This document describes manual methods for approximating the location and origin time of an earthquake using seismic wave data from multiple seismic stations. The earliest station method uses the first station to detect waves to estimate the epicenter location. Contouring P-wave arrival times can provide a better estimate if the network is dense. The arc or circle method uses S-P arrival time differences from three or more stations to estimate epicenter location and hypocenter depth. Plotting S-P time differences against P-wave arrival times on a Wadati diagram allows determining the earthquake origin time from the intercept of the best-fit line with the P-arrival time axis.

1. Earthquake Location

2. Manual Method
• To get an approximate location of an earthquake
is possible with the help of seismic waves.
• If the seismic network is dense and the
earthquake is originated inside the network, the
station with the earliest arrival can be
approximated as the epicentre.
• This is called earliest station method, and it gives
an estimate with a probable error of the same
order as the station spacing.

3. • Another approach is to contour the P-wave
arrival times.
• This is an extension of the earliest station
method.
• This may give fairly good estimate of the
epicentre location if the network is dense
enough.
• If the network is not dense and it consists of a
few stations only, then the method is not
effective.

4. • A good approximation of the epicentre can be
made by arc method or circle method with
three or more S-P times.
• Three parameters are calculated which include
epicentral distance X, hypocentral distance D
and depth of focus (H) of an earthquake.
• If Tp is arrival time of the P wave and Ts is that
of the S wave, then we can write:

5. • Where Vp and Vs are the velocity of the P-wave
and S-wave respectively.
• Equating both equations,

6. • Assuming Vp/Vs = 1.73, the hypocentre
distance can be estimated as
• where D is in kilometres, and S-P is in second.

9. • After determining D at three or more stations,
circles with radius D can be drawn with each
circle centred at the respective station.
• The epicentre lies in the region where the
circles overlap.
• This method was commonly used as a quick
means of locating earthquakes.

11. • The focal depth (H) can be obtained as:
• Adding more observations will give additional
intersections that theoretically should pass
through the epicentre.
• In practice, error is always present, both in
data and in assumptions, that the ray-paths
are straight and the Earth is homogeneous, so
scatter in the intersection usually occurs.

12. Origin Time of an Earthquake
• The origin time of an earthquake can be
determined with a very simple graphical
technique, called Wadati plot (Wadati, 1933).
• The time separation of the P and S phase (Ts – Tp)
is plotted against the arrival time of the Pwave.
• Since Ts – Tp = 0 at the hypocentre, a straight line
fit on the Wadati diagram gives the origin time at
the intercept with the P-arrival-time axis