Vector infidelity arises from unequal impulse responses on one or more of the components of a multicomponent geophone, as installed   . 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 to the geophone output prior to any vector operations.
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