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![]() | An eikonal based formulation for traveltime perturbation with respect to the source location | ![]() |
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Traveltime behavior due to source perturbations can be
estimated more accurately using higher-order
formulations. Considering that ,
, and
represent
source perturbations in the
,
, and
directions,
respectively, a full representation of the second derivative behavior
is given by the following symmetric matrix
Similarly, higher order approximations in and
are given by
To obtain the non-diagonal components of the matrix we differentiate
equation 3 with respect to , instead of
,
yielding:
Substituting the second derivative of traveltime with respect to
source location
into equation E-4 provides us with a first order
linear equation in
given by:
Similar equations for the rest of the matrix components are given by
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![]() | An eikonal based formulation for traveltime perturbation with respect to the source location | ![]() |
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