Interpretation approaches
Rule No. 1 (and 2 and...): Gravity anomalies
are produced by density contrasts
Uniqueness (ambiguity) Problem
- applies to all potential field methods, and, indeed,
all geophysical methods
- there is an inherent ambiguity in interpretation of
gravity data
- even if you had gravity at every point on Earth's
surface, there are multiple models that would produce those values
- because of integral nature of gravity, it can be proven
that any anomaly can be result of an infinite number of density
distributions!
Constraining Interpretations
- not hopeless: gravity eliminates even "more infinite"
number of density distributions
- combine gravity data with other constraints:
- density of crustal rocks, particularly in local area
- configuration of rocks: well data, regional geology,
etc.
- other geophysics: magnetics, seismic, etc.
Role of interpretation in survey planning
- should the survey be conducted?!
- how should it be conducted?
Simplifying density models
- because we are interested in (and indeed only measure)
change in g, we are only interested in
changes in density (density contrast)
- background density can always be subtracted
- furthermore, horizontal slab doesn't contribute to
gravity anomalies
- in some cases (e.g., sphere, horizontal cylinder),
mass excess/deficiency, is determinable quantity
- a datum shift may be made to compare model to data
Interpretation approaches
Forward modelling
- assume specific initial subsurface density model
- calculate gravity (always do-able, at least
numerically)
- compare with data
- adjust density model as necessary
- repeat steps 2 through 4
Inverse method
- assume general class of model (e.g., buried sphere)
- analyze anomaly (anomalies) to define specific model
Gravity of simple geometric shapes
- gravity of Earth >> any anomaly
- gravity defines vertical
- therefore gravity meters measure vertical component:
If
horizontal component is 100 mgals, angle between g and g' is 0.006 degrees!
Infinite slab
where h is the thickness
- works for gently sloping surfaces
- example: topography on basement
- error < 3% for slope < 1/5 (see Adams
and Hinze, vol. 3, SEG Geotech. & Environ. Gphy., p.99
- use estimate magnitude of anomaly for many flat-layer
situations:
- relief on density contrast boundary: basement,
bedrock, etc.
- dip-slip fault in horizontal strata
- laterally extensive mines
- water removal/recharge in horizontal aquifer
For a thin half-slab (h<<z),
Sphere
- applicable to approx. equidimensional bodies (longest
dimension << depth)
- gravity due to sphere:
- vertical component:
- Since,
, we
get
- Where is g 1/2 of maximum?
- Therefore, the depth can be determined by (depth criterion):
- example: find depth of sphere, z,
and, assuming density contrast of 1.0,
find radius of sphere.
Horizontal Cylinder
- applicable to bodies much longer in one horizontal
direction than in vertical or other horizontal direction
- tunnels, river channels, horst or graben block, etc.
(vertical component - what we measure)
Vertical Cylinder, Inclined Rod, Horizontal
Sheet, etc.
Case Histories
