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Physical Sciences · Earth and Planetary Sciences

Seismic Waves and Analysis
Research Guide

What is Seismic Waves and Analysis?

Seismic Waves and Analysis is the study and quantitative interpretation of elastic waves generated by earthquakes or other sources to characterize Earth structure, faulting, and time-varying subsurface properties using signal processing, forward modeling, and inverse methods.

The Seismic Waves and Analysis literature spans 207,737 works and includes methods for extracting physically meaningful constraints from waveforms, spectra, and arrays, as well as inverse problems that estimate subsurface models from seismic observations. "High-resolution frequency-wavenumber spectrum analysis" (1969) formalized frequency–wavenumber (f–k) array processing for traveling-wave fields, while "Application of the cross wavelet transform and wavelet coherence to geophysical time series" (2004) provided widely used time–frequency tools for comparing geophysical signals. Inversion-centered formulations are represented by "Inversion of seismic reflection data in the acoustic approximation" (1984) and "An overview of full-waveform inversion in exploration geophysics" (2009), which frame seismic imaging as data fitting under physical wave propagation.

Topic Hierarchy

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graph TD D["Physical Sciences"] F["Earth and Planetary Sciences"] S["Geophysics"] T["Seismic Waves and Analysis"] D --> F F --> S S --> T style T fill:#DC5238,stroke:#c4452e,stroke-width:2px
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207.7K
Papers
N/A
5yr Growth
682.2K
Total Citations

Research Sub-Topics

Why It Matters

Seismic-wave analysis underpins earthquake characterization, hazard assessment, and subsurface imaging used in both public safety and resource/engineering decisions. For earthquake size and scaling, Gutenberg and Richter (1944) in "Frequency of earthquakes in California*" established a statistical basis for earthquake occurrence, and Hanks and Kanamori (1979) in "A moment magnitude scale" defined a moment-magnitude relation (M = ⅔ log M0 − 10.7) that is used to report large-event magnitudes consistently across regions and instruments. For fault-source and deformation impacts, Okada (1985) in "Surface deformation due to shear and tensile faults in a half-space" provided closed-form expressions for surface displacements and strains from shear/tensile faults, which are routinely used to connect inferred fault slip to observable deformation. For imaging and monitoring, Tarantola (1984) in "Inversion of seismic reflection data in the acoustic approximation" and Virieux and Operto (2009) in "An overview of full-waveform inversion in exploration geophysics" describe inversion strategies that translate waveform misfits into quantitative Earth models; these approaches motivate modern regional-scale waveform tomography efforts such as "Seismic Full‐Waveform Inversion of the Crust‐Mantle Structure Beneath China and Adjacent Regions" (2025), which reports using three-component seismograms from 410 earthquakes recorded at 2,427 stations.

Reading Guide

Where to Start

Start with Nolet’s "Quantitative seismology, theory and methods" (1981) because it provides a theory-and-methods foundation that makes later papers on spectra, array processing, and inversion easier to read as a coherent toolkit.

Key Papers Explained

A common workflow links measurement, physical interpretation, and inversion. Capon’s "High-resolution frequency-wavenumber spectrum analysis" (1969) provides array-based spectral estimation for separating wavefields, while Brune’s "Tectonic stress and the spectra of seismic shear waves from earthquakes" (1970) connects observed spectra to earthquake source physics. Hanks and Kanamori’s "A moment magnitude scale" (1979) ties event size to seismic moment with M = ⅔ log M0 − 10.7, supporting consistent cataloging and comparison. Okada’s "Surface deformation due to shear and tensile faults in a half-space" (1985) supplies forward models for deformation from fault slip, bridging seismological source inference to observable ground motion and displacement. Tarantola’s "Inversion of seismic reflection data in the acoustic approximation" (1984) and Virieux and Operto’s "An overview of full-waveform inversion in exploration geophysics" (2009) then formalize how to estimate Earth models by fitting data with wave propagation, motivating modern regional FWI efforts such as "Seismic Full‐Waveform Inversion of the Crust‐Mantle Structure Beneath China and Adjacent Regions" (2025).

