Python scientific tools in geoscience

As we all know, all data science projects include three parts: retrieving data, numerical computation and result visualization. Take seismology as an example, ways for requesting seismic data from providers (IRIS, ISC and NIED etc.) are concluded here.

Thus, this post focuses on collecting serveral useful python library for general scientific numerial computation and visualization.

Danger in performing phase shift with Python for a time series

Mathmatical expression

For scientific purpose, we sometime need to shift phase of time series with specfic angles. To acheive this, we can transform the time series into freqeuency domain with $$F(\omega) = \int_{-\omega}^{\omega} f(t) e^{-i \omega t} dt$$

where $F(\omega)$ as Fourier spectrum of signal $f(t)$. Thus, the phase shifted Fourier spectrum $F_{sh}$ is

$$F_{sh}(\omega) = F(\omega) * e^{-i \alpha}$$