Emergent Properties of Models

Beside the model properties that are immediately visible from the list od model parameters (such as the existence of LVZ or liquid layers) other properties exist that emerge from the physics behind the model. Some of these properties may be analyzed by TTBOX routines.

Critical Rays

Critical rays are those that have their tunring points (or reflections) at the depths of structural features of the velocity model, e.g. velocity discontinuities. The question "At what distance do I see effects of the mantle transition zone?", for example, asks for the critical rays connected with the 410km and 660km discontinuities (on Earth).

The new shooting mechanism of TTBOX, invoked by MKSHOOTRAY, uses an analysis of critical rays to optimize the take off angle needed to reach a given epicentral distance. The ray parameters of the critical rays are appended to the model structure by MKIMPROVEMODEL.

But you can also use MKIMPROVEMODEL youself to determine and evaluate these critical rays:

  1. determine critical ray parameters by executing imodel=mkimprovemodel(model);
    where
    model
    a model structure as obtained from MKREADND or MKCLR2MODEL
    imodel
    a model structure with an additional .criticalrays substructure, containing depth and ray parameter information
  2. By plotting plot(imodel.criticalrays.p,imodel.criticalrays.z,'o-'); you get an approximation of the P-velocity model transformed into a slowness model.
  3. Transform e.g. the P ray parameters into the take off angles needed by MKRAYFAN using takeoff=mkrayp2angle(phase,h,imodel.criticalrays.p,imodel);
    where
    phase
    A valid seismic phase name
    h
    focal depth
    imodel.criticalrays.p
    P wave ray parameters as determined by MKIMPROVEMODEL
    imodel
    The velocity model (at this point it is not necessary to use the output of MKIMPROVEMODEL, but it avoids confusion)
    takeoff
    List of takeoff angles corresponding to the input ray parameters. Since each ray parameter describes an upgoing as well as a downgoing ray, the list of takeoff angles is twice as long as the list of ray parameters. The first half of the list is for upgoing rays (if h=0, the upgoing rays are omitted).
  4. Plot the corresponding rays using mkrayfan(phase,imodel,h,takeoff);
    You may notice that rays that touch the core mantle boundary sometimes do not appear in this plot - that's a numerical problem: although the ray parameters of such rays can be computed very precisely, the ray tracing may identify the rays as PKP or SKS and refuse to compute them if P or S is what is asked for. That's a problem of vertex depth differences in the order of 1e-13km and very difficult to handle exactly. :-(

eof.