Solving for earthquake transit time via Snell's Law

In summary, the conversation discusses solving for x in the second equation, which is represented by l2 and l2. However, this only provides the values in terms of other unknowns. The speaker believes they need to solve for t, but are struggling due to the unknowns. The equation for x is (l2*L*v2)/(l1*v1+l2*v2) where lowercase l represents the length of the hypotenuses and capital L represents the horizontal separation distance. The importance of Snell's law is also mentioned, but its relevance is not clear. The speaker assumes that u1 is equivalent to v1 and sin1 should be written as sin(θ1). The relationship between θ1, x, L
  • #1
peeballs
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Homework Statement
Calculate the travel time from Point 1 to Point 2. We know the velocity of
the two media (V1 and V2), the vertical distances to the interface (H1 and H2),
and the horizontal separation distance L.
Relevant Equations
u1sin1 = u2sin2, (x/(v2l2)) - ((L-x)/(v1l1)) = 0, t = (l1/v1) + (l2/v2)
I was told to solve the second equation above for x to get l2 and l2, but that only gets me those in terms of other unknowns. I'm assuming I just need to solve t for my knowns, but I keep getting caught up by my unknowns. i.e., solving for x gives x = (l2*L*v2)/(l1*v1+l2*v2). Please note "l" is a lowercase L. The lowercase denotes the length of the respective hypotenuses while the capital L denotes horizontal separation distance.

I know Snell's law is important here, but I'm not really sure how it helps me.
 

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  • #2
I presume u1 is the same as v1, etc., and sin1 should be sin(θ1), etc.
What is the relationship between θ1, x, L and H1?
 

1. What is Snell's Law and how does it relate to earthquake transit time?

Snell's Law is a principle in physics that describes how light or other waves travel through different mediums. In the context of earthquake transit time, Snell's Law is used to calculate the angle at which seismic waves travel through different layers of the Earth's crust, which allows us to determine the time it takes for the waves to reach a specific location.

2. How is Snell's Law used to solve for earthquake transit time?

To solve for earthquake transit time using Snell's Law, we first need to know the velocity of seismic waves in each layer of the Earth's crust. We can then use Snell's Law to calculate the angle of refraction for each layer, and from there we can determine the time it takes for the waves to travel through each layer and reach a specific location.

3. What factors can affect the accuracy of using Snell's Law to solve for earthquake transit time?

One of the main factors that can affect the accuracy of using Snell's Law to solve for earthquake transit time is the assumption that the Earth's crust is made up of distinct layers with uniform properties. In reality, the Earth's crust is more complex and can have variations in velocity and density within each layer. Other factors such as the curvature of the Earth's surface and the presence of seismic discontinuities can also affect the accuracy of using Snell's Law.

4. Can Snell's Law be used to solve for earthquake transit time in all types of geological environments?

Snell's Law can be applied to solve for earthquake transit time in most geological environments, as long as the layers of the Earth's crust can be approximated as distinct and uniform. However, in more complex environments such as in subduction zones or areas with significant variations in crustal properties, other methods may need to be used in conjunction with Snell's Law to accurately calculate earthquake transit time.

5. How does solving for earthquake transit time using Snell's Law contribute to our understanding of earthquakes?

By using Snell's Law to solve for earthquake transit time, we can gain a better understanding of the structure and properties of the Earth's crust, which can provide insights into the mechanisms and behavior of earthquakes. This information can also be used to improve earthquake hazard assessments and help with earthquake prediction and early warning systems.

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