Comparison of a single shot traveltimecurve and the corresponding CMP-sorted traveltime branch

Traveltime data put together and assigned to 3 different layers - for layer 2 one complete forward and reverse traveltime curve has been automatically generated which is the basis for a subsequent wavefront inversion      

1-dimensional traveltime adaptation

The 1-dimension traveltime adaptation allows the interactive calculation of a one-dimensional velocity-depth-distribution from refraction shot or CMP-data.

The intercepttime option allows to calculate a first starting model which may be refined interactively (depth and velocities). The resultant diving waves, reflections (incl. overcritical) and surface multiples are displayed in real time. A comparison can be done with either real traveltime data or the complete data set (in this case picking is not necessary).

wavefront inversion:

The wavefront inversion allows to migrate the combined forward and reverse traveltimes into depth using a Finite Difference approximation of the eikonal equation. The following traveltime processing steps must have been performed before:

• put the different traveltime curves together
• assignment to the actual layer
• combination to one single forward and reverse traveltime curve (see figure above).

The method allows:

• interactive back propagation of the wavefronts using finite differences approximation of the eikonal equation; the backpropagation is exact, even for very complicated overburdens.
• no parameter adjustments are necessary
• inversion of layer interfaces and layer velocities
• the topography can directly be included in the inversion process (no static correction is necessary)

The complete forward and reverse wavefronts are continued downward based on the given overburden model. The new refractor is automatically constructed at those points where the sum of the downward traveltimes is equal to the reciprocal traveltime. The refractor velocity is determined from the mean of the slopes of the forward and reverse wavefronts at the new calculated refractor points.

The method is iterative. This means that each layer must be inverted separately and that the overburden must be existent. It may contain any 2-dimensional structure.

The results (interfaces of the layers and layer velocities) can easily be manipulated (e.g. smoothed). A priori information can easily  be incorporated to the overburden prior to the inversion of the next interface. This guarantees that all available information contributes to the inversion result.

timeterm analysis

The timeterm analysis allows the reconstruction of a 3D-refractor from xy-traveltimedata. The essential feature of the method is, that each traveltime tij may be written in the form tij = ai + bj +  ij/v, where ai and bj are timeterms which are characteristic of the shot- and receiver point respectively,  ij is the distance between shot and receiver and v is the refractor velocity. Under special conditions it is possible to derive ai, bj and v which give the best fit to the observed traveltimes tij. The preconditions are :

• the velocity of the overburden varies only with depth within the critical refracted ray cone under the shot or receiver
• the refractor velocity is assumed to be constant
• slope and curvature of the refractor is small
• the model consists of one layer  and a half space

forward raytracing: 

A fast and reliable traveltime calculation for arbitrarily complicated 2D-models is possible. The method is based on a finite difference approximation of the eikonal equation for calculating first arrivals. It takes into the account the existence of different propagation waves like transmitted, diffracted or head waves. Therefore no practical limitation concerning the complexity of the medium is given. The method is very suitable for near surface investigations, because there is no need for approximations concerning the complexity of the models. The wavefronts and therefore the raypaths can be stored and displayed.

The information about the geometry (shot and receiver positions) can automatically be adopted from the shot records or from the traveltime files. Editing, if necessary, is easily possible. The number of shots (e.g. a complete refraction seismic line) is not limited.

refraction tomography:

The refraction tomography allows an automatic inversion of the combined traveltimes. The data coverage must be high enough but no assignment to layers is necessary. The inversion is based on a two-dimensional tomographic approach based on SIRT (simultaneous iterative reconstruction technique). The curved rays are calculated using a finite difference approximation of the eikonal equation (see forward raytracing). A start model must be defined. The resulting velocity model is a rasterfile stored in REFLEX-format whereby all possibilities of REFLEX are available for a further timedisplay.

Example of a refraction tomographic inversion - the original data are calculated from a 3-layer model with v1=300 m/s, v2=800 m/s and v3=1500 m/s. The result of the tomography is shown in the upper panel - the original layerboundaries are overlaid. The lower panel shows the original traveltimes in comparison to the calculated traveltimes based on the tomograhic result.

The module  forward modelling allows the calculation of the complete electromagnetic or seismic wavefield for a 2-dimensional subsurface model. You may interactively edit any layer boundary and some predefined elements (e.g. circle or rectangle). The physical parameters may vary along the boundary whereby lateral changes are easily defined. The parameters are entered within a table which also may be used for entering the boundary values (see right figure below).

The option RandomLayer allows to specify statistic parameters for a random perturbation of the physical parameters of the individual layer. It is possible to choose between fluctuations (see left figure below  - 2. layer) and discontinuous perturbations (see left figure below - 1.layer). Different spatial distributions as well as different statistic distributions for the physical parameters are available.

snapshot sequence for a point source - 25 snapshots between 0 and 50 nsec are shown

Synthetic radargrams for different source types. Upper panel left: Exploding Reflector Model, upper panel right: plane wave, lower panel left: point-source (gain-function in time-direction applied), lower panel right: Exploding Reflector Model with transmitter and receiver in the air

A 2- and 3-dimensional tomographic approach based on SIRT (simultaneous iterative reconstruction technique) may be used for the inversion of transmission traveltime data. The geometries of the individual sources and receivers are arbitrarily.

The figure below shows a synthetic example.

example for the 2-dimensional tomography

The starting model is interactively constructed and may contain any kind of inhomogeneities. The geometry of the rays may be loaded into the starting model (see figure below). Either straight rays or curved rays are used for the ray-tracing contained in the SIRT-algorithm. For the curved rays a finite difference approximation of the eikonal equation is used (see also refraction traveltime analysis). The 3D-tomography is restricted to straight rays.