Defining a user starting model together with region constraints

[HZeyen]

Question

For travel time inversion, I want to create a +/- complex starting model with region markers controlling the initial velocity model. To do so, I create first a mesh setting a marker for every cell. Then, I create a velocity/slowness vector ("start_model") having the same size and the same ordering as the cells. Finally, I set one region to single velocity (mgr.inv.setRegularization(nRegion, single=True) or fixed velocity (mgr.inv.setRegularization(nRegion, fix=velocity).

When I now run the inversion (v_est = mgr.invert(startModel=startModel, etc), the program complains that the velocity vector is too long and creates a gradient starting model, apparently also with the size of the mesh (nr cells = length of starting model), since later, there is a message that the model vector is resized to fit the constraint size.

How can I resize correctly my own starting model?

In addition, even with the automatically generated starting model, the sizes are not clear: If I want to plot the starting model using pg.show(mgr.inv.fop.mesh(), 1./mgr.inv.startModel, etc), it gives an error message because the start model is too large.
Example program with the used sgt file (extension changed to "txt") is attached.

Thanks for your help.

picks.txt

Pygimli_test_mini.py

[halbmy]

1. If a region is background (fixed is a special type of background), it is not part of the inversion anymore and the starting model should be shorter (by the number of cells in the region) appropriately.
2. A single region is represented by only one value and therefore the starting model is shorter (number of cells minus one).
3. The regions are reordered according to the regions and so is the starting model.
4. You can run a dummy inversion with inv.run(maxIter) and test your vector by inv.paraDomain.show(startModel).
5. If the starting values are homogeneous in every region, it is easier to pass the value by

inv.setRegularization(n, startValue=1/vn,, ...) # e.g. single=True)

instead of generating the vector by hand.

This should all be explained in the region example
Please try that. I cannot test it as the file

[HZeyen]

Thanks for your answer.
Point 3 is just the problem. How is it done?

Thanks for the tip: inv.setRegularization(n, startValue=1/vn,, ...) # e.g. single=True)
This is already a good starting point, however, is there also a possibility to start with more complicated models (e.g., in addition to the homogeneous velocity in every region, also a vertical gradient in every region?

By the way, I could not find "startValue=1/vn" anywhere in the examples, tutorials or manual. Is there a place, where all the options of all methods are explained?
Thanks for your help.

[halbmy]

Sorry, the region property is of course startModel and not startValue. Actually, it can also be a vector for a region although it is documented otherwise. Here's the full list (from Modelling.setRegionProperties)

    startModel : float
        starting model value
    limits : [float, float]
        lower and upper limit for value using a barrier transform
    trans : str
        transformation for model barrier: "log", "cot", "lin"
    cType : int
        constraint (regularization) type
    zWeight : float
        relative weight for vertical boundaries
    background : bool
        exclude region from inversion completely (prolongation)
    fix : float
        exclude region from inversion completely (fix to value)
    single : bool
        reduce region to one unknown
    correlationLengths : [floats]
        correlation lengths for geostatistical inversion (x', y', z')
    dip : float [0]
        angle between x and x' (first correlation length)
    strike : float [0]
        angle between y and y' (second correlation length)

[HZeyen]

Thanks for the answer (and for correcting the title, I didn't find out how to do it).
However, it does not really work.
Concerning your answer from 3 days ago: when doing "inv.paraDomain.show(startModel)", I get the error message that inv (I guess, it is mgr.inv) does not have the attribute paraDomain (I am using version 1.5.4). So, I searched around and found that inv.fop has it. However, using this, it does not plot the velocity in the region with fixed values. My command sequence is:

mgr = tt.TravelTimeManager(data)
mgr.setMesh(mesh_inv) #mesh_inv with the regions was defined earlier
mgr.inv.setRegularization(background=False)
mgr.inv.setRegularization(1, startModel=1./300.)
mgr.inv.setRegularization(2, startModel=0.001)
mgr.inv.setRegularization(3, startModel=0.0005)
mgr.inv.setRegularization(2, fix=1000.)
vest = mgr.invert(verbose=True, maxIter=20, lam=200, lambdaFactor=0.8, zWeight=0.1)
start_model = 1./mgr.inv.fop.startModel().array()
mgr.inv.fop.paraDomain.show(start_model, colorBar=True, logScale=False, label='v in m/s', cMap="Spectral_r")

Here is a plot with the regions:

Except for one or two cells in the border regions, they are as they should be. Here is the output of the starting model plot: It is strange... What has happened there? I guess it is a problem of association between mesh cells and starting model values. I attach the program:

Pygimli_test_mini.py

Concerning your last answer: It would be nice if in the manual, you explained the possible values and their signification of cType. I searched quite a bit and found some examples with different values. But this is very cumbersome...

Thanks for your patience.