When you travel from one place to another , the time taken to complete your journey is a Travel Time. However when it comes to seismic geophysics this time is measured between seismic source and seismic receiver.
Travel time can be defined as the time taken by seismic waves to travel from seismic source to seismic receiver.
If seismic waves move directly from source to receiver without either refracting or reflecting from a refractor (reflector), or time taken either from reflector to receiver or from source to reflector it is said to have One way travel time (OWT). For example in Earthquake seismology if seismic waves move directly from source (Focus) to seismic station (receiver), it may be regarded as One Way travel Time.
If after coming from the source then bounce to the interface then move to the receiver, it is said to have Two way Travel times (TWT). The term Two Way Travel time is more concerned in case of reflection rather than in refraction. In most cases the receiver records these travel times, so that we can estimate depth of interface (Reflector) and velocity of seismic waves within different layers. In Earthquake seismology we can predict or locate the source from where an Earthquake originated through the use of travel time.
P - waves have shorter travel times than S - waves, since P - waves have higher velocity compared to S - waves.
Figure 1: Two layer Seismic ray geometry
By consider the figure 1 above we find that, If A and D are the source and Receiver respectively, the following waves may be reported
Head (Refracted) waves, this will be described here below at total travel time.
Reflected wave (B to the midpoint between A and D, let's assume that point is K) such that at distance half of x such as x/2
Direct wave (AD): It's travel time (T) = X/V1
Total travel time.
For the seismic wave to complete travel from A to B then C to D, the travel time can be calculated as follows,
Since t = distance (d)/ Velocity (V)
T = AB/V1 + BC/V2 + CD/V1........................(i)
If you consider the triangle ∆ APB,
AB = Z / Cosic
Since AB = CD
CD = Z/Cosic
BC = X - 2Ztanic
From eqn (i), above T = Z/ V1Cosic + (X - 2Ztanic)/V2 + Z/V1Cosic
T = 2Z/V1Cosic + X/V2 - 2Ztanic/V2
It will simplifies to,
T = X/V2 + 2ZCosic/V1.......................(ii)
Remember Cos2ic + Sin2ic = 1
Then make Cos ic the subject and put in the above eqn (ii)
T = X/V2 + 2Z √(1 - Sin2ic) / V1
But at critical refraction r = 90°, then sin i° = V1/V2
It will simplifies to,
T = (1/V2)X + 2Z√(V22 - V12) / V1V2
For the T - X Plot curve and If you compare the equation above with y = mX + c
Slope = 1/V2, while the y - intercept (c) = 2Z√(V22 - V12) / V1V2 as shown in the figure 2 below, the depth (Z) of refractor and Velocity of seismic waves in medium 2 can be calculated.
Figure 2: Time (T) - distance (X) Plot.
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