Hilbert transform and the curious case of enveloping [My notes]

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: $latex … Continue reading Hilbert transform and the curious case of enveloping [My notes]

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Brief note on seismic migration and inversion

Seismic inversion can be classified as Methods based on iterative forward modeling Methods based on downward wave field extrapolation Inversion by iterative forward modeling: Essentially in this method, elastic properties of the geological subsurface are estimated. Given the seismic source and an initial subsurface model, a seismic data is simulated. The simulated data is then … 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