This example shows how to use the Refraction manager to generate the response of a three-layered sloping model and to invert the synthetic noisified data.
import numpy as np import pygimli as pg import pygimli.meshtools as mt from pygimli.physics import Refraction
We start by creating a three-layered slope (The model is taken from the BSc thesis of Constanze Reinken (University of Bonn).
layer1 = mt.createPolygon([[0.0, 137], [117.5, 164], [117.5, 162], [0.0, 135]], isClosed=True, marker=1, area=1) layer2 = mt.createPolygon([[0.0, 126], [0.0, 135], [117.5, 162], [117.5, 153]], isClosed=True, marker=2) layer3 = mt.createPolygon([[0.0, 110], [0.0, 126], [117.5, 153], [117.5, 110]], isClosed=True, marker=3) slope = (164 - 137) / 117.5 geom = mt.mergePLC([layer1, layer2, layer3]) mesh = mt.createMesh(geom, quality=34.3, area=3, smooth=[1, 10]) pg.show(mesh)
Next we define geophone positions and a measurement scheme, which consists of shot and receiver indices.
numberGeophones = 48 sensors = np.linspace(0., 117.5, numberGeophones) scheme = pg.physics.traveltime.createRAData(sensors) # Adapt sensor positions to slope pos = np.array(scheme.sensorPositions()) for x in pos[:, 0]: i = np.where(pos[:, 0] == x) new_y = x * slope + 137 pos[i, 1] = new_y scheme.setSensorPositions(pos)
Now we initialize the refraction manager and asssign P-wave velocities to the layers. To this end, we create a map from cell markers 0 through 3 to velocities (in m/s) and generate a velocity vector. To check whether the it is correct, we plot it # along with the sensor positions
We use this model to create noisified synthetic data and look at the traveltime curves showing three different slopes.
data = ra.simulate(mesh, 1.0 / vp, scheme, noiseLevel=0.001, noiseAbs=0.001, verbose=True) # ra.showData(data) # can be used to show the data.
Data error estimates (min:max) 0.00100753513903737 : 0.001142191584163894
And invert the synthetic data on an independent mesh without # information on the layered structure we create a new instance of the class using the data. Instead of the data, a file name can be given. This is probably where most users with data start. See refraction class for supported formats.
ra = Refraction(data) ra.showData() ra.createMesh(depth=30., paraMaxCellSize=5.0, secNodes=1) # ra.fop.createJacobian(np.ones(ra.fop.regionManager().parameterCount())) # exit() vest = ra.invert() # estimated velocity distribution
Data: Sensors: 48 data: 2256
The method showResult is used to plot the result. Note that only covered cells are shown by default. For comparison we plot the geometry on top.
ax, cb = ra.showResult(cMin=min(vp), cMax=max(vp), logScale=False) pg.show(geom, ax=ax, fillRegion=False, regionMarker=False) # lines on top
Note that internally the following is called
ax, _ = pg.show(ra.mesh, vest, label="Velocity [m/s]", **kwargs)
Another useful tool is to show the model along with its respone on the data_
Takeaway message: A default data inversion with checking of the data consists of only few lines (Everthing else can be looked at by introspecting the Refraction manager)
Total running time of the script: ( 0 minutes 37.765 seconds)