SIRR — Slope Intersection Reduced Reconstruction Method: Reconstruction of Clipped Seismic Peaks, Historical Formulation (1999–2000) and 2026 Single-Parameter Evolution

SIRR — Slope Intersection Reduced Reconstruction Method is a seismic signal reconstruction methodology developed to recover clipped seismic peaks in strong-motion accelerograms when the true ground acceleration exceeds the recording range of the instrument. The method originated in Japan during 1999–2000 as the Reduced Intersection Method (RIM) and has been reformulated in 2026 as SIRR, preserving the original physical-geometric concept while introducing a more compact single-parameter correction framework. SIRR reconstructs the missing portion of a clipped seismic waveform by extending the measurable ascending and descending slopes surrounding the clipped region until they intersect. Because this geometric intersection generally overestimates the actual missing peak, a reduction factor is applied to estimate the reconstructed acceleration. The 2026 formulation incorporates two measurable local waveform descriptors: the normalized clipping width, χ\chi, the slope-asymmetry index, AmA_m, together with a single adjustable coefficient, KK. The methodology was evaluated using strong-motion records from: Kobe 1995 El Centro 1940 Tohoku 2011 with artificial clipping levels of 100 gal and 30 gal. The results show that the optimized SIRR coefficients cluster around: K≈1K \approx 1 while producing substantially lower mean reconstruction errors than the independently optimized historical 1999 formulation. Across the six analyzed cases, the mean optimized coefficient is approximately: Kˉ=0.990\bar K = 0.990 These results support the interpretation of KK as a secondary fine-tuning coefficient, while the reconstruction is primarily governed by the local geometry of the clipped seismic waveform. SIRR is intended for research and engineering applications involving strong-motion seismology, clipped accelerogram recovery, earthquake engineering, seismic signal processing, seismic instrumentation, ground-motion analysis, response-spectrum reconstruction, historical earthquake records, and seismic data restoration. The work also preserves the historical development of the method and its original applications to the 1998 Bahía de Caráquez earthquake, connecting the first-generation RIM formulation with the current SIRR framework. For scientific collaborations, institutional partnerships, conferences, courses, technical consulting, seismic engineering advisory services, methodology implementation, licensing, or technology transfer, contact: [email protected] Subjects Seismic Engineering; Earthquake Engineering; Strong-Motion Seismology; Seismic Signal Processing; Accelerogram Reconstruction; Clipped Seismic Records; Ground-Motion Analysis; Seismic Instrumentation; Structural Dynamics; Response Spectra; Earthquake Data Reconstruction; Seismic Risk; Computational Seismology; Signal Restoration; Engineering Methodologies. Keywords SIRR, Slope Intersection Reduced Reconstruction Method, Reduced Intersection Method, RIM, clipped accelerogram, clipped seismic signal, seismic peak reconstruction, strong-motion records, seismic waveform reconstruction, earthquake engineering, seismic engineering, strong-motion seismology, seismic signal processing, ground-motion reconstruction, accelerogram recovery, response spectra, seismic instrumentation, earthquake records, Kobe earthquake, El Centro earthquake, Tohoku earthquake, Bahía de Caráquez earthquake, seismic data restoration, peak ground acceleration, PGA, THEK Research Institute, Marcelo Moncayo Theurer. Hashtags #SIRR #EarthquakeEngineering #SeismicEngineering #Seismology #StrongMotion #Accelerogram #SeismicSignals #SignalProcessing #GroundMotion #SeismicReconstruction #EarthquakeResearch #StructuralDynamics #ResponseSpectra #SeismicInstrumentation #ComputationalSeismology #DisasterRiskReduction #EngineeringResearch #ScientificResearch #Innovation #THEKResearchInstitute #MarceloMoncayoTheurer