Use of Magnetic Data in Geothermal
Studies
D. Ravat
University of Kentucky
Premise

Bottom of the magnetic layer could be related
to Curie temperature of magnetic minerals
(Magnetite, Hematite, Titanomagnetites)
 Temperatures in the deep crust/lithosphere
difficult to measure directly and modeling of
heat flow requires parameters not always
available
 Seismic, magnetic, gravity/topography
coherence methods may provide independent
constraints
The Magnetic Bottom:
Data and Methods
 Near-surface Anomalies -  < 500-1000 km
Spectral methods (slopes related to depth)
 Analytical methods (centroids of idealized
sources)
 Inversion (layers with depth weighting)

 Satellite-derived Anomalies –  > 500 km

Inversion (volume magnetization variation
sensing simultaneously changes in
magnetization and the thickness of the layer)
Spectral Methods:
Background
 Spector & Grant (1970)
- slopes of logarithms
of azimuthally averaged power spectra of
magnetic anomalies from ensemble of simple
sources are related to depths to top of the
ensemble and have peaks related to thickness
of the layers
F(T )2  4 2Cm2 m f Mo2 e
2
2
2 k z t

1e
k t
 S (a,b)
2
2
Depth to the Bottom of Magnetic Sources
 Slope approach for centroid on 1/f spectra
[ G (k) = 1/f F(k) ] Bhattacharyya & Leu (1975)
- used by Okubo et al. (1985) for “Curie depth”
of Kyushu, Japan
Okubo et al. suggested that
centroid estimates could be
derived from data windows as
small as 40 km x 40 km (?).
However, this can lead to
estimates on shallow/intermediate
layers and not the deepest
layers….
Depth to the Bottom of Magnetic Sources
 Slope approach for centroid on 1/f spectra
Tanaka et al. (1999) - picking slopes from different
wavenumber ranges
“F(k)” Spectra
“G(k) = 1/f F(k)” Spectra
Valid argument, but one could end up picking slopes from
different layers….
Depth to the Bottom of Magnetic Sources
 Spectral Peak Approach of Spector & Grant
(1970) - also used by Shuey et al. (1977),
Connard et al. (1983), Blakely (1989)
kmax 
ln z2  ln z1
z2  z1
 And recently used for “forward modeling” by
Ross et al. (2006) and Ravat et al. (2007)
2

