A very interesting thing I re-discovered today is the angular wavenumber. Although it seems like I had understood that pretty well long back, I had forgotten quite some things about it. The rumination came from my continuous learning process of Fourier Transform. While I seem to have gotten a hang of temporal Fourier transform, spacial … Continue reading Angular wavenumber

# Author: aparajitanath

## Born Approximation

## 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

## Hessian and Jacobian Matrix

## My notes on Hilbert transform

http://complextoreal.com/wp-content/uploads/2013/01/tcomplex.pdf Hilbert transform in frequency domain -It is a peculiar sort of filter that changes the phase of the spectral components depending on the sign of their frequency. -It only effects the phase of the signal. It has no effect on the amplitude at all.For any signal g(t), its Hilbert Transform has the following property: … Continue reading My notes on Hilbert transform

## Brief note on seismic migration and inversion

Seismic Inversion Essentially in this method, elastic properties of the geological subsurface are estimated. The method is carried out by minimizing the difference between simulated and recorded data. Hence, forward modeling is central in inversion & residual carried forth the iterative estimation process. Seismic Migration In this method, reflectivity of the geological boundaries is estimated … Continue reading Brief note on seismic migration and inversion

## Conjugate gradient method

Disclaimer: The notes are made from information available here and wikipedia. Conjugate gradient is effective for solving systems of the form: $latex \mathbf{A}x=b$ $latex x$ is an unknown vector $latex \mathbf{A}$ is a known positive-definite, square, symmetric matrix $latex b$ is a known vector The CG method is most effective in solving systems where $latex \mathbf{A}$ is … Continue reading Conjugate gradient method