Stereo tomography is based on Ray tracing. The basis of the Stereo Tomography concept is to recognize any locally coherent events characterized by their travel times and local slopes (two slopes) in the prestack data to provide some information about velocity model. (Stereo tomography: Past, present and future - Gilles Lambaré). The locally coherent events can be interpreted as pairs of ray segments and provide the velocity information independently.
How it works?
A stereo tomographic dataset consists of locally coherent events parametrized by source & receiver positions, travel time and slopes of the events in the common shot and receiver domain.
As in standard travel time tomography, an iterative non-linear local optimization scheme is used for optimizing the stereo tomographic model. The computation of the Fréchet derivatives is based on paraxial ray tracing (Farra and Madariaga, 1987) and requires some smoothness of the velocity macro-model. In all our numerical implementations we use smooth velocity macro - models defined by cubic cardinal Bsplines. There is no need for interfaces but if necessary they could be introduced as soon as they are sufficiently smooth.
In order to mitigate the non-linearity, in our local optimization scheme. We first optimize for the pairs of ray segments fixing the velocity macro-model to its initial value. It is the localization step that allows us to greatly reduce the cost function before the joint inversion of velocity and pairs of ray segments. For this joint optimization we use a conjugated gradient optimization, taking advantage of the large sparse matrices involved in the stereotomographic inverse problem (Billette et al., 2003), i.e. the LSQR scheme (Paige and Saunders, 1982). Some regularization also has to be introduced to insure the robustness of the optimization scheme, and we also use a multi-scale approach for the velocity macro-model (Billette et al., 2003, Lambaré et al., 2004a).
This module is used to generate the updated velocity models. We generate the Tomo items from the PSDM Imaging module. Within the PSDM imaging module, we have "Create tomo parameters" action items and it will create the Tomo item for Stereo Tomography as an input.
Input
Tomo Item
Input velocity or stack (Geometry)
Trace headers
Output
Updated depth velocity model.
In the "create tomo params" of PSDM Imaging module, the user should provide the First Step X(meter), Step Y(meter) & Depth (meter). This is important and the size shouldn't be big number otherwise it will thrown error of "Bad allocation" while running the Stereo tomography.
Connect/reference the Tomo item to PSDM Imaging -> Tomo item
Connect/reference Initial velocity or Stack (for Geometry) to Read seismic traces (here the user can read either velocity model or stack for geometry purpose)
Connect/reference Trace headers to Read seismic traces where the velocity/stack is read.
Parameters
Tomo file name. Not required
Use Init velocity By default FALSE however if the user check this option as TRUE then the user can ignore the InitialVelocityMin and V0(Velocity) & InitialVelocityMax(Velocity).
Global iteration count Define total number of iterations to be carried out. By default 3
Joint inversion iteration count Define the inversion iteration count. By default 5.
InitialVelocityMin and V0(Velocity) Provide the initial velocity value. This will be the starting gradient value
InitialVelocityMax(Velocity) Provide the maximum velocity value. This will be the maximum gradient value.
InitStepX (Distance) This is the initial step in X direction which considers the pickets in the X direction. By default 1200
InitStepY(Distance) This is the initial step in Y direction which considers Depth in the Y direction.By default 400.
Sealing factor By default 0.5. This value defines the InitStepX & InitStepY values in the subsequent velocity iterations.
We have 3 global iterations and 5 joint inversion iterations. So in total we'll have 15 iterations. Now these 15 iterations are generated initially with 1200 & 400 as the Initial Step X & Y parameters. So we will have
Iteration1-1200-400
Iteration2-1200-400
Iteration3-1200-400
Iteration4-1200-400
Iteration5-1200-400
Now with the sealing factor of 0.5, Step X 200 becomes 600 and Step Y 400 becomes 200
Iteration6-600-200
Iteration7-600-200
Iteration10-600-200
Similarly Step X 600 becomes 300 and Step Y 200 becomes 100.
Iteration11-300-100
Iteration15-300-100
By using Save seismic by gather module, the user can save the final updated velocity model for next iteration or can be used as a final velocity model.