Arias intensity¶

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

Version: v2 · 2026-09-19 · History
Domain-specific #: 3327
Domain group: Applied Sciences & Engineering
Origin domain: Engineering & Design (beyond software)
Subdomain: Earthquake Engineering → Engineering & Design (beyond software)

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.

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Adding Up All the Shaking

During an earthquake, the ground shakes back and forth many times. Arias intensity adds up all of that shaking from start to finish, not just the one biggest shake. A short, sharp quake and a long, steady one can have the same biggest shake but very different totals.

Total Earthquake Shaking Score

Arias intensity is a number engineers use to describe how much total shaking an earthquake causes at a place. Instruments record how fast the ground speeds up and slows down (its acceleration) over time. Arias intensity squares those values and adds them up over the whole recording, then multiplies by a fixed factor, so both strong shaking and long shaking make the number bigger. That makes it different from just measuring the single strongest jolt. The result depends on which direction of shaking was recorded and how the data was cleaned up, so those details must be stated.

Cumulative Ground-Shaking Measure

Arias intensity is a measure of the total shaking in an earthquake recording. It is calculated from an accelerogram, a record of ground acceleration over time: you square the acceleration at every moment, add it up over the whole record (an integral), and multiply by pi divided by twice the acceleration due to gravity. Squaring makes strong shaking count much more, and integrating over time means long shaking adds up, so it measures cumulative shaking rather than just the peak. The value depends on choices: which direction component is used, how long the record is, how the data are corrected for baseline errors, and the value of gravity used. It's used in models of landslides and damage, and in measures of how long the strong part of the shaking lasts.

Arias intensity is a ground-motion measure of cumulative shaking, defined as I_a = (pi / 2g) times the integral over the record of a(t)^2 dt, where a(t) is a corrected acceleration history from one accelerogram component and g is gravitational acceleration. Integrating squared acceleration accumulates acceleration energy over the whole record, so it reflects both amplitude and duration rather than peak amplitude alone. Reported values depend on the component or direction analyzed, sampling and units, baseline correction, the integration bounds or record duration, and the gravitational normalization, all of which must be declared. The normalized buildup of Arias intensity over time underlies duration measures, such as the interval between chosen fractions of the total. The measure is commonly used as an input to landslide-displacement and damage models, and correct use requires stating how it enters those models.

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¶

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.
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) — outgoing typed relations

Arias intensity is a kind of Aggregation Prime

It remains its own entry because its identity is 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.

Hierarchy path (1) — routes to 1 parentless root

Arias intensity → is a kind of Aggregation → is a kind of Transformation → is a kind of, typical Function (Mapping)

Neighborhood in Abstraction Space¶

Arias intensity sits in a crowded region of the domain-specific corpus (28^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Structural Vibration & Seismic Analysis (13 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-25