function [TOTAL9403]=Mogi_Hekla_94_03(VCh94_03,dpth94_03);
% Program written by: Stephanie
Scheiber
% Date: 2007-2008
% Input and output values: Volume
change (VCh94_03) and depth (dpth94_03)
% of Hekla
source; Rate of deformation at each site (TOTAL9403,horizontal
% deformation is the component
parallel to spreading (N78W))
% Reference: Mogi, K. (1958).
"Relations between the eruptions of various
% volcanoes and the deformations of
the ground surfaces around them."Bull
% of Earthquake Research Institute
36: 99-134.
% Description: Horizontal and
vertical displacements and rates (for 1994-
% 2003) over a Mogi source
% User inputted values
VChange=VCh94_03; % Volume Change (km3)
depth=dpth94_03; % Chamber depth (km)
rdist=108; % Length of grid area (km)
sspace=200; % Grid spacing (km)
% Converting from kilometres to
metres
depth2 = depth*10^3;
VChange2 = VChange*10^9;
rdist2 = rdist*10^3;
% MESHGRID generates X and Y
matrices for the grid area
[x,y]=meshgrid((-1*rdist2/2):sspace:(rdist2/2));
% Radial Distance
r = sqrt(x.^2+y.^2);
% Vertical displacement due to a
Mogi source
const = 3/(4*pi);
Uz = (const*VChange2*depth2)./((depth2^2+r.^2).^(3/2));
% Horizontal displacement due to a
Mogi source
Ur =
(const*VChange2*r)./((depth2^2+r.^2).^(3/2));
% Site and Mogi source locations in
WGS84, UTM Zone 27N
mogix=565000.4372;
mogiy=7096999.581;
D353x=580323.0411;
D356x=587262.2914;
D359x=592590.3579;
D361x=595094.6002;
ISAKx=560874.8819;
VALAx=572178.0131;
KROKx=578057.3671;
D364x=595822.0785;
D365x=596868.8406;
SKHRx=555092.5163;
PALAx=562381.5899;
SATUx=585955.0103;
KGILx=599775.4237;
BRSKx=571560.1012;
DROPx=570164.8208;
THRAx=588598.9273;
D353y=7112541.316;
D356y=7108269.393;
D359y=7109538.698;
D361y=7107384.464;
ISAKy=7110983.683;
VALAy=7106767.333;
KROKy=7105794.749;
D364y=7099601.906;
D365y=7097404.294;
SKHRy=7079668.451;
PALAy=7084263.139;
SATUy=7084821.087;
KGILy=7083000.709;
BRSKy=7091147.335;
DROPy=7087771.71;
THRAy=7078205.599;
% Determining the calculated
displacement at each site due to the Mogi
% source deformation.
%UTM co-ordinates are transformed
into grid co-ordinates (column and row values).
D353coly=int16(271-((D353y-mogiy)/200));
D353rowx=int16(271-((D353x-mogix)/200));
D356coly=int16(271-((D356y-mogiy)/200));
D356rowx=int16(271-((D356x-mogix)/200));
D359coly=int16(271-((D359y-mogiy)/200));
D359rowx=int16(271-((D359x-mogix)/200));
D361coly=int16(271-((D361y-mogiy)/200));
D361rowx=int16(271-((D361x-mogix)/200));
