- Junwei Huang

# Seismic Interferometry, reverse time migration, reverse time source imaging, and many other jargons

Posted on __August 20, 2012__

Believe it or not, when you are locating microseismic events without picking the arrivals you may be using one of the above techniques. More importantly they are actually describing the same thing (more or less) in the application of locating micro-earthquakes. Here is why (non-math version):
(1) **Seismic Interferometry**: is to calculate a green’s function by correlating a complex conjugate green function with another green’s function. In time domain, the complex conjugate green’s function is to **back-propagate** the other green’s function into the medium. If the complex conjugate green’s function is a natural green’s function recorded from the real medium, you are doing **seismic interferometry**.
(2) **Reverse time migration**: if the complex conjugate green’s function is based on a velocity model and the other green’s function is related to the reflection response of the medium, you are doing reverse time migration started since McMechan 1983.
(3) **Reverse time source imaging**: if the complex conjugate green’s function is based on a velocity model and the other green’s function is related to the transmission response of the medium, you are doing **reverse time source imaging**. In other field, people call it **time reversal method**, **time reversal acoustics**, or call the device that can reverse time signal **time reversal mirror**. Someone even finds that adding a “sink” (the opposite of source) at the original source location, super-resolution can be achieved. In other words, in a dark night you see a car 1~2 km away approaches you with its light on, you only see one big light not two till it gets closer. Now if your eye and brain can do time reverse, you see two lights crystal clear even when the car is still 1~2km away from you. Isn’t that cool? But you need more than your eye and brain to achieve this super-resolution.
(4) **Time reversal mirror**: see (3)
(5) **Back-projection method**: you use ray-tracing method to calculate the complex conjugate green’s function. In other words, you are lightening up the medium, the wavelength is zero and likely you only use the first arrivals. Some specific ray-tracing methods may give you later arrivals. So you can select what late arrivals include. The more the better, and of course, the complex conjugate green’s function from the natural medium include all multiples.
(6) **Back-propagation method**: the function of the complex conjugate green’s function, see (1).
(7) **Diffraction stacking**: it works like this, (a) define a source location, (b) use ray-tracing to calculate its first arrivals for all sensors, (c) sum up the amplitude along the arrival time curve. Obviously you are using ray-tracing to do the back-projection, so see (5).
(8) **Adjoint method**: it uses a model based complex conjugate green’s function and **back-propagate** the difference between modeled data and observed data into the medium, till the difference is reduced to a certain level. At the beginning, you have no idea about the source, so you just **back-propagate** the observation. Obviously, its first iteration is (3). After the first iteration, you have some ideas about the source so you add a sink at the estimated location and repeat **back-propagation**, this is similar to (4) with a sink. If it converged, you just did **reverse time source inversion**. If you are happy with the first iteration, you just finished the **reverse time source imaging**. The rest is somewhere in between, and I guess we don’t have a name for each of them yet. But considering that we already coined 8 different key words for basically the same thing, we will coin more fancy words for them in no time. Just keep an eye on the literature.

In summary, you are using seismic Interferometry, reverse time migration, reverse time source imaging, time reversal mirror, back-projection method, back-propagation method, diffraction stacking, and adjoint method, to locate micro-earthquakes; you are just unaware of it.