1. Time Series Analysis of Elephant Acoustic and Seismic Signals Alex Williamson Physics Dept

2. Infrasonic Elephant Calls  Fundamentals in the 10-20 Hz infrasonic range  Travel in air as sound waves and ground as Rayleigh waves  Long distance talking? Elephants may hear up to 4-10 km away  Detect only acoustic signals, or seismic signals also?  What if speed in ground different?

3. Data collection  Two data sets studied: Hohenwald Elephant Sanctuary in Tennesse Hohenwald Elephant Sanctuary in Tennesse Dzanga National Park in the Cental African Republic Dzanga National Park in the Cental African Republic http://www.elephants.com/sis_winks_creek.htm http://www.birds.cornell.edu/brp/elephant/ELPresearchDz.html

4. Digital Sampling  Sensors: Geophones detect seismic velocities Geophones detect seismic velocities Microphones detect air pressure Microphones detect air pressure Translated into proportional output voltage. Translated into proportional output voltage.  Computer measures this voltage periodically at the sampling rate (44,100 times a second for a 44.1 kHz rate)  Frequencies above Nyquist (half the sampling rate) cause aliasing, must be filtered out  Worked with data at rates of 1- 2 kHz, as signals < 500 Hz

5. Cross Correlations  Determines the phase difference between two digital signals  Used to find time difference between a signal reaching two different sensors  Multiplies the signals together and takes the sum, repeating for every possible phase combination

6. Cross Correlations  Determines the phase difference between two digital signals  Used to find time difference between a signal reaching two different sensors  Multiplies the signals together and takes the sum, repeating for every possible phase combination  The result is a data series where the phases with the best fits have the highest value  In some cases, the peak is hard to determine so a low-pass digital filter can be used.

7. The first signal leads the second by 20π, which we know is correct.

8. Using Cross-Correlations  Find speed of propagation using multiple sensors, knowing the position of the source (and vice versa, a la GPS)  In Hohenwald, had two microphones and two geophones  X-correlate between the mics for air speed  Between the geophones for ground speed

9. Using Cross-Correlations

10. Digital filtering  A time series is digitally filtered by running each data point through the equation: where a & b are vector characteristic to the filter  A time series is digitally filtered by running each data point through the equation: a 1 y n = b 1 x n + b 2 x n-1 +... + b nb+1 x n-nb - a 2 y n-1 -... - a na+1 y n-na where a & b are vector characteristic to the filter

11. Advantages and Uses  Matlab’s “filtfilt” function avoids phase problems filtering by running filtered signal through filter again in the opposite order, reversing phase shifts and doubling filter strength.  Filter used for: Getting rid of narrow-band electrical noise, such as 60 Hz hum Getting rid of narrow-band electrical noise, such as 60 Hz hum Focus on specific frequency bands individually, as some bands were noisier than others Focus on specific frequency bands individually, as some bands were noisier than others Digitally undo analog filtering Digitally undo analog filtering

12. Attenuation from 200 meter calls  Octave band filtering (5-10 Hz, 10-20, 20- 40, etc) on four elephant calls, background noise samples from similar time, and electrical noise model for accuracy baseline  Found RMS values of filtered signals  Convert to velocities using freqency-based gain factor (taking out filters for real speeds)  Found acceleration and displacement by multiplying and dividing by ω

13. Attenuation from 200 meter calls

14. Signal to noise  Signal and noise orthogonal so S rms 2 =T rms 2 -N rms 2 to separate signal from background  Used four different noise samples, and averaged ratios in plot.  Power is proportional to the voltage squared, and falls off at 1/r (vs 1/r 2 for air during day)

15. Signal to noise

16. Future Plans  What problems with data and analysis? High noise levels High noise levels Over-filtering Over-filtering Phase problems Phase problems  What will we want to do differently in future measurements? Multiple sensors Multiple sensors Uniform filtering Uniform filtering Avoid human interference Avoid human interference  Plans for Syracuse Zoo next month: Use new shaker (R2D3) Use new shaker (R2D3) Mechanical model of elephant leg Mechanical model of elephant leg Sound of a footstep Sound of a footstep