Arias intensity

A seismic ground-motion measure proportional to the time integral of squared acceleration.

Version

v1 · 2026-09-08 · History

Domain-specific #

3327

Origin domain

earthquake engineering

Subdomain

earthquake engineering

Core Idea

Component direction, record duration, baseline correction and gravitational normalization affect values, and it summarizes cumulative shaking rather than peak amplitude alone. Acceleration energy is accumulated over the record by integrating its square and scaling by pi over twice gravitational acceleration. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

The load-bearing residual is not the broad topic of earthquake engineering. It is the domain-specific identity fixed by the accelerogram component, sampling and units, corrected acceleration history, integration bounds, gravitational constant, formula and result, duration fractions and relation to landslide or damage models are explicit.

Scope of Application

Arias intensity belongs to earthquake engineering and is useful where the analyst can specify the typed earthquake engineering carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, then evaluate the accelerogram component, sampling and units, corrected acceleration history, integration bounds, gravitational constant, formula and result, duration fractions and relation to landslide or damage models are explicit. The scope is broad within that domain but bounded by the need for the accelerogram component, sampling and units, corrected acceleration history, integration bounds, gravitational constant, formula and result, duration fractions and relation to landslide or damage models are explicit. Descriptive seismic metric only; no structural safety decision procedure is provided.

Clarity

The abstraction clarifies a crowded vocabulary by making the accelerogram component, sampling and units, corrected acceleration history, integration bounds, gravitational constant, formula and result, duration fractions and relation to landslide or damage models are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Arias intensity can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.

Manages Complexity

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Arias intensity. Arias intensity compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning

1. Identify the carrier. State what the elements, states, objects, or observations are: the typed earthquake engineering carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the accelerogram component, sampling and units, corrected acceleration history, integration bounds, gravitational constant, formula and result, duration fractions and relation to landslide or damage models are explicit independently of one notation or implementation.

Knowledge Transfer

Knowledge transfers strongly among subfields of earthquake engineering because they reuse the typed earthquake engineering carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, Acceleration energy is accumulated over the record by integrating its square and scaling by pi over twice gravitational acceleration., and type the carrier, state every parameter and convention in the definition, test that the accelerogram component, sampling and units, corrected acceleration history, integration bounds, gravitational constant, formula and result, duration fractions and relation to landslide or damage models are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions

Current abstraction Arias intensity Domain-specific

Parents (1) — more general patterns this builds on

• Arias intensity is a kind of Aggregation Prime

  The proposed strict upward parent is prime:aggregation.

Hierarchy path (1) — routes to 1 parentless root

• Arias intensity → Aggregation → Micro Macro Linkage

Neighborhood in Abstraction Space

Arias intensity sits in a moderately populated region (43^rd percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Seismology, Geophysics & Surveying (25 abstractions)

Nearest neighbors

• Long-period ground motion — 0.93
• Gutenberg–Richter law — 0.92
• Elastic instability — 0.89
• Seismic attribute — 0.89
• Intraplate deformation — 0.88

Computed from structural-signature embeddings · 2026-09-08