How to modify the objective function?

[LiuQian19970208]

Hello, I want to modify the default objective function of Gauss-Newton inversion, but I don't know how to do it ?

My objective function is as follows data=ert.load('diploe190d.dat') data["err"] = ert.estimateError(data) mgr = ert.ERTManager() inv = mgr.invert(data=data,lam=10,verbose=True) mgr.saveResult() mgr.showResult()

[halbmy]

What are the $p_i$ and $r_i$? Do they depend on the m?

[halbmy]

And what's the relation between $m_1$ and $m_2$?

[LiuQian19970208]

Yes, I want to perform joint constrained inversion of spontaneous potential data m1 and resistivity data m2.

[halbmy]

spontaneous potential data m1 and resistivity data m2

Well, m1 are not the SP and ERT data, but resistivity and current density or something else.

At any rate, the functional is quite a bit more complex and similar to coupling schemes like cross-gradients (e.g. done by Jordi et al., 2020 with pyGIMLi). So you will have to formulate the derivatives and insert them into the inversion framework, in this case I recommend the LSQRInversion where any equations can be added (like in Wagner et al., 2019). I realize that several examples are needed for that.

Jordi, C., Doetsch, J., Günther, T., Schmelzbach, C., Maurer, H. & Robertson, J. (2020): Structural Joint Inversion on Irregular Meshes. Geophys. J. Int. 220(3), 1995-2008, doi:10.1093/gji/ggz550. Wagner, F.M., Mollaret, C., Günther, T., Kemna, A., Hauck, A. (2019): Quantitative imaging of water, ice, and air in permafrost systems through petrophysical joint inversion of seismic refraction and electrical resistivity data. Geophys. J. Int. 219, 1866-1875. doi:10.1093/gji/ggz402.

[halbmy]

Closing as I don't expect any activity now. Adding examples and tutorials for cross-gradients is on the list.