Full Waveform Inversion (tutorials)

I will try to enlist as many tutorials I find in this post! https://www.slim.eos.ubc.ca/Publications/Public/Journals/TheLeadingEdge/2017/louboutin2017fwi/louboutin2017fwi.html

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Enjoy(nt) the Adjoints

Most of the modeling we do requires linear operations that predict data from models. However, in Imaging, the usual task is to find inverse of these operators to find the models from the data. This is where the Adjoint operator comes to rescue as a part of the inversion process. Adjoint of a matrix is … Continue reading Enjoy(nt) the Adjoints

Singular Value Decomposition

An intuitive approach: https://www.quora.com/What-is-an-intuitive-explanation-of-singular-value-decomposition-SVD/answer/Jason-Liu-21?srid=uSFD Two part in-depth description: https://jeremykun.com/2016/04/18/singular-value-decomposition-part-1-perspectives-on-linear-algebra/ https://jeremykun.com/2016/05/16/singular-value-decomposition-part-2-theorem-proof-algorithm/ Use of SVD in finding pseudo inverse of a matrix: https://www.cse.unr.edu/~bebis/CS791E/Notes/SVD.pdf https://math.stackexchange.com/questions/1541986/what-is-the-best-way-to-compute-the-pseudoinverse-of-a-matrix https://math.stackexchange.com/questions/1939962/singular-value-decomposition-and-inverse-of-square-matrix

My notes on Laplace transform

The Laplace transform of a function f(t), defined for all real numbers t ≥ 0, is the function F(s), which is a unilateral transform defined by: $latex F(s)=\int_{0}^{\infty} f(t)e^{-st} dt$ where s is a complex number frequency parameter $latex s=\sigma +i\omega $, with real numbers $latex \sigma$ and $latex \omega$. In the case of the Laplace transform, … Continue reading My notes on Laplace transform