ISAKcoly=int16(271-((ISAKy-mogiy)/200));
ISAKrowx=int16(271-((ISAKx-mogix)/200));
VALAcoly=int16(271-((VALAy-mogiy)/200));
VALArowx=int16(271-((VALAx-mogix)/200));
KROKcoly=int16(271-((KROKy-mogiy)/200));
KROKrowx=int16(271-((KROKx-mogix)/200));
D364coly=int16(271-((D364y-mogiy)/200));
D364rowx=int16(271-((D364x-mogix)/200));
D365coly=int16(271-((D365y-mogiy)/200));
D365rowx=int16(271-((D365x-mogix)/200));
SKHRcoly=int16(271-((SKHRy-mogiy)/200));
SKHRrowx=int16(271-((SKHRx-mogix)/200));
PALAcoly=int16(271-((PALAy-mogiy)/200));
PALArowx=int16(271-((PALAx-mogix)/200));
SAcoly=int16(271-((SATUy-mogiy)/200));
SArowx=int16(271-((SATUx-mogix)/200));
KGcoly=int16(271-((KGILy-mogiy)/200));
KGrowx=int16(271-((KGILx-mogix)/200));
BRcoly=int16(271-((BRSKy-mogiy)/200));
BRrowx=int16(271-((BRSKx-mogix)/200));
DRcoly=int16(271-((DROPy-mogiy)/200));
DRrowx=int16(271-((DROPx-mogix)/200));
TAcoly=int16(271-((THRAy-mogiy)/200));
TArowx=int16(271-((THRAx-mogix)/200));
% Angle between the site and Mogi
source relative to an east-west axis
D353angle=atan((D353y-mogiy)/(D353x-mogix))*180/pi;
D356angle=atan((D356y-mogiy)/(D356x-mogix))*180/pi;
D359angle=atan((D359y-mogiy)/(D359x-mogix))*180/pi;
D361angle=atan((D361y-mogiy)/(D361x-mogix))*180/pi;
ISAKangle=atan((ISAKy-mogiy)/(ISAKx-mogix))*180/pi;
VALAangle=atan((VALAy-mogiy)/(VALAx-mogix))*180/pi;
KROKangle=atan((KROKy-mogiy)/(KROKx-mogix))*180/pi;
D364angle=atan((D364y-mogiy)/(D364x-mogix))*180/pi;
D365angle=atan((D365y-mogiy)/(D365x-mogix))*180/pi;
SKHRangle=atan((SKHRy-mogiy)/(SKHRx-mogix))*180/pi;
PALAangle=atan((PALAy-mogiy)/(PALAx-mogix))*180/pi;
SAangle=atan((SATUy-mogiy)/(SATUx-mogix))*180/pi;
KGangle=atan((KGILy-mogiy)/(KGILx-mogix))*180/pi;
BRangle=atan((BRSKy-mogiy)/(BRSKx-mogix))*180/pi;
DRangle=atan((DROPy-mogiy)/(DROPx-mogix))*180/pi;
TAangle=atan((THRAy-mogiy)/(THRAx-mogix))*180/pi;
% The horizontal displacement
experienced at each site
% due to Mogi deformation [in m]
D353=Ur(D353rowx,D353coly);
D356=Ur(D356rowx,D356coly);
D359=Ur(D359rowx,D359coly);
D361=Ur(D361rowx,D361coly);
ISAK=Ur(ISAKrowx,ISAKcoly);
VALA=Ur(VALArowx,VALAcoly);
KROK=Ur(KROKrowx,KROKcoly);
D364=Ur(D364rowx,D364coly);
D365=Ur(D365rowx,D365coly);
SKHR=Ur(SKHRrowx,SKHRcoly);
PALA=Ur(PALArowx,PALAcoly);
SATU=Ur(SArowx,SAcoly);
KGIL=Ur(KGrowx,KGcoly);
BRSK=Ur(BRrowx,BRcoly);
DROP=Ur(DRrowx,DRcoly);
THRA=Ur(TArowx,TAcoly);
% Calculating the x and y components
of the horizontal displacements [in m]
