Data Processing

Data ProcessingChapter 3As a science major, you will all eventually have to deal with data.All data has noiseDevices do not give useful measurements; must convert dataThe better you can handle data, the more employable you will be

Wavelength and Fourier AnalysisThe granite produces a negative gravity anomalyVariations in the sediment cover cause noise in the dataThe noise and the anomaly have different wavelength scalesFourier analysisSeparates signals by wavelengthA Simple ExampleGeneral Wave TermsAmplitude (a) =

Wavelength () =

Frequency =

Period = 0.5 1.5 2 -a0.5a00.5aaAmplitudeWavelength ()

Harmonic AnalysisHarmonics: multiples of a signals half wavelength, LWhy use harmonics?Found in nature and musicLike a guitar!Any wiggly line can be mathematically reproduced by adding together a series of wavesExact match requires waves1st 5 harmonics0.2 L0.4 L0.6 L0.8 LL-10.500.51

Fourier AnalysisA type of harmonic analysis where wiggly data are separated into various harmonics of differing amplitudeAdjusts the amplitudes of each harmonicCan isolate dominant frequencies/wavelengths in data and remove unwanted onesSum of harmonics reproduces data exactly

Sum of same harmonics, but with different amplitudesData Separated by WavelengthIn this tide data, what type of wavelengths (short or long) should we remove?What causes each?

What to Remove?

Caveats of Fourier AnalysisRequires a complete signalStarts and ends at same valueOnly analyzes wavelengths that are multiples of the signal lengthGeologic targets likely have multiple wavelengths and may share some wavelengths with noise.

Digital FilteringAn alternative way to remove unwanted wavelengths/frequencies: FilteringUsually applied to regularly space dataIf data not regular, interpolation can be usedE.g. A simple 3-point filter :: 1/3 (yn-1 + yn + yn+1)Also called3-point running average3-point moving window

1 0 5 4 9 4 2 3 1 51 2 3 4 5 6 7 8 9 10Time or DistanceValueFiltered Value2X36There are also 5-point, 7-point, and n-point filters.Some are weighted to remove certain wavelengths

Effects of Digital FiltersLow-pass filterAlso called Smoothing filterAllows low freqto pass throughHigh-pass filterAllows high freqTo pass throughBand-pass filterConstructed to only let certain bands or frequencies through

A subwoofer in a bandpass box

Effects of Digital FiltersA given filter may have a very different effect on data depending on:WavelengthSampling Rate / ResolutionA filter can completely decimate a signal

AliasingIf sampling rate (resolution) approaches wavelength of signalMay see false patternsIf sampling rate is less than signals wavelengthMay see false long wavelength signalsAliasing: Discrete (non-continuous) data can suggest patterns that are not realNyquist wavelength = half the signals wavelength. This is the minimum sampling rate to avoid aliasing

Gridded Data ProcessingAll of the data processing techniques discussed here can also be applied to gridded or even three-dimensional dataCan filter directional noiseHighlights directional featuresGeologists should pay attention in multivariable calculus class! E.g. MAT 2130 - CALCUL ANALY GEOM IIIDo not rely on black box computer programsE.g. Arc GIS

Filtering in 2D :: Gridded DataFilters can be created to filter all types of dataNo technique is perfectGreat care must be given when creating a filter or processing data in general