Hi Jason,
Thanks for your response.
I have a few conceptual questions.
This assumption isn't strictly true in the case of modelling sound through rocks but it is generally made. See the "blocky model" used to separate out different impedance layers with small scale perturbation within each...
An update... this looks to have the answer but it's not as simple as I had hoped: https://www.crewes.org/ForOurSponsors/ResearchReports/2011/CRR201159.pdf
The answer seems to be the Born Approximation. Using this approach the classical equation for the boundary between two half-spaces,
T = 1 +...
I am interested to know what is the impact of various length scales of impedance changes on wave propagation.
From undergraduate physics (a few years ago for me) I roughly remember how to derive reflection and transmission coefficients for a wave traveling from one medium to another with a...
Hi,
I have no background in statistics/econometrics but some theory I'm applying to geophysics data requires the data to be stationary (or at least trend-stationary) and I don't believe they are.
I've found MATLAB code to apply the Augmented Dickey-Fuller test (from here -...
I needed the solution for this to run a computer model. I have since just solved the problem iteratively in MATLAB but I am interested to know if the maths leads to a reasonably neat solution. Any ideas?
Lets say that D/2 is the sum of the horizontal distances traveled in the two layers (only considering the downgoing wave):
D/2 = (d_1+d_2=) z_1tan\theta_1+z_2tan\theta_2
From Snell's Law:
\theta_2=sin^{-1}(\frac{v_2}{v_1}sin\theta_1)
D/2 =...
Yes v2/v1 =n1/n2. But whether I use the ratio of refractive indices or the ratio of velocities doesn't really matter. Either way they are just two known variables that carry through.
Without writing out my attempt at a derivation in full, what I did was re-write Θ2 in terms of Θ1. Then you get...
I'm looking for a general solution when you know the velocity contrast of the layers (to give the ratio for snells law) and you know the thickness of the two layers as well as the separation of the source and receiver.
A single ear does not have any directionality to its recording. We hear the total energy from all of our surroundings. This answers my question! Thanks.
It has the same power per unit solid angle but less total power to the eye. But the paper looks the same, so brightness is related to power per unit solid angle?
Ha, I should have italicized brightness. What the eye sees is mainly just color then? The effect of the lamp I mentioned though is related to the power.
Afterthought. If I held a bright lamp to the side of my face it would obviously be very bright, but it wouldn't be as painfully bright if I looked at its reflection in a mirror some distance away. I think this adds to what I was trying to say above
Svein: Ok, obviously the energy has decreased according to the square of the distance, and the amplitude falls of as the distance. So you hear it as if the source was at 2x. This is identical to seeing yourself in the mirror as you would see yourself at 2x.
Haruspex: The difference must arrive...