F(k)  C e
 k Zt
e
 k Zb

Example of Modeling and Ambiguity
2
Removing long-wavelength
trends or lowcut filtering can
result in false spectral peaks….
Other Issues:
 Fedi et al. (1997) recognized that shape factor,
S2, in the Spector & Grant (1970) equation has
power law form for large source dimension
variations, such that
F(k)  k 2.9
2
 Pilkington & Todoeschuck (1993) and Maus &
Dimri (1994) and other papers also suggest k-
dependence from fractal source distributions
Correction to the spectra by k factor leads to
shallower depths to top
From Fedi et al. (1997)
Many methods and caveats exist…
exist…
How well can we really do, given a power spectrum, not
knowing much about the nature of the sources?
We tested several methods:
Top:
Spector & Grant (1970) with and without k3 correction
(Fedi et al.,1997), which is also appropriate for fractal
sources
Bottom:
1/f Spectra (Bhattacharyya and Leu, 1975; Okubo et al.,
1985; Tanaka et al.,1999)
Spectral Peak method, and the forward modeling of the
spectral peak
Several types of models tested:
Layered source distribution having an upwarp geometry
with thin and thick layers
Random source distribution within the above geometry
with thin and thick layers
A large layered and upwarped source model
Magnetic Anomaly
Top
Bottom
Constant magnetization layer
Observation height 1 km
Inclination 60°, Declination 0°
Uniform Magnetization Upwarp Source, Thin Layer
Window 200 km
Center Location (350, 350)
Window 200 km
Center Location (350, 350)
Spector & Grant
k corrected spectra
1/f spectra for centroid
modeled
Actual Depth to Top = 4.52 ± 0.82 km; Depth to Bottom = 6.23 ± 1.23 km
Derived Depth to Top:
From slope on k corrected spectra = 3.75 km (within 1 SD)
Modeled = ~ 4-5 km
Derived Depth to Bottom:
From 1/f spectra = 6.67 km (within 1 SD)
Modeled = No observed spectral peak; (minimum est.) ~ 6 km (illustrated ~ 7 km)
Actual Model
“Forward Modeled” Depths
Estimation Error
Top
Top
Top
Top
Bottom
Bottom
Bottom
Bottom
Uniform Magnetization Upwarp Source, Thin Layer
Top
Top
Bottom
Error in different
estimations (km)
(positive is deeper):
Spector & Grant:
Top: 5.01±2.05
Bottom: 1.16±1.56
K3 factor corrected:
Top: 4.73±1.88
Bottom: 0.84±1.44
Forward Modeled:
Top: 1.15±1.148
Bottom: 0.89±1.36
(no peak; minimum estimate)
Random Magnetization Random Sources
within Thin Upwarped Layer
Window 160 km
Center Location (230, 230)
Window 160 km
Center Location (230, 230)
Spector & Grant Spectra
Spector & Grant Spectra
Modeled Spectra
k corrected spectra inappropriate
No Clear Low
Wavenumber
Spectral Peak
Observed !
Actual Depth to Top = 8.89 ± 2.05 km; Depth to Bottom = 10.34 ± 1.88 km
Derived Depth to Top:
From slope (Spector & Grant) = 5.25 km (shallower than 1 SD)
Modeled = ~ 6.5 km
Derived Depth to Bottom:
From 1/f spectra = 7.55 km (shallower than 1 SD)
Modeled = No clear observed spectral peak; minimum ~ 8-9 km
Random Magnetization Random Sources within Thin Upwarped Layer
“Forward Modeled” Depths
Actual Model
Estimation Error
Top
Top
Top
Bottom
Bottom
Bottom
Bottom
Top
Random Magnetization Random Sources
within Thin Upwarped Layer Error in different
Top
Bottom
estimations (km)
(negative is shallower):
Spector & Grant:
Top: -2.83±0.59
Bottom: -6.16±0.94
K3 factor corrected:
Top: -1.27±0.95
Bottom: -4.58±0.87
Forward Modeled:
Top: -1.57±0.44
Bottom: -0.32±0.71
(minimum estimate)
Uniform Magnetization Upwarp Source, Thick Layer Not deducible
Representative Example
Window 300 km
Center Location (300, 300)
1/f spectra
Spector & Grant Spectra
modeled
k corrected spectra
The best estimate of top lies
between Spector & Grant and
K3 corrected depth estimates.
Bottom not decipherable from any
method; minimum estimate too low
to be useful….
Error in different
estimations (km)
(positive are deeper):
Spector & Grant:
Top: 2.27±0.57
Bottom: -27.78±1.15
K3 factor corrected:
Top: -1.67±0.38
Bottom: -31.60±0.91
Forward Modeled:
Top: -1.13±0.38
Bottom: -19.69±4.46
(no peak; minimum estimate)
Conclusions of the model studies
- Thin layers of random or uniform magnetization
appear suitable for spectral depth estimates to top
and bottom of magnetic sources
- Forward modeling of spectral peak showed that
there can be large uncertainty in the bottom
estimate, especially for thick layers
- In the cases of large variance of model tops and
bottoms, all methods appear to fail. But spectra
don’
don’t indicate anything odd…
odd….
North American Magnetic Data
with  > 500 km corrected using
CHAMP satellite-altitude anomalies
1/f Spectra
Modeling
F(k)
320 km window
3 Spectra deemed inappropriate
Depth to Top:
Slope = ~12-13 km
Modeling = ~ 1212-15 km
Depth to Bottom:
1/f Spectra = ~ 36 km
Spectral Peak (Kmax) = ~36 km
Modeling = ~ 3535-50 km
US Magnetic
Anomalies
Curie Depth
Using Forward
Modeling of
LW- Magnetic
Spectra
Seismic
Crustal
Thickness
Satellite-Derived Long-wavelength
Magnetic Anomalies (CHAMP)
Volume Susceptibility Variation
Random Magnetization Upwarp Source, Thick Layer
Large Std. Dev. of Top and Bottom (± 7-10 km)
Example where none of the spectral methods
are appropriate for either top or bottom
Window 300 km
Center Location (300, 300)
1/f spectra
Spector & Grant Spectra
Error in different
estimations (km)
(negative is shallower):
Spector & Grant:
Top: -14.41±0.75
Bottom: -20.25±1.20
modeled
k corrected spectra
K3 factor corrected:
Top: -17.91±1.95
Bottom: -25.95±3.75
Slope doesn’t represent depth to top,
but can’t tell that from spectra
Forward Modeled:
themselves…
Top: -13.80±1.13
Spectral peak not consistent with
Bottom: -4.87±7.94
average depths to top and bottom….