Gravity Gradient Noise from Ground Waves

Outline

    I. Project plan

   II. Description of gravity gradient

  III. Description of ground waves

  IV. Previous data and estimates for LLO

   V. Description of model

  VI. Model results to date

Supervisor: Mark Coles
Team members: William Quarles, Michael Cheung

Gravity gradient--any nonuniform component of the gravitational field.

On the Earth, both the magnitude and direction of gravitational acceleration varies due to:

• nonspherical Earth
• uneven distribution of the Earth's mass (mascons, etc.)

There is also an apparent gradient due to the Earth's rotation for observers in the rotating
frame of reference.

Gravitational wave observations can be affected by time-dependent gravity gradients from:

• ground waves
• air movements
• moving objects

This is a concern for interferometers more than for resonant bar detectors.

(wave illustrations from Fowler, The Solid Earth, 1990, 1992)

Rayleigh waves are the greatest concern in terms of producing gravity
gradient noise, since they fall off more slowly with distance than body waves and
represent most seismic energy from localized surface sources.

Rayleigh wave properties

• surface wave with both vertical and longitudinal components
• diplacement decreases exponentially with depth, with rate of decrease dependent
  on wavelength
• motion of point on surface is retrograde ellipse
• motion of points below ~0.2/L is prograde ellipse
• waves are nondispersive (i.e. wave velocity is independent of frequency)
  for uniform ground properties (in practice, properties vary with depth leading to
  dispersion)
• amplitude decreases as ~1/ r from localized sources
• localized impulsive sources on the surface tend to produce more seismic energy
  in Rayleigh waves than in other waves

Elements of current model:

• Considers a region of ground as a 3-D grid of mass elements (e.g. 100 m x 100 m x 20 m)
• Simulates a simple sinusoidal Rayleigh wave (single frequency) displacing the mass elements both vertically and horizontally
• Incremental gravity gradient for a test mass 1.5 m above the surface is found from the expression below
• Results from individual simulations provide gravity gradient as a function of frequency and wave amplitude
• Model provides 3-D gravity gradient, although component parallel to detector arm is of primary interest

Expression for gravity gradient:

Strain from simulated gravity gradient (acceleration) amplitude:

where L = arm and B = transfer function

© 2002 by Wm. Robert Johnston.
Last modified 3 October 2002.
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