Vector infidelity

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Vector infidelity arises from unequal impulse responses on one or more of the components of a multicomponent geophone, as installed [1] [2] . The vector infidelity may arise from instrumental design, for example different engineering details (e.g. gimballed vs un-gimballed). Or it may arise from from unequal coupling of the various components to the earth (e.g. different bracing of a VSP receiver to the borehole wall). It may consist of unequal sensitivity of the various components, and/or unequal frequency or phase response in their output.

All geophones are unfaithful, in the sense that the output differs from the input; this difference is characterized by the impulse response. If all "vector" components of a multi-component geophone have the same unfaithful response, that geophone still has vector fidelity.

The wavefield input to a geophone is a vector. But the output of a geophone with vector infidelity is no longer a vector. Hence, it should not be subjected to vector operations, such as rotations, which would mix the infidelity onto other components. Hence, vector fidelity should be restored[3] to the geophone output prior to any vector operations.

References

  1. Thomsen, L., Barkved, O., Haggard, B., Kommedal, J., and Rosland, B., 1997b. A study of the dependence of OBS data-quality on seafloor equipment: Dragged versus cable data: Presented at 67th Ann. Internat. Mtg., Soc. Expl. Geophys., Research Workshopon 4C Applied Technology.
  2. Thomsen, L., 1998. Converted-Wave Reflection Seismology over inhomogeneous, anisotropic media, Soc. Expl. Geoph. Conv. Expnd. Absts., 68, 2048-2051.
  3. Dellinger, J. A., R. Clarke, and P. Gutowski, 2001, Horizontal vector infidelity correction by general linear transform: Ann. Intl. Mtg., Soc. Expl. Geoph. Expdd. Absts., 71, MCP1.1.