VES inversion for a blocky model

This tutorial shows how an built-in forward operator is used for inversion. A DC 1D (VES) modelling is used to generate data, noisify and invert them.

We import numpy, matplotlib and the 1D plotting function

import numpy as np
import matplotlib.pyplot as plt
import pygimli as pg
from pygimli.physics import VESManager

some definitions before (model, data and error)

ab2 = np.logspace(-0.5, 2.5, 40)  # AB/2 distance (current electrodes)

define a synthetic model and do a forward simulatin including noise

synres = [100., 500., 30., 800.]  # synthetic resistivity
synthk = [0.5, 3.5, 6.]  # synthetic thickness (nlay-th layer is infinite)

the forward operator can be called by f.response(model) or simply f(model)

synthModel = synthk + synres  # concatenate thickness and resistivity
ves = VESManager()
rhoa, err = ves.simulate(synthModel, ab2=ab2, mn2=ab2/3,
                         noiseLevel=0.03, seed=1337)

ves.invert(data=rhoa, relativeError=err, ab2=ab2, mn2=ab2/3,
           nLayers=4, lam=1000, lambdaFactor=0.8)

7 [0.4825899923714223, 3.303908903637452, 8.495898121775843, 96.69006658660493, 508.39516916123904, 41.4920681563085, 835.2425040326069]

show estimated & synthetic models and data with model response in 2 subplots

fig, ax = plt.subplots(ncols=2, figsize=(8, 6))  # two-column figure
ves.showModel(synthModel, ax=ax[0], label="synth", plot="semilogy", zmax=20)
ves.showModel(ves.model, ax=ax[0], label="model", zmax=20)
ves.showData(rhoa, ax=ax[1], label="data", color="C0", marker="x")
out = ves.showData(ves.inv.response, ax=ax[1], label="response", color="C1")