MCCC Alignment

When to run MCCC

ICCS alignment produces relative arrival-time picks that are directly usable for many purposes. MCCC is the natural next step for most analyses because it adds formal standard errors to those picks — derived from a pairwise least-squares inversion — making the output suitable for applications that require timing uncertainties, such as tomographic inversion.

MCCC works best on data that is already well aligned. It cannot recover poor alignment: if seismograms are badly misaligned, many pairwise correlations will be weak and the inversion will be poorly constrained. Running ICCS first is therefore the standard approach — not because of a strict rule, but because ICCS provides tools that MCCC does not: interactive parameter adjustment, autoflip to correct polarity, and autoselect to remove seismograms that consistently fail to align. Once the dataset is in a state where those tools are no longer improving things, MCCC is ready to run.

Take a snapshot before running MCCC.

How MCCC differs from ICCS

ICCS aligns each seismogram against a running stack: a reference constructed from the combined array. MCCC takes a different approach — it computes cross-correlation delays between all pairs of selected seismograms simultaneously, then finds the set of time shifts that best satisfies all of those pairwise constraints at once, using a weighted least-squares inversion with Tikhonov regularisation.

Because every seismogram pair contributes a constraint, the solution is not anchored to any single reference waveform. The resulting picks are relative shifts that sum to zero across the array — they express how much each seismogram needs to move relative to the group mean, not relative to a stack.

Because the solution comes from a least-squares inversion, MCCC also produces a standard error for each delay estimate, derived from the covariance matrix of the solution. ICCS provides no equivalent — its CC norms indicate alignment quality but carry no formal uncertainty. The standard errors are what make MCCC picks suitable as direct input to further analyses.

This makes MCCC more rigorous but also slower — roughly three to five times slower than a comparable ICCS run. More importantly, MCCC offers no equivalent of ICCS's interactive controls: there is no autoflip, no autoselect, no parameter tuning loop. It solves the problem it is given; shaping that problem — deciding which seismograms to include, what window to use, whether to apply a filter — is done beforehand with ICCS.

Running MCCC

aimbat align mccc <ID>          # selected seismograms only
aimbat align mccc <ID> --all    # include deselected seismograms

align mccc          # selected seismograms only
align mccc --all    # include deselected seismograms

MCCC updates t1 for all participating seismograms and writes the results back to the database immediately. Inspect the stack and matrix image afterwards to confirm the picks improved.

Parameters

Minimum CC norm (mccc_min_cc)

Pairs of seismograms whose cross-correlation coefficient falls below this threshold are excluded from the inversion. Unlike ICCS's min_cc, which operates on whole seismograms, this threshold applies to pairs: a seismogram can still contribute to the solution through its good pairs even if some of its pairings are weak.

Setting this too low allows noisy pairs to degrade the inversion; setting it too high may leave too few constraints for a stable solution. The ICCS correlation coefficients give a rough sense of which seismograms are likely to correlate well with each other.

Damping (mccc_damp)

Tikhonov regularisation applied to the inversion. A small amount of damping stabilises the solution when the constraint matrix is poorly conditioned — for example, when a seismogram has few pairs above mccc_min_cc and its time shift is therefore weakly constrained. Higher damping pulls all shifts closer to zero (the group mean), producing a more conservative solution.

Setting damping to zero disables regularisation entirely, which is fine when the dataset is large and well-correlated but can produce unstable results on sparse or noisy datasets.

The --all flag

By default, MCCC only includes seismograms with select = True — the same subset that contributed to the ICCS stack. Passing --all includes deselected seismograms in the inversion. Their picks are still updated, but they may degrade the inversion if they are genuinely noisy or misaligned. Use with caution.

Exporting results

Once MCCC has run and you are satisfied with the picks, take a snapshot and export the results:

aimbat snapshot create <ID> "post-MCCC"
aimbat snapshot results <SNAPSHOT_ID> --output results.json

The output is a JSON document with event-level header fields (snapshot metadata, event coordinates, MCCC RMSE) and a seismograms list containing the frozen t1 pick, ICCS and MCCC correlation coefficients, and formal timing standard errors for each station. See Exporting Results for the full field reference and examples of working with the output.