Paper Timeline

100%
graph LR P0["Frequency of earthquakes in Cali...
1944 · 4.2K cites"] P1["High-resolution frequency-wavenu...
1969 · 6.1K cites"] P2["Tectonic stress and the spectra ...
1970 · 5.1K cites"] P3["A moment magnitude scale
1979 · 3.9K cites"] P4["Quantitative seismology, theory ...
1981 · 3.6K cites"] P5["Surface deformation due to shear...
1985 · 5.0K cites"] P6["Application of the cross wavelet...
2004 · 6.0K cites"] P0 --> P1 P1 --> P2 P2 --> P3 P3 --> P4 P4 --> P5 P5 --> P6 style P1 fill:#DC5238,stroke:#c4452e,stroke-width:2px
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Most-cited paper highlighted in red. Papers ordered chronologically.

Advanced Directions

Recent work emphasizes large-scale, iterative waveform tomography and array-based coherence constraints. "Seismic Full‐Waveform Inversion of the Crust‐Mantle Structure Beneath China and Adjacent Regions" (2025) reports a first-generation crust–mantle model using three-component seismograms from 410 earthquakes recorded at 2,427 stations, illustrating the scale of contemporary inversions. "WUS324: Multiscale Full Waveform Inversion Approaching Convergence Improves Waveform Fits While Imaging Seismic Structure of the Western United States" (2025) highlights multiscale strategies aimed at improved waveform fits, and "Seismic Waveform-Coherence Controlled by Earthquake Source Dimensions" (2026) proposes using coherence decay across arrays as an observational constraint on source size.

Papers at a Glance

# Paper Year Venue Citations Open Access
1 High-resolution frequency-wavenumber spectrum analysis 1969 Proceedings of the IEEE 6.1K
2 Application of the cross wavelet transform and wavelet coheren... 2004 Nonlinear processes in... 6.0K
3 Tectonic stress and the spectra of seismic shear waves from ea... 1970 Journal of Geophysical... 5.1K
4 Surface deformation due to shear and tensile faults in a half-... 1985 Bulletin of the Seismo... 5.0K
5 Frequency of earthquakes in California* 1944 Bulletin of the Seismo... 4.2K
6 A moment magnitude scale 1979 Journal of Geophysical... 3.9K
7 Quantitative seismology, theory and methods 1981 Earth-Science Reviews 3.6K
8 Inversion of seismic reflection data in the acoustic approxima... 1984 Geophysics 3.5K
9 An overview of full-waveform inversion in exploration geophysics 2009 Geophysics 3.5K
10 Inverse Methods for Atmospheric Sounding 2000 Series on atmospheric,... 3.4K

In the News

Code & Tools

Recent Preprints

Seismic Waveform-Coherence Controlled by Earthquake Source Dimensions

Jan 2026 insu.hal.science Preprint

independently from far-field seismological observations. Here, we develop a novel observational constraint on source size based on the decay rate of wavefield coherence across a seismic array. For...

Seismic Full‐Waveform Inversion of the Crust‐Mantle Structure Beneath China and Adjacent Regions

Nov 2025 research-collection.ethz.ch Preprint

Abstract We present the first-generation full-waveform tomographic model (SinoScope 1.0) for the crust-mantle structure beneath China and adjacent regions. The three-component seismograms from 410...

WUS324: Multiscale Full Waveform Inversion Approaching Convergence Improves Waveform Fits While Imaging Seismic Structure of the Western United States

Nov 2025 research-collection.ethz.ch Preprint

inaccessible solid Earth through interpretations of seismic waves measured at the surface. Full waveform inversion tomography uses three‐dimensional (3D) wave propagation simulations to image subsu...

Seismic wave studies | Research Starters

Oct 2025 ebsco.com Preprint

Ben-Menachem, Ari, and Sarva Jit Singh.*Seismic Waves and Sources*. Mineola, N.Y.: Dover, 1998. Presents data on seismic waves from nearly two centuries of seismic events. Discusses the basic eleme...

Seismology articles within Nature

Aug 2025 nature.com Preprint

Two analyses of seismic waves that traversed Mars paint the clearest picture yet of the red planet’s core and deep mantle — and rationalize the puzzling implications of a previous interpretation of...

