Abstract
A gross datum of the Earth is a single measurable number describing some property of the whole Earth, such as mass, moment of inertia, or the frequency of oscillation of some identified elastic-gravitational normal mode. We prove that the collection of Earth models which yield the physically observed values of any independent set of gross Earth data is either empty or infinite dimensional. We exploit this very high degree of non-uniqueness in real geophysical inverse problems to generate computer programs which iteratively produce Earth models to fit given gross Earth data and satisfy other criteria. We describe techniques for exploring the collection of all Earth models which fit given gross Earth data. Finally, we apply the theory to the normal modes of elastic-gravitational oscillation of the Earth.
Keywords
Geodetic datumEarth modelInverse problemUniquenessGeophysicsInverseEarth structureGravitationMoment of inertiaInverse theoryGeodesyMathematicsGeologyMathematical analysisPhysicsClassical mechanicsGeometryDeformation (meteorology)
Affiliated Institutions
Related Publications
An application of normal mode theory to the retrieval of structural parameters and source mechanisms from seismic spectra
A cyclic process of refining models of the mechanical structure of the Earth and models of the mechanism of one or more earthquakes is developed. The theory of the elastic-gravi...
Earth Structure from Free Oscillations and Travel Times
An extensive set of reliable gross Earth data has been inverted to obtain a new estimate of the radial variations of seismic velocities and density in the Earth. The basic data ...
GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs
We present the results from three gravitational-wave searches for coalescing compact binaries with component masses above <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" di...
Importance of physical dispersion in surface wave and free oscillation problems: Review
Physical dispersion resulting from anelasticity is investigated from the point of view of linear viscoelastic models and causality relations. It is concluded that inasmuch as Q ...
Pulse distortion and Hilbert transformation in multiply reflected and refracted body waves
abstract Many seismic body waves are associated with rays which are not minimum travel-time paths. Such arrivals contain pulse deformation due to a phase shift in each frequency...
Publication Info
- Year
- 1967
- Type
- article
- Volume
- 13
- Issue
- 1-3
- Pages
- 247-276
- Citations
- 932
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
932
OpenAlex
Cite This
George E. Backus,
Jock Gilbert
(1967).
Numerical Applications of a Formalism for Geophysical Inverse Problems.
Geophysical Journal International
, 13
(1-3)
, 247-276.
https://doi.org/10.1111/j.1365-246x.1967.tb02159.x
Identifiers
- DOI
- 10.1111/j.1365-246x.1967.tb02159.x