roadband and narrowband variability in abyssal hill bathymetry - - PowerPoint PPT Presentation

Βroadband and narrowband variability in abyssal hill bathymetry

Cristian Proistosescu (University of Washington, Harvard University) May 17, 2017 VOICE meeting LDEO, Columbia University

1/41 kyr-1 1/23 kyr-1 1/100 kyr-1

Pleistocene sea level variability characterized by Milankovitch frequencies

(Crowley et al., 2015,Science)

Australian-Antarctic ridge

Milankovitch frequency variability identified in abyssal hill bathymetry

model bathymetry

Milankovitch frequency variability identified in abyssal hill bathymetry

(Huybers et al., 2015,Science)

Chilean Rise

Stay tuned: Comprehensive Survey

(Olive et al., 2015,Science)

• Filtering by width of emplacement
• Filtering by flexural compensation
• Intermittent Magma Supply

Tectonic processes imply a decrease in abyssal hill wavelength with increasing spreading rate

(Goff et al., 2015,Science)

Wavelength defined as covariance length scale

(Goff 1998)

Kν : modified Bessel function C(r) = σ2 · [(r/λ)ν · Kν(r/λ)/Kν(0)] Commonly referred to as Matérn process λ

200 400 600 800 1000

bath [normalized]

• 5

5 20 40 60 80 100 120

freq

10-3 10-2 10-1

PSD [m2/cycle]

100 102 10-2 10-1 100

lag

• 100
• 50

50 100

acf

0.5 1-15

• 10
• 5

5 10 15

Matérn process is a broadband process yielding a spectral continuum

kyr km kyr km 1/kyr 1/km

S=6.6 cm/yr

ν λ 2πλ

Three parameters

• variance
• smoothness
• characteristic scale

σ2, ν, λ

σ2

200 400 600 800 1000

bath [normalized]

• 5

5 20 40 60 80 100 120

freq

10-3 10-2 10-1

PSD [m2/cycle]

100 10-2 10-1 100

lag

• 100
• 50

50 100

acf

0.5 1-15

• 10
• 5

5 10 15

Influence of characteristic length scale

kyr km kyr km 1/kyr 1/km

S=6.6 cm/yr

λ 2πλ

• characteristic scale

ν, λ 2πλ

200 400 600 800 1000

bath [normalized]

• 5

5 20 40 60 80 100 120

freq

10-3 10-2 10-1

PSD [m2/cycle]

100 10-2 10-1 100

lag

• 100
• 50

50 100

acf

0.5 1-15

• 10
• 5

5 10 15

Influence of smoothness

kyr km kyr km 1/kyr 1/km

S=6.6 cm/yr

λ

• smoothness parameter

2, ν,

ν = 2 ν = 0

Broadband variability can arise from filtering of anomalies

freq

10-3 10-2 10-1

PSD [m2/cycle]

10-1 100 101 102 10-2 10-1 100

⇥ r2 + λ−2⇤(ν+1)/2 | {z } b(r) = εσ2(r) F−1 b(f) = F(f) · ε(f)

(Olive et al., 2015,Science)

Melt flux Crustal thickness Filter

∆h(τ) = Fw(τ) · φ(τ) ∆h

Filtering by width of emplacement

(adapted from Olive et al., 2015,Science)

Filtering by flexural compensation

λ[km] Fc[%] b(λ) = Fc(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

Characteristic length scale

Fit to bathymetry transects

Matérn fit

ν = 0.25 2π · λ/S = 95 ± 45[kyr]

Null Hypothesis for a single transect

db/dt b

Null hypothesis distribution for 16 transects

Each Monte Carlo draw: average over 16 Matern process realizations, each with λ set to λ of profile

db/dt b

Work in progress

…provided one has access to a reasonable amount of time

• n 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

1/41 kyr-1 1/23 kyr-1 1/100 kyr-1

Pre-whitening highlights higher frequency

1/41 kyr-1 1/23 kyr-1 1/100 kyr-1

100kyr cycle contains most of the variance

5% 18% 45%

Narrowband variability

• 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).

• Obliquity and Precession can be identified despite increased

additional variance at lower frequencies

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:

Τhanks!

Abyssal hill bathymetry

(Science News, 2015)