Model Validation

The model validation module compares HyFI rupture plane estimates with independent focal mechanism solutions to assess reconstruction accuracy and determine active fault planes based on hypocenter distribution constraints. For details, see the original HyFI publication (Truttmann et al., 2023).

Core Concepts

Angular Differences (ε) as Quality Measure

HyFI calculates the angle between the computed rupture plane and the active nodal plane of the focal mechanism.

Physical Interpretation:

  • 0°: Perfect alignment (computed plane ≡ focal mechanism plane)

  • < 15°: Excellent agreement (typical for well-constrained cases)

  • 15-30°: Good agreement (acceptable for seismic data quality)

  • 30-45°: Fair agreement (visible discrepancy)

  • 45°: Poor agreement (significant misalignment)

Pre-specified vs. Auto-determined Planes

HyFI can be used to verify pre-specified nodal planes (A=1 or A=2) and automatically determines unspecified nodal planes (A=0 or A=NaN) based on the fit with the calculated rupture plane from the fault network module.

Note that the pre-specified nodal planes are always preserved!

Computational Workflow

The validation module is executed according to the following structured pipeline:

Step 1: Data Merging - Focal Mechanism Integration

Focal mechanism data is merged with hypocenter data using two strategies (tried in order):

Strategy A: ID-Based Matching (Primary)

  • Match events by event ID across catalogs

  • Requires identical ID formatting in both files

  • Most reliable when ID numbers are unique and consistent

  • Fastest approach - direct one-to-one correspondence

Strategy B: Temporal Matching (Fallback)

  • If ID matching fails, use merge_asof on datetime

  • Matches events within 60-second tolerance window

  • Sorted by date before merging

  • More robust for catalogs with ID formatting differences or with unconsistent/missing catalog IDs

The algorithm also performs two Quality Control Checks (Optional, configurable):

  1. Magnitude Consistency Check:

    • Compare hypocenter magnitude (MAG) with focal mechanism magnitude

    • Remove focal data if |MAG_hypo - MAG_focal| > threshold (default: 0.2)

    • Reports events with significant magnitude mismatches

    • Protects against erroneous cross-catalog associations

  2. Location Consistency Check:

    • Compare hypocenter location (X, Y, Z) with focal mechanism location

    • Depth threshold: km units (default: 1.0 km)

    • Latitude/Longitude: converted from km to degrees (~0.009°/km)

    • Reports mismatches but does NOT remove data (just warnings)

    • Identifies potential duplicate events in different catalogs

Step 2: Normal Vector Conversion

In step 2, both nodal planes are converted from azimuth/dip to normal vectors. This results in normal vectors for both focal mechanism nodal planes

Step 3: Angular Difference Calculation

For each event with both a computed rupture plane and a focal mechanism, the angular difference from the rupture plane to both nodal planes (1 and 2) is calculated:

  1. Plane 1 angular difference:

    • angle1 = angle_between(nor_computed, nor_focal_plane1)

    • Ensure acute angle: angle1 = min(angle1, 180 - angle1)

  2. Plane 2 angular difference:

    • angle2 = angle_between(nor_computed, nor_focal_plane2)

    • Ensure acute angle: angle2 = min(angle2, 180 - angle2)

Geometric meaning: Angular difference measures the angle between the normal vectors and thus how well the computed rupture plane aligns with each focal mechanism nodal plane

Step 4: Preferred Plane Selection

In the next step, a two-tier selection process to define the active nodal plane is exexuted:

Tier 1: Active Plane Indicator (if available)

  • Check column A (specifies the known 1active plane) from the focal mechanism catalog: values 1, 2 indicate pre-specified active plane

  • If A = 1: Use angle1 (Strike1, Dip1, Rake1) as final angular difference (epsilon)

  • If A = 2: Use angle2 (Strike2, Dip2, Rake2) as final angular difference (epsilon)

  • If A = 0: Fall through to Tier 2 (unknown nodal plane, use geometry)

  • If A = NaN: Fall through to Tier 2 (no pre-specification, use geometry)

Tier 2: Geometric Selection

  • Compare: angle1 vs. angle2

  • Choose plane with MINIMUM angular difference (epsilon = min(angle1, angle2))

Rationale:

  • Pre-specified active planes (A=1 or A=2) take priority and are always maintained

  • For unknown planes (A=0 or A=NaN), the algorithm selects the nodal plane based on the best geometric fit to the computed rupture plane

Output columns:

  • epsilon: Angular difference of the preferred focal plane in degrees (0-90°)

  • pref_foc: HyFI-based preferred focal plane (1 or 2)

  • plane_determination_method: Categorical description

    • “Pre-specified (A=1 or A=2)”

    • “Newly determined (A=0, geometric selection)”

    • “Newly determined (no A, geometric selection)”

    • “Not determined (A specified but no rupture plane)”

    • “Not determined (no computed rupture plane)”

Step 5: Reporting

Finally, the validation module generates comprehensive summary files on the preferred plane determination (see below).

Main Outputs

Active Plane Statistics: active_plane_statistics.txt

This file includes the statistics summary in a human-readable format for quick understanding of validation results quality.

  • Total events with focal mechanisms

  • Breakdown by determination method with counts

  • For newly determined planes: selection distribution (plane 1 vs. 2)

  • Angular difference statistics: mean, median, min, max

  • For pre-specified planes: similar angular difference statistics

  • For not-determined events: reasons and counts

  • Interpretation guidance

Active Plane Determination Summary: active_plane_determination_summary.csv

Detailed row-by-row documentation including:

  • Event ID, Date, Location (X, Y, Z), Magnitude

  • Focal mechanism data: Strike1, Dip1, Rake1, Strike2, Dip2, Rake2

  • Focal mechanism active plane indicator: A

  • Computed fault plane: rupt_plane_azi, rupt_plane_dip

  • Validation results: pref_foc, epsilon

  • Preferred strike/dip/rake extracted from selected plane

  • Determination method: How was pref_foc determined?

Sorted by:

  1. Determination method (pre-specified → newly determined → not determined)

  2. Angular difference (best matches first)

References

  • Truttmann, S., Diehl, T., & Herwegh, M. (2023). Hypocenter-based 3D imaging of active faults: Method and applications in the Southwestern Swiss Alps. Journal of Geophysical Research: Solid Earth, 128, e2023JB026352. https://doi.org/10.1029/2023JB026352

Happy fault imaging! 🎉