*W6))/(W7*W8);
        L1=2*z;
        L2=3*z;
        L3=z;
        L4=(s(j)^2)+(z^2);
        L5=(9*(s(j)^2))+(z^2);
        L6=(25*(s(j)^2))+(z^2);
        L=(L1/L4)-(L2/L5)+(L3/L6);
        FF=((length(T4(find(T4~=0))))+1)/2;
        A=(T4(find(T4~=0)));
        F=(A(FF-s(j))+A(FF+s(j)))/A(FF);
        zz=sqrt((F*W)/L);
        n_iter4(j)=iter_min;
        if (zz-z)<err
            iter_min=iter_max;
        end
        z=zz;
    end
    z4(j)=z;
end

% Printing results including depths, iteration numbers and standard deviations
% results.out is compatible with notepad

str1 = date;
str3 = datestr(now,'HH:MM:SS');
fid = fopen('results.out','w');
fprintf(fid,'%6s\r\n','Depth Estimation from Higher-Order Horizontal');
fprintf(fid,'%6s\r\n','  Derivatives of Magnetic Profile Datasets');
fprintf(fid,'%6s\r\n','   Coded by Yunus Levent Ekinci June 2016');
fprintf(fid,'%6s\r\n','');
fprintf(fid,'%6s\r\n',str1);
fprintf(fid,'%6s\r\n','');
fprintf(fid,'%6s %6s\r\n','Analysed Data  : ',filename);
fprintf(fid,'%6s\r\n','');
fprintf(fid,'%6s %6s\r\n','start   : ',str2);
fprintf(fid,'%6s %6s\r\n','finish  : ',str3);
fprintf(fid,'%6s\r\n','');
fprintf(fid,'%6s\r\n','----------------------------------------');
fprintf(fid,'%6s\r\n','------------ Depths in unit ------------');
fprintf(fid,'%6s %14s %14s %14s\r\n','2nd Derv.','3rd Derv.','4th Derv.','s values');
for i=1:length(s)
    fprintf(fid,'%6.2f %14.2f %14.2f %14.0f\r\n',z2(i),z3(i),z4(i),s(i));
end
fprintf(fid,'%6s\r\n','----------------------------------------');
fprintf(fid,'%6s\r\n','------------ Depths in meter -----------');
fprintf(fid,'%6s %14s %14s %14s\r\n','2nd Derv.','3rd Derv.','4th Derv.','s values');
for i=1:length(s)
    fprintf(fid,'%6.2f %14.2f %14.2f %14.0f\r\n',z2(i)*unit,z3(i)*unit,z4(i)*unit,s(i));
end
fprintf(fid,'%6s\r\n','----------------------------------------');
fprintf(fid,'%6s\r\n','--------- Number of iterations ---------');
fprintf(fid,'%6s %14s %14s %14s\r\n','2nd Derv.','3rd Derv.','4th Derv.','s values');
for i=1:length(s)
    fprintf(fid,'%5.0f %14.0f %14.0f %15.0f\r\n',n_iter2(i),n_iter3(i),n_iter4(i),s(i));
end
fprintf(fid,'%6s\r\n','----------------------------------------');
fprintf(fid,'%6s\r\n','-------- Average depths in unit --------');
fprintf(fid,'%6s %14s %14s\r\n','2nd Derv.','3rd Derv.','4th Derv.');
fprintf(fid,'%6.2f %14.2f %14.2f\r\n',mean(z2),mean(z3),mean(z4));
fprintf(fid,'%6s\r\n','----------------------------------------');
fprintf(fid,'%6s\r\n','-------- Average depths in meter -------');
fprintf(fid,'%6.2f %14.2f %14.2f\r\n',mean(z2)*unit,mean(z3)*unit,mean(z4)*unit);
fprintf(fid,'%6s\r\n','----------------------------------------');
fprintf(fid,'%6s\r\n','---------- Standard Deviations ---------');
fprintf(fid,'%6.2f %14.2f %14.2f\r\n',std((z2)*unit),std((z3)*unit),std((z4)*unit));
fclose(fid)