Field data inversion (“Koenigsee”)

This minimalistic example shows how to use the Refraction Manager to invert a field data set. Here, we consider the Koenigsee data set, which represents classical refraction seismics data set with slightly heterogeneous overburden and some high-velocity bedrock. The data file can be found in the pyGIMLi example data repository.

# We import pyGIMLi and the traveltime module.

import matplotlib.pyplot as plt
import pygimli as pg
import pygimli.physics.traveltime as tt

The helper function pg.getExampleData downloads the data set to a temporary location and loads it. Printing the data reveals that there are 714 data points using 63 sensors (shots and geophones) with the data columns s (shot), g (geophone), and t (traveltime). By default, there is also a validity flag.

data = pg.getExampleData("traveltime/koenigsee.sgt", verbose=True)
print(data)

[::::::::::::::::::::::::::::::::::::: 83% :::::::::::::::::::::::             ] 8193 of 9844 complete
[:::::::::::::::::::::::::::::::::::: 100% ::::::::::::::::::::::::::::::::::::] 9844 of 9844 complete
md5: 641890bb17cb2bdf052cbc348669dfd0
Data: Sensors: 63 data: 714, nonzero entries: ['g', 's', 't', 'valid']

Let’s have a look at the data in the form of traveltime curves.

fig, ax = plt.subplots()
lines = tt.drawFirstPicks(ax, data)

We initialize the refraction manager.

mgr = tt.TravelTimeManager(data)

# Alternatively, one can plot a matrix plot of apparent velocities which is the
# more general function also making sense for crosshole data.

ax, cbar = mgr.showData()

Finally, we call the invert method and plot the result.The mesh is created based on the sensor positions on-the-fly.

mgr.invert(secNodes=3, paraMaxCellSize=5.0,
           zWeight=0.2, vTop=500, vBottom=5000, verbose=1)

fop: <pygimli.physics.traveltime.modelling.TravelTimeDijkstraModelling object at 0x7fe155b5d260>
Data transformation: Identity transform
Model transformation (cumulative):
         0 Logarithmic LU transform, lower bound 0.0, upper bound 0.0
min/max (data): 3.5e-04/0.03
min/max (error): 3%/3%
min/max (start model): 2.0e-04/0.002
--------------------------------------------------------------------------------
inv.iter 0 ... chi² =  156.33
--------------------------------------------------------------------------------
inv.iter 1 ... chi² =   12.31 (dPhi = 91.50%) lam: 20.0
--------------------------------------------------------------------------------
inv.iter 2 ... chi² =    8.91 (dPhi = 27.36%) lam: 20.0
--------------------------------------------------------------------------------
inv.iter 3 ... chi² =    6.71 (dPhi = 24.19%) lam: 20.0
--------------------------------------------------------------------------------
inv.iter 4 ... chi² =    6.10 (dPhi = 8.65%) lam: 20.0
--------------------------------------------------------------------------------
inv.iter 5 ... chi² =    5.56 (dPhi = 8.43%) lam: 20.0
--------------------------------------------------------------------------------
inv.iter 6 ... chi² =    5.39 (dPhi = 2.81%) lam: 20.0
--------------------------------------------------------------------------------
inv.iter 7 ... chi² =    4.89 (dPhi = 8.68%) lam: 20.0
--------------------------------------------------------------------------------
inv.iter 8 ... chi² =    4.49 (dPhi = 7.48%) lam: 20.0
--------------------------------------------------------------------------------
inv.iter 9 ... chi² =    4.13 (dPhi = 7.22%) lam: 20.0
--------------------------------------------------------------------------------
inv.iter 10 ... chi² =    3.85 (dPhi = 5.91%) lam: 20.0
--------------------------------------------------------------------------------
inv.iter 11 ... chi² =    3.70 (dPhi = 3.59%) lam: 20.0
--------------------------------------------------------------------------------
inv.iter 12 ... chi² =    3.61 (dPhi = 2.18%) lam: 20.0
--------------------------------------------------------------------------------
inv.iter 13 ... chi² =    3.53 (dPhi = 1.98%) lam: 20.0
################################################################################
#                Abort criterion reached: dPhi = 1.98 (< 2.0%)                 #
################################################################################

1090 [899.007107170486,...,2649.613254468948]

Look at the fit between measured (crosses) and modelled (lines) traveltimes.

mgr.showFit(firstPicks=True)

You can plot only the model and customize with a bunch of keywords

ax, cbar = mgr.showResult(logScale=False, cMin=500, cMax=3000, cMap="plasma_r",
                          coverage=mgr.standardizedCoverage())
rays = mgr.drawRayPaths(ax=ax, color="k", lw=0.3, alpha=0.5)

# mgr.coverage() yields the ray coverage in m and standardizedCoverage as 0/1

You can play around with the gradient starting model (vTop and vBottom arguments) and the regularization strength lam and customize the mesh.