MCCC alignment

When to run MCCC

ICCS produces relative arrival-time picks that are directly usable for many purposes. MCCC is the usual next step because it adds a formal standard error to each pick, from a pairwise least-squares inversion, making the output suitable where timing uncertainties are required, such as tomographic inversion.

MCCC works best on already well-aligned data. It cannot recover poor alignment: badly misaligned seismograms give weak pairwise correlations and a poorly constrained inversion. Running ICCS first is standard, not by rule but because ICCS has the tools MCCC lacks: interactive parameter adjustment, autoflip, autoselect. Once those stop improving things, MCCC is ready.

Snapshotting beforehand preserves the pre-MCCC state, in case the run needs to be undone.

How MCCC differs from ICCS

ICCS aligns each seismogram against a running stack, a single reference built from the array. MCCC instead computes cross-correlation delays between all pairs of selected seismograms, then solves for the set of time shifts that best satisfies every pairwise constraint at once, by weighted least squares with Tikhonov regularisation.

Because every pair contributes a constraint, the solution is not anchored to any one reference waveform. The picks are relative shifts that sum to zero across the array: how far each seismogram moves relative to the group mean, not relative to a stack.

The least-squares solution also yields a standard error for each delay, from the covariance matrix. ICCS has no equivalent: its CC values indicate alignment quality but carry no formal uncertainty. These standard errors are what make MCCC picks suitable as direct input to further analysis.

MCCC is more rigorous but slower, roughly three to five times a comparable ICCS run. It also has no interactive controls: no autoflip, no autoselect, no tuning loop. It solves the problem it is given; shaping that problem (which seismograms, what window, whether to 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
align mccc --all

from sqlmodel import Session, select
from aimbat.db import engine
from aimbat.core import create_iccs_instance, run_mccc
from aimbat.models import AimbatEvent

with Session(engine) as session:
    event = session.exec(select(AimbatEvent)).first()
    bound = create_iccs_instance(session, event)
    run_mccc(session, event, bound.iccs, all_seismograms=False)

MCCC updates t1 for all participating seismograms and writes the results to the database immediately. The stack and matrix image afterwards show whether the picks improved.

Parameters

Minimum CC (mccc_min_cc)

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

Too low, and noisy pairs degrade the inversion. Too high, and too few constraints remain for a stable solution. The ICCS correlation coefficients give a rough sense of which seismograms correlate well.

Damping (mccc_damp)

Tikhonov regularisation applied to the inversion. A little 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 shift is weakly constrained. Higher damping pulls all shifts towards zero (the group mean), a more conservative solution.

Zero damping disables regularisation, fine on a large well-correlated dataset but unstable on sparse or noisy ones.

The --all flag

By default MCCC includes only select = True seismograms, the same subset that formed the ICCS stack. --all includes the deselected ones: their picks are updated too, but they may degrade the inversion if genuinely noisy or misaligned, so it is best used with caution. See aimbat align mccc for the full flag reference.

After MCCC, results export from a snapshot: see Exporting Results.