First, let's look at some real gravity:

This is a free-air global map from the GRACE (twin satellite).

• note small g range; indicates near complete isostatic compensation, at this scale
• little correlation with continents (isostasy!)
• Hawaiian, Yellowstone, Iceland hotspots
• subduction zones - asymmetrical low/high
• Rockies, Appalachians - nada - why?
• Himalayas - dynamic uplift; not in isostatic equilibrium
• Hudson Bay - glacial rebound not complete

Bouguer gravity map of United States

• smaller scale, small, isostatically uncompensated features show up
• Bouguer correction "innapropriate" for longer scale anomalies, like Rocky Mts.
• Mid-continent geophysical anomaly, and into Mich - Keweenwan (1 GA) failed rift; extends into OK?
• Oklahoma aulacogen
• Ouachitas - compensated?

Note the remarkable resemblance:

Blue Spruce:

Spruce Goose:

Anomaly Separation and Filtering

• applies to gravity and magnetics!
• gravity and magnetic fields are each the sum of many anomalies
• core, mantle, relief on Moho, deep crustal density anomalies, all produce long-wavelength anomalies
• short-wavelength effect of shallow crustal bodies may overlap
• N.B.:
  • deep bodies produce only long wavelengths; shallow bodies can produce long or short wavelengths!
  • shortest wavelength that can be produced at given depth is due to point mass (or spherically symmetric mass)
• in exploration surveys, usually interested in shallow features
• removal of long-wavelength anomalies (usually due to deep sources) enhances short-wavelength (i.e., necessarily shallow) features
• regional: gravity due to deep-seated body, not of interest(?!)
• residual: what is left after removal of regional
• mustn't "throw out baby with bath water"

regional field: long-wavelength "background" field

residual field: total field - regional field

• removal of regional corresponds to high-pass filter (pass high wavenumber anomalies, reject small)

• methods:

  • graphical smoothing

  • polynomial fitting

  • averaging

  • upward continuation

  • wavelength filtering

• examples:
  • profile, regional removal
  • another profile, regional removal
  • contour data, smoothing
  • ring method, contour data
  • picking ring size
  • grid method of regional removal
  • running average, profile
  • matrix smoothing (running average), contour data
  • LA Basin, regional removal

Happy St. Patrick's Day!

Trend surfaces

• fit a smooth (polynomial) surface to data to represent regional
• subtract calculated regional value from observed value at each point to get residual field (Fig. 6-26, 27, 28)
• examples:
  • north-central Iowa trend surfaces

Upward and downward continuation

• knowing field at one elevation, can compute what field would look like at a higher elevation (upward continuation) or lower elevation (downward continuation
• downward continuation enhances near-surface bodies more than deeper bodies, hence lessens effect of regional
• Complete Bouguer Anomaly, 25-km upward-continued, residual Bouguer

Second derivatives

• enhances short wavelength anomalies relative to long wavelength anomalies
• note, for modelling purposes, that result does not have units of g
• Tends to delineate edges of anomalous body (Fig. 6-31)

• examples:
  • effect of 2nd derivative
  • radius of curvature and 2nd derivative
  • salt domes, Texas
  • LA Basin
  • Cement field, OK

Filtering

• high-pass filtering passes high frequencies; cuts low frequencies (long wavelengths) and hence reduces regional
• The fourier transform, a mathematical operation, can be applied to digital data quickly using the "fast Fourier transform," or FFT
• amplitude vs. distance, or spatial domain
  • FFT converts to amplitude vs. wavenumber, or wavenumber domain
  • inverse FFT transforms back to spatial domain
    
• amplitude vs. time, or time domain
  • FFT converts to amplitude vs. frequency, or frequency domain
  • inverse FFT transforms back to time domain
• Common filters:
   

  highpass
  lowpass:
  bandpass:
  tapered bandpass:
  before and after Fourier transform:
  Above, bandpass filtered:

• practical examples
  • Fourier filtering
  • eastern Sierra Nevada, complete Bouguer, low-pass filtered (keep wavelengths >50 km)
  • eastern Sierra Nevada, high-pass filtered (keep wavelengths <50 km)
  • comparison of low-pass filtering and upward continuation
• filtering sound:
  • no filtering
  • highpass filtered (2000 Hz cutoff)
  • lowpass filtered
  • bandpass filtered (1000 - 2000 Hz)