D353x=D353*cos(D353angle*pi/180);
D353y=D353*sin(D353angle*pi/180);
D356x=D356*cos(D356angle*pi/180);
D356y=D356*sin(D356angle*pi/180);
D359x=D359*cos(D359angle*pi/180);
D359y=D359*sin(D359angle*pi/180);
D361x=D361*cos(D361angle*pi/180);
D361y=D361*sin(D361angle*pi/180);
ISAKx=ISAK*cos(ISAKangle*pi/180);
ISAKy=ISAK*sin(ISAKangle*pi/180);
VALAx=VALA*cos(VALAangle*pi/180);
VALAy=VALA*sin(VALAangle*pi/180);
KROKx=KROK*cos(KROKangle*pi/180);
KROKy=KROK*sin(KROKangle*pi/180);
D364x=D364*cos(D364angle*pi/180);
D364y=D364*sin(D364angle*pi/180);
D365x=D365*cos(D365angle*pi/180);
D365y=D365*sin(D365angle*pi/180);
SKHRx=SKHR*cos(SKHRangle*pi/180);
SKHRy=SKHR*sin(SKHRangle*pi/180);
PALAx=PALA*cos(PALAangle*pi/180);
PALAy=PALA*sin(PALAangle*pi/180);
SATUx=SATU*cos(SAangle*pi/180);
SATUy=SATU*sin(SAangle*pi/180);
KGILx=KGIL*cos(KGangle*pi/180);
KGILy=KGIL*sin(KGangle*pi/180);
BRSKx=BRSK*cos(BRangle*pi/180);
BRSKy=BRSK*sin(BRangle*pi/180);
DROPx=DROP*cos(DRangle*pi/180);
DROPy=DROP*sin(DRangle*pi/180);
THRAx=THRA*cos(TAangle*pi/180);
THRAy=THRA*sin(TAangle*pi/180);
% Vertical displacements for each
site
D353z=Uz(D353rowx,D353coly);
D356z=Uz(D356rowx,D356coly);
D359z=Uz(D359rowx,D359coly);
D361z=Uz(D361rowx,D361coly);
ISAKz=Uz(ISAKrowx,ISAKcoly);
VALAz=Uz(VALArowx,VALAcoly);
KROKz=Uz(KROKrowx,KROKcoly);
D364z=Uz(D364rowx,D364coly);
D365z=Uz(D365rowx,D365coly);
SKHRz=Uz(SKHRrowx,SKHRcoly);
PALAz=Uz(PALArowx,PALAcoly);
SATUz=Uz(SArowx,SAcoly);
KGILz=Uz(KGrowx,KGcoly);
BRSKz=Uz(BRrowx,BRcoly);
DROPz=Uz(DRrowx,DRcoly);
THRAz=Uz(TArowx,TAcoly);
% Table of horizontal (x and y) and
vertical displacements
D3531=[D353x,D353y,D353z];
D3561=[D356x,D356y,D356z];
D3591=[D359x,D359y,D359z];
D3611=[D361x,D361y,D361z];
ISAK1=[ISAKx,ISAKy,ISAKz];
VALA1=[VALAx,VALAy,VALAz];
KROK1=[KROKx,KROKy,KROKz];
D3641=[D364x,D364y,D364z];
D3651=[D365x,D365y,D365z];
SKHR1=[SKHRx,SKHRy,SKHRz];
PALA1=[PALAx,PALAy,PALAz];
SATU1=[SATUx,SATUy,SATUz];
KGIL1=[KGILx,KGILy,KGILz];
BRSK1=[BRSKx,BRSKy,BRSKz];
DROP1=[DROPx,DROPy,DROPz];
THRA1=[THRAx,THRAy,THRAz];
TOTAL=[D3531;D3561;D3591;D3611;ISAK1;VALA1;KROK1;D3641;D3651;SKHR1;PALA1;SATU1;KGIL1;BRSK1;DROP1;THRA1];
% Calculating the rate of
deformation due to the Mogi source for each site [in m/yr]
% (i.e., Displacement divided by 9
years [1994-2003])
D353_v=D353/9;
D353x_v=D353x/9;
D353y_v=D353y/9;
D356_v=D356/9;
D356x_v=D356x/9;
D356y_v=D356y/9;
D359_v=D359/9;
D359x_v=D359x/9;
D359y_v=D359y/9;
D361_v=D361/9;
D361x_v=D361x/9;
D361y_v=D361y/9;
