This post summaries notes from official guidence of IELTS.

# Listening skills

• understanding the context
• listening for specific details
• using correct spelling
• understanding numbers

## 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

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

Collection of all known data providers and comparison between them.

Including earthquake location, waveforms, mechanism and earth reference models.