Department

Earth ScienceCourse Code

EARTH 135Professor

TanimotoStudy Guide

FinalThis

**preview**shows page 1. to view the full**4 pages of the document.**Figure 1: Figure 1: Seamount loading. xpis the distance to the bulge.

Lecture 7 : Plate Flexure due to a Seamount

1. Buoyancy: The equation for plate ﬂexure by seamounts is slightly diﬀerent from the

one for bending plates. This diﬀerence is due to the buoyancy force. The new

equation is

DW ′′′′ + (ρm−ρw)gW =q(x) (1)

where the second term on the lefthand side is the buoyancy term. ρmis density of

mantle and ρwis density of sea water. We assume a uniform half-space for the solid

earth, ignoring the crust.

2. The vertical load by the seamount is treated as a point force at x= 0 and will be

included in the boundary condition. The equation is then

DW ′′′′ + (ρm−ρw)gW = 0 (2)

3. General solutions: For a more detailed derivation, see the later section in pages 3

and 4. Here we note that an equation of the form

W′′′′ +4

α4W= 0 (3)

has four independent solutions that can be written

ex/α cos(x/α), ex/α sin(x/α), e−x/α cos(x/α), and e−x/α sin(x/α).

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