ISAK_v=ISAK/9;
ISAKx_v=ISAKx/9;
ISAKy_v=ISAKy/9;
VALA_v=VALA/9;
VALAx_v=VALAx/9;
VALAy_v=VALAy/9;
KROK_v=KROK/9;
KROKx_v=KROKx/9;
KROKy_v=KROKy/9;
D364_v=D364/9;
D364x_v=D364x/9;
D364y_v=D364y/9;
D365_v=D365/9;
D365x_v=D365x/9;
D365y_v=D365y/9;
SKHR_v=SKHR/9;
SKHRx_v=SKHRx/9;
SKHRy_v=SKHRy/9;
PALA_v=PALA/9;
PALAx_v=PALAx/9;
PALAy_v=PALAy/9;
SATU_v=SATU/9;
SATUx_v=SATUx/9;
SATUy_v=SATUy/9;
KGIL_v=KGIL/9;
KGILx_v=KGILx/9;
KGILy_v=KGILy/9;
BRSK_v=BRSK/9;
BRSKx_v=BRSKx/9;
BRSKy_v=BRSKy/9;
DROP_v=DROP/9;
DROPx_v=DROPx/9;
DROPy_v=DROPy/9;
THRA_v=THRA/9;
THRAx_v=THRAx/9;
THRAy_v=THRAy/9;
% Vertical velocities
D353z_v=D353z/9;
D356z_v=D356z/9;
D359z_v=D359z/9;
D361z_v=D361z/9;
ISAKz_v=ISAKz/9;
VALAz_v=VALAz/9;
KROKz_v=KROKz/9;
D364z_v=D364z/9;
D365z_v=D365z/9;
SKHRz_v=SKHRz/9;
PALAz_v=PALAz/9;
SATUz_v=SATUz/9;
KGILz_v=KGILz/9;
BRSKz_v=BRSKz/9;
DROPz_v=DROPz/9;
THRAz_v=THRAz/9;
% Table of horizontal (x, y, and
radial) and vertical velocities
D3532=[D353x_v,D353y_v,D353z_v];
D3562=[D356x_v,D356y_v,D356z_v];
D3592=[D359x_v,D359y_v,D359z_v];
D3612=[D361x_v,D361y_v,D361z_v];
ISAK2=[ISAKx_v,ISAKy_v,ISAKz_v];
VALA2=[VALAx_v,VALAy_v,VALAz_v];
KROK2=[KROKx_v,KROKy_v,KROKz_v];
D3642=[D364x_v,D364y_v,D364z_v];
D3652=[D365x_v,D365y_v,D365z_v];
SKHR2=[SKHRx_v,SKHRy_v,SKHRz_v];
PALA2=[PALAx_v,PALAy_v,PALAz_v];
SATU2=[SATUx_v,SATUy_v,SATUz_v];
KGIL2=[KGILx_v,KGILy_v,KGILz_v];
BRSK2=[BRSKx_v,BRSKy_v,BRSKz_v];
DROP2=[DROPx_v,DROPy_v,DROPz_v];
THRA2=[THRAx_v,THRAy_v,THRAz_v];
TOTALv=[D3532;D3562;D3592;D3612;ISAK2;VALA2;KROK2;D3642;D3652;SKHR2;PALA2;SATU2;KGIL2;BRSK2;DROP2;THRA2];
% Calculating the component of the horizontal
velocity parallel to spreading
% (i.e. N78E) for each site [in
m/yr]
DiffD353=abs(282-(360+(90-D353angle)));
comptD353=D353_v*cos(DiffD353*pi/180);
comptxD353=comptD353*cos((282-270)*pi/180)*-1*1000;
comptyD353=comptD353*sin((282-270)*pi/180)*1000;
DiffD356=abs(282-(360+(90-D356angle)));
comptD356=D356_v*cos(DiffD356*pi/180);
comptxD356=comptD356*cos((282-270)*pi/180)*-1*1000;
comptyD356=comptD356*sin((282-270)*pi/180)*1000;
DiffD359=abs(282-(360+(90-D359angle)));
comptD359=D359_v*cos(DiffD359*pi/180);
comptxD359=comptD359*cos((282-270)*pi/180)*-1*1000;
comptyD359=comptD359*sin((282-270)*pi/180)*1000;
DiffD361=abs(282-(360+(90-D361angle)));
comptD361=D361_v*cos(DiffD361*pi/180);
comptxD361=comptD361*cos((282-270)*pi/180)*-1*1000;
comptyD361=comptD361*sin((282-270)*pi/180)*1000;
DiffISAK=abs(282-(360+(90-ISAKangle)));