Latest Developments

Recent developments in seismic waves and analysis research include the use of earthquake sensors to track space debris via sonic booms (ScienceDaily, 2026), advancements in AI-driven seismic wavefield simulation using generative AI models (Nature, 2025), and the application of machine learning to improve earthquake forecasting and fault mapping (Eos, 2025). Additionally, new models like SegPhase employing hierarchical vision transformers have enhanced seismic phase picking accuracy (SpringerOpen, 2025).

Frequently Asked Questions

What is frequency–wavenumber (f–k) analysis used for in seismic arrays?

Capon (1969) in "High-resolution frequency-wavenumber spectrum analysis" treated array outputs as a homogeneous random field with a traveling-wave spectral representation, enabling estimation of frequency–wavenumber power. In practice, f–k analysis is used to separate and characterize wave arrivals by their apparent slowness and propagation direction across an array.

How do wavelet methods help analyze seismic or geophysical time series?

Grinsted, Moore, and Jevrejeva (2004) in "Application of the cross wavelet transform and wavelet coherence to geophysical time series" described cross-wavelet and wavelet-coherence tools for comparing two time series in time–frequency space. These methods help identify when and at which periods two signals share common power or coherent variability.

Why do seismologists use moment magnitude (Mw) rather than older magnitude scales for large earthquakes?

Hanks and Kanamori (1979) in "A moment magnitude scale" gave a relation between seismic moment and magnitude, M = ⅔ log M0 − 10.7, intended to be uniformly valid across ranges where traditional scales saturate. Moment magnitude ties reported size to a physical source parameter (seismic moment), improving comparability for large events.

How is earthquake source scaling linked to seismic shear-wave spectra?

Brune (1970) in "Tectonic stress and the spectra of seismic shear waves from earthquakes" derived a model relating effective stress on a fault to displacement-time functions and spectra in near and far fields. The formulation explains observed spectral shapes in terms of stress and stress drop effects.

How are surface displacements from faults modeled in a half-space?

Okada (1985) in "Surface deformation due to shear and tensile faults in a half-space" presented compact closed analytical expressions for surface displacements, strains, and tilts from inclined shear and tensile faults, for both point and finite rectangular sources. These solutions are used to compute expected deformation fields from hypothesized fault geometry and slip.

Which inversion approaches are central to seismic imaging, from reflection data to full waveforms?

Tarantola (1984) in "Inversion of seismic reflection data in the acoustic approximation" posed seismic reflection inversion as a nonlinear inverse problem solved with a generalized least-squares criterion incorporating data errors and prior information. Virieux and Operto (2009) in "An overview of full-waveform inversion in exploration geophysics" summarized full-waveform inversion as a wavefield-modeling, data-fitting procedure aimed at extracting quantitative subsurface information from seismograms.

Open Research Questions

  • ? How can array-based coherence constraints, as explored in "Seismic Waveform-Coherence Controlled by Earthquake Source Dimensions" (2026), be integrated with spectral source models like "Tectonic stress and the spectra of seismic shear waves from earthquakes" (1970) to jointly estimate source dimensions and stress parameters?
  • ? What practical strategies best reduce non-uniqueness and local minima in iterative gradient-based full-waveform tomography as implemented in "Seismic Full‐Waveform Inversion of the Crust‐Mantle Structure Beneath China and Adjacent Regions" (2025) while remaining consistent with least-squares inverse-problem formulations in "Inversion of seismic reflection data in the acoustic approximation" (1984)?
  • ? How should multiscale convergence behavior reported in "WUS324: Multiscale Full Waveform Inversion Approaching Convergence Improves Waveform Fits While Imaging Seismic Structure of the Western United States" (2025) be diagnosed and quantified using array/spectral tools such as "High-resolution frequency-wavenumber spectrum analysis" (1969)?
  • ? Which combinations of fault-deformation forward models from "Surface deformation due to shear and tensile faults in a half-space" (1985) and magnitude/occurrence constraints from "A moment magnitude scale" (1979) and "Frequency of earthquakes in California*" (1944) yield the most defensible, testable hazard-relevant source scenarios for specific regions?

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