Plus–minus method¶

A reciprocal seismic-refraction analysis that combines travel times from opposite shot points to estimate refractor depth and velocity.

Version: v1 · 2026-09-08 · History
Domain-specific #: 6098
Origin domain: exploration geophysics
Subdomain: exploration geophysics

Core Idea¶

The method forms plus-time and minus-time combinations from reciprocal source-receiver travel times under a layered, gently dipping refractor approximation; one combination estimates delay depth and the other lateral velocity. Adding paths cancels lateral position effects to isolate intercept-like delay, while subtracting them emphasizes travel along the refractor, separating two unknown structures from reciprocal observations. 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.

Scope of Application¶

Plus–minus method belongs to exploration geophysics and is useful where the analyst can specify the typed exploration geophysics carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate source geometry, picked arrivals, reciprocal path assumption, layer model, velocity variation, dip bound, and plus/minus sign convention are declared. The scope is broad within that domain but bounded by the need for source geometry, picked arrivals, reciprocal path assumption, layer model, velocity variation, dip bound, and plus/minus sign convention are declared. Conceptual geophysical inverse method only; no field-survey operation or subsurface intervention instructions are provided.

Clarity¶

The abstraction clarifies a crowded vocabulary by making source geometry, picked arrivals, reciprocal path assumption, layer model, velocity variation, dip bound, and plus/minus sign convention are declared 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 Plus–minus method 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 Plus–minus method. Plus–minus method 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 exploration geophysics carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express source geometry, picked arrivals, reciprocal path assumption, layer model, velocity variation, dip bound, and plus/minus sign convention are declared independently of one notation or implementation.

Knowledge Transfer¶

Knowledge transfers strongly among subfields of exploration geophysics because they reuse the typed exploration geophysics carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Adding paths cancels lateral position effects to isolate intercept-like delay, while subtracting them emphasizes travel along the refractor, separating two unknown structures from reciprocal observations., and type the carrier, state every parameter and convention in the definition, test that source geometry, picked arrivals, reciprocal path assumption, layer model, velocity variation, dip bound, and plus/minus sign convention are declared, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions¶

Current abstraction Plus–minus method Domain-specific

Parents (1) — more general patterns this builds on

Plus–minus method is a kind of Triangulation Prime

The proposed strict upward parent is prime:triangulation.

Hierarchy paths (2) — routes to 2 parentless roots

Plus–minus method → Triangulation → Aggregation → Micro Macro Linkage

Show alternative path (1)

Neighborhood in Abstraction Space¶

Plus–minus method sits in a crowded region of the domain-specific corpus (37^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Seismology, Geophysics & Surveying (25 abstractions)

Nearest neighbors

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