comptISAK=ISAK_v*cos(DiffISAK*pi/180);
comptxISAK=comptISAK*cos((282-270)*pi/180)*1000;
comptyISAK=comptISAK*sin((282-270)*pi/180)*-1*1000;
DiffVALA=abs(282-(360+(90-VALAangle)));
comptVALA=VALA_v*cos(DiffVALA*pi/180);
comptxVALA=comptVALA*cos((282-270)*pi/180)*-1*1000;
comptyVALA=comptVALA*sin((282-270)*pi/180)*1000;
DiffKROK=abs(282-(360+(90-KROKangle)));
comptKROK=KROK_v*cos(DiffKROK*pi/180);
comptxKROK=comptKROK*cos((282-270)*pi/180)*-1*1000;
comptyKROK=comptKROK*sin((282-270)*pi/180)*1000;
DiffD364=abs(282-(360+(90-D364angle)));
comptD364=D364_v*cos(DiffD364*pi/180);
comptxD364=comptD364*cos((282-270)*pi/180)*-1*1000;
comptyD364=comptD364*sin((282-270)*pi/180)*1000;
DiffD365=abs(282-(360+(90-D365angle)));
comptD365=D365_v*cos(DiffD365*pi/180);
comptxD365=comptD365*cos((282-270)*pi/180)*-1*1000;
comptyD365=comptD365*sin((282-270)*pi/180)*1000;
DiffSKHR=abs(282-(360+(90-SKHRangle)));
comptSKHR=SKHR_v*cos(DiffSKHR*pi/180);
comptxSKHR=comptSKHR*cos((282-270)*pi/180)*1000;
comptySKHR=comptSKHR*sin((282-270)*pi/180)*-1*1000;
DiffPALA=abs(282-(360+(90-PALAangle)));
comptPALA=PALA_v*cos(DiffPALA*pi/180);
comptxPALA=comptPALA*cos((282-270)*pi/180)*1000;
comptyPALA=comptPALA*sin((282-270)*pi/180)*-1*1000;
DiffSA=abs(282-(360+(90-SAangle)));
comptSA=SATU_v*cos(DiffSA*pi/180);
comptxSA=comptSA*cos((282-270)*pi/180)*-1*1000;
comptySA=comptSA*sin((282-270)*pi/180)*1000;
DiffKG=abs(282-(360+(90-KGangle)));
comptKG=KGIL_v*cos(DiffKG*pi/180);
comptxKG=comptKG*cos((282-270)*pi/180)*-1*1000;
comptyKG=comptKG*sin((282-270)*pi/180)*1000;
DiffBR=abs(282-(360+(90-BRangle)));
comptBR=BRSK_v*cos(DiffBR*pi/180);
comptxBR=comptBR*cos((282-270)*pi/180)*-1*1000;
comptyBR=comptBR*sin((282-270)*pi/180)*1000;
DiffDR=abs(282-(360+(90-DRangle)));
comptDR=DROP_v*cos(DiffDR*pi/180);
comptxDR=comptDR*cos((282-270)*pi/180)*-1*1000;
comptyDR=comptDR*sin((282-270)*pi/180)*1000;
DiffTA=abs(282-(360+(90-TAangle)));
comptTA=THRA_v*cos(DiffTA*pi/180);
comptxTA=comptTA*cos((282-270)*pi/180)*-1*1000;
comptyTA=comptTA*sin((282-270)*pi/180)*1000;
% Table of components of the
horizontal velocities parallel to plate
% spreading
TOTAL9403=[comptxD353,comptyD353;comptxD356,comptyD356;comptxD359,comptyD359;comptxD361,comptyD361;comptxISAK,comptyISAK;comptxVALA,comptyVALA;comptxKROK,comptyKROK;comptxD364,comptyD364;comptxD365,comptyD365;comptxSKHR,comptySKHR;comptxPALA,comptyPALA;comptxSA,comptySA;comptxKG,comptyKG;comptxBR,comptyBR;comptxDR,comptyDR;comptxTA,comptyTA];