Seismic Sound Lab: Sights, Sounds and Perception of the Earth as an Acoustic Space

Abstract

We construct a representation of earthquakes and global seismic waves through sound and animated images. The seismic wave field is the ensemble of elastic waves that propagate through the planet after an earthquake, emanating from the rupture on the fault. The sounds are made by time compression (i.e. speeding up) of seismic data with minimal additional processing. The animated images are renderings of numerical simulations of seismic wave propagation in the globe. Synchronized sounds and images reveal complex patterns and illustrate numerous aspects of the seismic wave field. These movies represent phenomena occurring far from the time and length scales normally accessible to us, creating a profound experience for the observer. The multi-sensory perception of these complex phenomena may also bring new insights to researchers.

Appendix: Scaling Frequency and Duration

In the process of shifting the frequency of a seismic signal, the number of samples (or data points) in the waveform signal ($n$) does not change. All that changes is the time interval assigned between each sample, $dt$, where the sampling frequency, $f_{Sam} = 1/dt$. Broadband seismometers generally have sampling rates of 1, 20 or 40 Hz. For sound recording a typical sampling frequency is 44.1 kHz. In the context of frequency shifting, consider an arbitrary reference frequency $f_{Ref}$ such that $f_{Ref}/f_{Sam}<1$, because $f_{Ref}$ must exist in the signal. When considering frequency shifting in which the number of samples does not change, this ratio must be equal before and after frequency shifting.

In the problem at hand, we refer to the original sampling rate of the seismic data as $f_{Sam}^e$ (for “earth”), with reference frequency $f_{Ref}^e$, and the shifting sampling rate and reference frequency as $f_{Sam}^s$ and $f_{Ref}^s$, (for “sound”) respectively, such that

$$\begin{aligned} \frac{f_{Ref}^e}{f_{Sam}^e} = \frac{f_{Ref}^s}{f_{Sam}^s} \end{aligned}$$

(1)

As illustrated in Fig. 2, we look at the Fourier transform (FFT) of the original signal, choose a reference frequency based on what part of the signal spectrum that we want to hear (e.g. 1 Hz for body waves), and then choose a reference frequency to shift that value to (e.g. 220 Hz, towards the low end of our hearing). We then re-arrange Eq. 1 to determine the new sampling rate:

$$\begin{aligned} f_{Sam}^s = \frac{f_{Ref}^s}{f_{Ref}^e} f_{Sam}^e \end{aligned}$$

(2)

which is entered as an argument into the “wavwrite” function in MATLAB.

Similarly, duration is $t=n.dt$ where $n$ is the total number of samples, and $dt$ is the time step in seconds between each data point or sample. Since $n$ is constant for the original data and the sound ($n_e = n_s$), we can write $\frac{t_e}{dt_e} = \frac{t_s}{dt_s}$. This is usefully re-arranged to

$$\begin{aligned} t_s = \frac{f_{Sam}^e}{f_{Sam}^s} t_e, \end{aligned}$$

(3)

which is useful for synchronizing the sounds with animations.