b'Data trends Data trendsSegments small enough you can assumes : scale. For a number of stationarity independent of the rest ofpredetermined scales, the wavelet the signal. This increases time resolutionwill be stretched or compressed. (where frequencies occur in the signal)Different scales will resolve difference but ignores signal outside the windowedfrequencies.section of time/space. It has reducedt : the offset by which the centre frequency resolution and cannot resolveof the wavelet is translated along the frequencies outside the time windowsignalthat also contribute. An easier general description, which Now we have the shotgun approach ofborrows heavily from Vinay Yuvashankars the Wavelet Transform which combinespseudocode (Yuvashankar 2016) is as piecewise convolution of the signal withfollows:a wavelet that changes size to resolve aDetermine the range of scales and range of frequencies (see Figure 1). translationsFT the signalTim Keeping=For each scaleAssociate Editor for geophysical data Scale the waveletmanagement and analysis For each translationtechnical-standards@aseg.org.au Figure 1.Continuous wavelet transform equation Translate wavelet along the signal Convolve wavelet withWavelet transforms It is still a conventional convolution ofsignalsignal f(t) with wavelet (), and |s| ensures Invert the resultThe wavelet transform is a relativethe energy of the result remains constant Store the magnitude newcomer to potential fields, but iswith input. I want to focus on the terms starting to appear more frequently inthat influence the wavelet functionThe magnitudes derived from various literature. While most of us are familiar(), which show the wavelet transformscales are used as coefficients to model with the Fourier Transform (FT), what isis really just an iterative series of FTthe signal (Figure 2). The coefficients this new application of the FT? convolutions. The keywords are scales (s)are used in deep neural networks, and translations (t - ). compression such as ECW (Enhanced Luckily there are people like Robi Polikar of Rowan University who in 2006 published the second edition of his 70 page introduction for the rest of us, the Wavelet Tutorial (Polikar 2006). He informs us he wrote the tutorial for mathematics professors and engineers confused by the idea, and that the rest of us should not feel embarrassed if we are also confused.Geophysicist Jean Morlet and Alexandre Grossmanns technique (Grossmann and Morlet 1984) purports to improve on Heisenbergs Principle in signal analysisthat we can only pick one property to defineeither the frequency or its position in time/space, but not both. Polikar demonstrates with both stationary and non-stationary signals that transform into near identical frequency graphs. This shows the Fourier Transform accounts for all frequencies within a signal (has full frequency resolution) but cannot distinguish where they occur (poor time resolution).Figure 2.Example of coefficients produced by the continuous wavelet transform. Generated using MatLab The Short Time Fourier Transform (STFT)cwtft2 command running default settings on an Analytical Signal grid of the Delamerian project area. Starting introduced time/space windows to breakfrom left, wavelet scaling resolved high frequency from outcropping in the shallow northern area (far left), the signal into piecewise segments.progressing to lower frequencies resolved in the centre and south around the Renmark Trough (right).OCTOBER 2020 PREVIEW 34'