Graham Heinson, Jon Kirby, Kent Inverarity, Katherine Stoate, Tania DhuFrome AEM Survey Data Interpretation WorkshopWednesday 30th November 2011Mawson Laboratories, University of Adelaide, Adelaide SA 5001

The Fractal Dimension of the Frome AEM Data

40-60 m Conductivity slice

“We show here that electromagnetic responses are fractal signals, reflecting a very rough distribution of electrical conductivity. Apparent conductivity profiles across a floodplain and a fractured sandstone aquifer both show that the fractal properties of the surface response depend on the complexity of the causative geological structure.”

Sandstones (heterogeneous) have greater slopes of power spectra than (well sorted) alluvial sediments

Many physical and geophysical phenomena arefractal in nature, such as topography and gravity field. These data have spectra with a power-law decay |k|-, where |k| = kx

2+ ky2

The slope of the power spectra is related to thefractal dimension by = 8 - 2FD (or FD = 4-/2)

Wavelet Transform

Wavelet Transform

Wavelet transform enables a ‘‘power spectrum’’ to be calculated at each and every location of a specified signal, i.e., power as a function of space and frequency

Fourier power spectrum, yields power as a function only of frequency - spatial information has been lost

Wavelets use localised basis functions, rather thaninfinitely repeating sines and cosines.

Wavelet transform of a signal,g(x,y) is computed from the convolution of the signal with the complex conjugate of a wavelet, (x,y)

Australian DEM (a), and its scalograms at 21 km scale, for (b) DoG, (c) Fan, (d) Halo, (e) Morlet, (f) Paul, (g) Perrier, and (h) Poisson wavelets. Grey-scale for scalograms is log10(power), from high (light) to low (dark) power.

What information is contained in the Frome AEM data set?•Preliminary study looked at the 40-60 m conductivity slice•Gridded at 0.625 km squaresCan wavelet analysis indicate variability in power and fractal scaling?

DoG Wavelet ScalogramPower contained in

wavelet

40-60 m Conductivity Slice DoG Wavelet at 10 km scale

DoG Fan Halo

Morlet Perrier Poisson

40-60 m Conductivity Slice

Fractal dimension indicates spatial correlation

Conclusion

• Why might is be worth this analysis?– Power-spectra indicate localised change, edges– Differences between homogenous and

heterogeneous Earth– Fractal dimension indicates spatial self similarity

over different scale lengths (correlation with wavelengths)

– Potentially link fractal dimension with geology (fractures, lithology, stratigraphy, groundwater, etc)