%% Loma Prieta Earthquake
% This demo shows how to analyze and visualize real-world earthquake data.
% 
% Authors: C. Denham, 1990, C. Moler, August, 1992.

% Copyright 1984-2004 The MathWorks, Inc. 
% $Revision: 5.17.4.1 $  $Date: 2004/03/22 23:54:35 $

%%
% The file QUAKE.MAT contains 200Hz data from the October 17, 1989 Loma Prieta
% earthquake in the Santa Cruz Mountains.  The data are courtesy of Joel Yellin
% at the Charles F. Richter Seismological Laboratory, University of California,
% Santa Cruz.  Start by loading the data.

load quake e n v
whos e n v

%%
% In the workspace now are three variables containing time traces from an
% accelerometer in the Natural Sciences' building at UC Santa Cruz.  The
% accelerometer recorded the main shock of the earthquake.  The variables n, e,
% v refer to the three directional components measured by the instrument, which
% was aligned parallel to the fault, with its N direction pointing in the
% direction of Sacramento.  The data is uncorrected for the response of the
% instrument.
%
% Scale the data by the gravitational acceleration.  Also, create a fourth
% variable, t, containing a time base.

g = 0.0980;
e = g*e;
n = g*n;
v = g*v;
delt = 1/200;
t = delt*(1:length(e))';

%%
% Here are plots of the accelerations.

yrange = [-250 250];
limits = [0 50 yrange];
subplot(3,1,1), plot(t,e,'b'), axis(limits), title('East-West acceleration')
subplot(3,1,2), plot(t,n,'g'), axis(limits), title('North-South acceleration')
subplot(3,1,3), plot(t,v,'r'), axis(limits), title('Vertical acceleration')

%%
% Look at the interval from t=8 seconds to t=15 seconds.  Draw black lines at
% the selected spots.  All subsequent calculations will involve this interval.

t1 = 8*[1;1];
t2 = 15*[1;1];
subplot(3,1,1), hold on, plot([t1 t2],yrange,'k','LineWidth',2); hold off
subplot(3,1,2), hold on, plot([t1 t2],yrange,'k','LineWidth',2); hold off
subplot(3,1,3), hold on, plot([t1 t2],yrange,'k','LineWidth',2); hold off

%%
% Zoom in on the selected time interval.

trange = sort([t1(1) t2(1)]);
k = find((trange(1)<=t) & (t<=trange(2)));
e = e(k);
n = n(k);
v = v(k);
t = t(k);
ax = [trange yrange];

subplot(3,1,1), plot(t,e,'b'), axis(ax), title('East-West acceleration')
subplot(3,1,2), plot(t,n,'g'), axis(ax), title('North-South acceleration')
subplot(3,1,3), plot(t,v,'r'), axis(ax), title('Vertical acceleration')

%%
% Focusing on one second in the middle of this interval, a plot of "East-West"
% against "North-South" shows the horizontal acceleration.

subplot(1,1,1)
k = length(t);
k = round(max(1,k/2-100):min(k,k/2+100));
plot(e(k),n(k),'.-')
xlabel('East'), ylabel('North');
title('Acceleration During a One Second Period');

%%
% Integrate the accelerations twice to calculate the velocity and position of a
% point in 3-D space.

edot = cumsum(e)*delt;  edot = edot - mean(edot);
ndot = cumsum(n)*delt;  ndot = ndot - mean(ndot);
vdot = cumsum(v)*delt;  vdot = vdot - mean(vdot);

epos = cumsum(edot)*delt;  epos = epos - mean(epos);
npos = cumsum(ndot)*delt;  npos = npos - mean(npos);
vpos = cumsum(vdot)*delt;  vpos = vpos - mean(vpos);

subplot(2,1,1);
plot(t,[edot+25 ndot vdot-25]); axis([trange min(vdot-30) max(edot+30)])
xlabel('Time'), ylabel('V - N - E'), title('Velocity')

subplot(2,1,2);
plot(t,[epos+50 npos vpos-50]);
axis([trange min(vpos-55) max(epos+55)])
xlabel('Time'), ylabel('V - N - E'), title('Position')

%%
% The trajectory defined by the position data can be displayed with three
% different 2-dimensional projections.  Here is the first with a few values of t
% annotated.

subplot(1,1,1); cla; subplot(2,2,1)
plot(npos,vpos,'b');
na = max(abs(npos)); na = 1.05*[-na na];
ea = max(abs(epos)); ea = 1.05*[-ea ea];
va = max(abs(vpos)); va = 1.05*[-va va];
axis([na va]); xlabel('North'); ylabel('Vertical');

nt = ceil((max(t)-min(t))/6);
k = find(fix(t/nt)==(t/nt))';
for j = k, text(npos(j),vpos(j),['o ' int2str(t(j))]); end

%%
% Similar code produces two more 2-D views.

subplot(2,2,2)
plot(npos,epos,'g');
for j = k; text(epos(j),vpos(j),['o ' int2str(t(j))]); end
axis([ea va]); xlabel('East'); ylabel('Vertical');

subplot(2,2,3)
plot(npos,epos,'r');
for j = k; text(npos(j),epos(j),['o ' int2str(t(j))]); end
axis([na ea]); xlabel('North'); ylabel('East');

%%
% The fourth subplot is a 3-D view of the trajectory.

subplot(2,2,4)
plot3(npos,epos,vpos,'k')
for j = k;text(npos(j),epos(j),vpos(j),['o ' int2str(t(j))]); end
axis([na ea va]); xlabel('North'); ylabel('East'), zlabel('Vertical');
box on

%%
% Finally, plot a dot at every tenth position point.  The spacing between
% dots indicates the velocity.

subplot(1,1,1)
plot3(npos,epos,vpos,'r')
hold on
step = 10;
plot3(npos(1:step:end),epos(1:step:end),vpos(1:step:end),'.')
hold off
box on
axis tight
xlabel('North-South')
ylabel('East-West')
zlabel('Vertical')
title('Position (cms)')