Β roadband and narrowband variability in abyssal hill bathymetry Cristian Proistosescu (University of Washington, Harvard University) May 17, 2017 VOICE meeting LDEO, Columbia University
Pleistocene sea level variability characterized by Milankovitch frequencies 1/100 kyr -1 1/41 kyr -1 1/23 kyr -1
Milankovitch frequency variability identified in abyssal hill bathymetry Australian-Antarctic ridge model bathymetry (Crowley et al., 2015,Science)
Milankovitch frequency variability identified in abyssal hill bathymetry Chilean Rise (Huybers et al., 2015,Science)
Stay tuned: Comprehensive Survey
Tectonic processes imply a decrease in abyssal hill wavelength with increasing spreading rate (Olive et al., 2015,Science) (Goff et al., 2015,Science) Filtering by width of emplacement • Filtering by flexural compensation • Intermittent Magma Supply •
Wavelength defined as covariance length scale λ Commonly referred to as Matérn process C ( r ) = σ 2 · [( r/ λ ) ν · K ν ( r/ λ ) /K ν (0)] K ν : modified Bessel function (Goff 1998)
Matérn process is a broadband process yielding a spectral continuum 1-15 -10 -5 0 5 10 15 km λ Three parameters 0.5 acf σ 2 , ν , λ 0 lag variance • kyr -100 -50 0 50 100 smoothness • 10 -2 10 -1 10 0 characteristic scale • 1/km PSD [m 2 /cycle] 10 2 σ 2 2 πλ ν 10 0 freq 1/kyr 10 -3 10 -2 10 -1 0 20 40 60 80 100 120 bath [normalized] km 5 0 -5 kyr 0 200 400 600 800 1000 S=6.6 cm/yr
Influence of characteristic length scale 1-15 -10 -5 0 5 10 15 km λ characteristic scale • 0.5 acf ν , λ 0 lag kyr -100 -50 0 50 100 10 -2 10 -1 10 0 1/km PSD [m 2 /cycle] 10 0 2 πλ 2 πλ freq 1/kyr 10 -3 10 -2 10 -1 0 20 40 60 80 100 120 bath [normalized] km 5 0 -5 kyr 0 200 400 600 800 1000 S=6.6 cm/yr
Influence of smoothness 1-15 -10 -5 0 5 10 15 km λ smoothness parameter • 0.5 acf 2 , ν , 0 lag kyr -100 -50 0 50 100 10 -2 10 -1 10 0 1/km PSD [m 2 /cycle] ν = 0 10 0 freq ν = 2 1/kyr 10 -3 10 -2 10 -1 0 20 40 60 80 100 120 bath [normalized] km 5 0 -5 kyr 0 200 400 600 800 1000 S=6.6 cm/yr
Broadband variability can arise from filtering of anomalies 10 -2 10 -1 10 0 10 2 PSD [m 2 /cycle] 10 1 b ( f ) = F ( f ) · ε ( f ) 10 0 10 -1 10 -3 10 -2 10 -1 freq r 2 + λ − 2 ⇤ ( ν +1) / 2 ⇥ } b ( r ) = ε σ 2 ( r ) | {z F − 1
Filtering by width of emplacement ∆ h ∆ h ( τ ) = F w ( τ ) · φ ( τ ) Crustal thickness Melt flux Filter (Olive et al., 2015,Science)
Filtering by flexural compensation F c [%] λ [km] b ( λ ) = F c ( λ ) · ∆ h ( λ ) λ = τ · S (adapted from Olive et al., 2015,Science)
Continuum variability: Summary • Characteristic length scale ( λ ), is a decorrelation length scale/ frequency: ✦ Excursions above/below mean bathymetry last, on average, λ . • Record looks peaked, but it has no true periodicity. • Arises naturally in geophysical processes as a consequence of integrating perturbations • Implications for detecting orbital peaks (adapted from Olive et al., 2015,Science)
Characteristic length scale
Fit to bathymetry transects
Matérn fit ν = 0 . 25 2 π · λ /S = 95 ± 45[ kyr ]
Null Hypothesis for a single transect db/dt b
Null hypothesis distribution for 16 transects db/dt b Each Monte Carlo draw: average over 16 Matern process realizations, each with λ set to λ of profile
Work in progress …provided one has access to a reasonable amount of time on a reasonably powerful computer, an exact test of significance is something one never need be without. G.A. Bamard. 1963 • Caveats: • Improve fitting algorithm • Generate processes with non-integer ν
Glacial Cycles: Ice Sheet Dynamics filters Insolation forcing V ( f ) = F ( f ) · I ( f ) (Huybers & Tziperman 2008)
Glacial Cycles 1/100 kyr -1 1/41 kyr -1 1/23 kyr -1
Pre-whitening highlights higher frequency 1/100 kyr -1 1/41 kyr -1 1/23 kyr -1
100kyr cycle contains most of the variance 45% 18% 5%
Narrowband variability Obliquity and Precession can be identified despite increased • additional variance at lower frequencies 100kyr Glacial Cycle is not a direct orbital response. One • likely mechanism is pacing by Obliquity and Precision of thresholding processes in Ice-Sheets (Calving?) or Carbon Cycle. More general: Non-linear phase locking (Tziperman et al • 2006).
Last thoughts: Thresholding process faulting 100kyr Glacial Cycle is not a direct orbital response. One • likely mechanism is pacing by Obliquity and Precision of thresholding processes in Ice-Sheets (Calving?) or Carbon Cycle. More general: Non-linear phase locking (Tziperman et al • 2006). Can lead to quasi-periodic features:
Τ hanks!
Abyssal hill bathymetry (Science News, 2015)
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