Inverse modeling

im.csem recovers a conductivity model from observed CSEM data. It reuses the forward kernel’s assembly and solver: each iteration solves forward and adjoint problems for every frequency, assembles the gradient of the data misfit by the adjoint-state method, and updates the model with L-BFGS. The model is parameterized per material, not per cell: one conductivity value per row of sigmas.txt, with materials flagged fixed excluded from the update.

Workflow

1. Generate or import a mesh (see Mesh generation).

2. Define the starting model in sigmas.txt, marking materials to hold fixed with the fixed column.

3. Run utils/preprocess.py -mode im to assemble the input bundle.

4. Run im.csem.

5. Inspect the recovered model (optionally via VTU snapshots).

Inverse inputs

Inverse preprocessing requires two inputs that forward modeling does not, both embedded into the bundle:

• -im_source_filename - a multi-frequency source file: one row per (frequency, dipole) pair, 8 fields each (freq x y z current length dip azimuth). Stored under /sources.

• -observed_filename - the observed field, either an HDF5 file with /Ex [N_freq, N_recv] or a raw MATLAB-style invEx.dat text file (parsed inline). Stored under /observed/Ex. Both layouts are described in Data formats.

Two further quantities are derived during preprocessing and embedded in the bundle, each overridable on the kernel command line:

• Noise level (/observed @error_level) - the relative data error used to weight the misfit. Set with -error_level at preprocessing time (or read from the HDF5 file’s attribute); override at run time with -im_error_level.

• Fixed materials (/im_meta/fixed_materials) - the 0-based material ids flagged in the fixed column of sigmas.txt. Override with -im_fixed_materials.

Kernel options

im.csem accepts the forward kernel’s required options (-input_filename, -output_dir, -output_filename) and -order, plus the inversion options below. Values in brackets are the kernel defaults, which apply when the option is absent from both the parameter file and the command line.

Option	Default	Meaning
-im_max_iter	80	Maximum L-BFGS iterations.
-im_lbfgs_memory	5	Number of correction pairs kept by L-BFGS.
-im_lambda	0.1	Tikhonov regularization weight.
-im_error_level	0.01	Relative data-error level. Overrides the bundle’s @error_level.
-im_gtol	1e-5	Gradient-norm convergence tolerance.
-im_rms_tol	0 (off)	Absolute RMS misfit early-stop threshold.
-im_rms_rtol	1e-3	Relative RMS-improvement threshold for the plateau stop. 0 disables it.
-im_rms_stall_window	3	Consecutive iterations below -im_rms_rtol required to declare a plateau and stop.
-im_diag_weight	0 (off)	Self-weight of the neighbor smoother applied to the gradient.
-im_fixed_materials	from bundle	Comma-separated material ids excluded from the update and from smoothing.
-im_snapshot_interval	0 (off)	Write a VTU snapshot every N accepted L-BFGS steps, into -output_dir. Each snapshot carries a single cell field, rho_ohm_m.
-im_observed_mode	external	Where the observed data comes from. external reads the bundle’s /observed/Ex; fm_native reads an fm.csem responses file through its /sources/src{k}/fields/Ex layout (source k → frequency row k).
-im_observed_file	bundle	Path to the observed-data file. Optional in external mode (defaults to -input_filename); required in fm_native mode. Any noise must already be present in that file.

Besides the absolute -im_rms_tol, the L-BFGS loop stops when the RMS misfit plateaus: when the relative improvement stays below -im_rms_rtol for -im_rms_stall_window consecutive iterations.

Parameter file

utils/preprocess.py -mode im emits:

-input_filename <case_dir>/input.h5
-ksp_type preonly
-pc_type                    lu
-pc_factor_mat_solver_type  mumps
-mat_mumps_icntl_14         80
-mat_mumps_icntl_28         1
-im_max_iter               150
-im_lbfgs_memory           2
-im_lambda                 0.1
-im_diag_weight            0.0
-im_gtol                   1.0e-5
-im_rms_tol                1.05
-im_snapshot_interval      1
-output_dir <case_dir>/
-output_filename responses

This template overrides several kernel defaults and selects a direct solve (MUMPS) instead of the iterative forward default; see Solver options.

-im_error_level and -im_fixed_materials are accepted but absent from the template, since their values come from the bundle.

Running

mpirun -n 4 build/im.csem -options_file path/to/params.txt

or through the dispatcher:

mpirun -n 4 build/petgem im -options_file path/to/params.txt

Any option can be overridden on the command line, e.g. -im_max_iter 30.