THEK Research InstituteTHEK Research InstituteRRAM · Ground-Motion Models
Indexable academic technical page

RRAM - Real-Record Attenuation Method: Structural Evolution and Second-Generation Attenuation Law — Paper II

Author: Marcelo Moncayo Theurer, M.Sc. (TUM)
Institution: THEK Research Institute
Publication date: 2026-09-07
DOI: 10.5281/zenodo.22650007
ORCID: 0000-0002-8456-1571
License: CC BY-NC-ND 4.0 · NonCommercial · NoDerivatives
Download PDFZenodo DOIPaper directory

Abstract

Paper II documents the structural evolution of RRAM from the four 1G laws to the 2G law. The new formulation incorporates M² and the MD interaction so that spatial attenuation depends on magnitude, addressing the near-source–tail limitation observed in the first generation.

Second-Generation Law

The 2G formulation replaces the fixed 1G spatial slope with a magnitude-dependent rate:

a2G = (105 − 5M)e(0.235M + 0.025M²) e(−0.0285D + 0.0025MD)
CC BY-NC-ND 4.0 · NonCommercial · NoDerivatives
a2G = (105 − 5M)e(0.235M + 0.025M²) eD(−0.0285 + 0.0025M)
k(M) = −0.0285 + 0.0025M
CC BY-NC-ND 4.0 · NonCommercial · NoDerivatives

Variables and meaning

a₂G: predicted acceleration in Gal (cm/s²); M: earthquake magnitude; D: epicentral distance in km. The M² term introduces nonlinear magnitude dependence in amplitude, while MD makes magnitude modify the spatial decay.

Mathematical change from 1G to 2G

1G: ∂ln(a1G)/∂D = −0.005
2G: ∂ln(a2G)/∂D = −0.0285 + 0.0025M

In 1G, every magnitude shares the same slope. In 2G, the slope varies with M, allowing the tail of the curve to evolve with magnitude.

CMAR in 2G

CPAR < aTHEK-RRAM < CMAR
aTHEK-RRAM ≈ (0.75–0.80)aCMAR

License

RRAM and the papers available on this site are published under the Creative Commons Attribution–NonCommercial–NoDerivatives 4.0 International license (CC BY-NC-ND 4.0).

NonCommercial · NoDerivatives. Sharing is permitted with proper attribution, but commercial use and distribution of modified versions are not permitted without authorization.

Official CC BY-NC-ND 4.0 license

References

  1. Moncayo Theurer, M. (2026). RRAM - Real-Record Attenuation Method: Structural Evolution and Second-Generation Attenuation Law — Paper II. Zenodo. DOI: 10.5281/zenodo.22650007.
  2. Moncayo Theurer, M., Velasco, G., Rodríguez, J., & Terán, A. (2016). Análisis comparativo entre 13 leyes de atenuación y los registros de un evento de 7.1 en magnitud Richter ocurrido el 7 de abril de 2011, en las costas de Miyagi, Japón. Ingeniería—Revista Académica FI-UADY, 20(3), 137–146.
  3. Ramón Casquete, A. L., & Zamora, I. (2023). Eficiencia de las leyes de atenuación frente a sismos reales. Universidad de Guayaquil.
  4. Moncayo Theurer, M. (2026). Formula Genomics and Evolution Theory (FGET). Zenodo. DOI: 10.5281/zenodo.20780971.
  5. Moncayo Theurer, M. (2026). Nested Formula Framework (NFF). Zenodo. DOI: 10.5281/zenodo.20781769.

Scientific collaboration, conferences, courses and licensing

For independent validation, regional applications, scientific collaboration, courses, conferences, consulting, or authorized RRAM implementation, contact research@hithek.com.