Download Flexural "deconvolution" of surface and internal loads

Geology 6600/7600
Signal Analysis
16 Nov 2015
Last time: Deconvolution in Flexural Isostasy
• Flexural isostasy reflects convolution of mass load
distributions with lithospheric response (a function of
mass density  and flexural rigidity D):
HT = HI + WT
• Using relations to observable signals (gravity, topography)
can express as a system of linear equations and solve for the
loads (e.g, SHD relations for Mars areoid and shape):
• Densities and flexural rigidity must be independently
determined…
© A.R. Lowry 2015
The Tharsis Rise Loading Controversy:
Surface topography
constructed by volcanism?
[e.g., Willemann & Turcotte, 1982;
Solomon & Head, 1982]
Thermal/chemical buoyancy
of a single mantle plume?
[e.g., Sleep & Phillips, 1979; Harder
& Christensen, 1996; Harder, 2000]
Probably some combination of both!
A Tricky-Bit: If Tharsis results from plume
dynamics, this analysis must examine
loading depths in the flow field!
And it does. The l parameter in equation 3 is the surface
deformation response kernel for an instantaneous viscous
flow model with appropriate thickness, density and viscosity
for the assumed planetary model…
Mars
Earth
Another Tricky-Bit: What if the matrix is
singular?
In the presence of membrane stress (as here), these equations
are not automatically ~singular at long wavelengths (but they
will be singular given some choice of load depth!)
By algebraically evaluating the determinant of the matrix and
setting it = 0, find that:
Another Tricky-Bit: What if the matrix is
singular?
Singularity happens when the
geoid/topography ratio predicted
for pure surface loading is
identical to that predicted for
pure internal loading.
Max surface load
400 km load depth
100 km load depth
Max surface load
Test criterion
Reduce the
problem by
“capping”
load
amplitudes
when matrix
is nearsingular…
Effects of lithosphere thickness and internal load depth
on the estimate of internal load contribution
Effects of crustal density and crustal thickness
on the estimate of internal load contribution
Constraining Parameter Space:
• Correlation of the load estimates is very sensitive
to parameter-induced error, because errors in
one load must be balanced by error in the other
• Hence we assume surface and internal load fields
are uncorrelated, and search for model params
that minimize the correlation of the two!
Using the model
parameterization that
minimizes load coherence,
the “best” estimate of
surface loading has an
average thickness of 17 km
within the Tharsis rise, and
average flexure is 12 km.
The averaged internal load
is buoyant but small.
Anomalous elevation of
the western U.S.
Cordillera
(Lowry, Ribe & Smith, JGR 2000)
Researchers have long noted that
elevation of the actively extending
Basin and Range province in the
western United States is anomalously
high (average ~1650 m) given the
anomalously thin (30–35 km) crust.
Hypotheses include hot lithosphere
due to rifting (stretching) and hot
asthenosphere introduced by the
Yellowstone hotspot.