{ "id": "eprwfyt49d", "slug": "amplitude-versus-offset-analysis", "title": "Amplitude versus offset analysis", "updated": "2026-09-30", "topic_path": [ { "id": "physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical" }, { "id": "physical.earth", "label": "Earth sciences", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.earth" }, { "id": "physical.earth.planet", "label": "Earth systems and geophysics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.earth.planet" }, { "id": "physical.earth.planet.seismic-survey-and-processing", "label": "Seismic survey and processing", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.earth.planet.seismic-survey-and-processing" } ], "geo": [ { "id": "geo.nongeo.t1946.physical.earth.planet", "label": "Non-geographic · 1946 to 2000: Earth systems and geophysics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.earth.planet", "path": [ { "id": "geo.nongeo", "label": "Non-geographic", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo" }, { "id": "geo.nongeo.t1946", "label": "Non-geographic · 1946 to 2000", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946" }, { "id": "geo.nongeo.t1946.physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical" }, { "id": "geo.nongeo.t1946.physical.earth", "label": "Earth sciences", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.earth" }, { "id": "geo.nongeo.t1946.physical.earth.planet", "label": "Earth systems and geophysics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.earth.planet" } ] } ], "excerpt": "Amplitude versus offset (AVO) analysis measures how seismic reflection amplitude changes with source-receiver offset, and uses that variation to constrain subsurface rock properties and fluid content, notably free gas.", "snippet": "Amplitude versus offset (AVO) analysis measures how seismic reflection amplitude changes with source-receiver offset, and uses that variation to constrain subsurface rock properties and fluid content, notably free gas.", "node": "physical.earth.planet.seismic-survey-and-processing", "markdown": "# Amplitude versus offset analysis\n\n[Amplitude versus offset](https://www.edgepedia.org/amplitude-versus-offset) (AVO) analysis measures how the amplitude of a seismic reflection changes with the distance between source and receiver, and uses that variation to constrain subsurface rock properties and fluid content.[1](https://faculty.kfupm.edu.sa/ES/ashuhail/Graduate/GEOP501/Ch2/Feng-2006.pdf) Because the angle of incidence grows with offset, each interface produces a characteristic amplitude-versus-angle signature governed by the contrasts in P-wave velocity, S-wave velocity, and density across it. Inverting that signature can indicate porosity, density, lithology, fluid content, or the presence of free gas.[1](https://faculty.kfupm.edu.sa/ES/ashuhail/Graduate/GEOP501/Ch2/Feng-2006.pdf) • [2](https://www.kgs.ku.edu/Publications/Bulletins/237/Knapp1/) In practice the analysis reduces to fitting two numbers per reflection, the intercept and the gradient, and reading rock and fluid meaning from their combination.[3](https://www.nature.com/articles/s41598-026-35935-2)\n\n| Key fact | Detail |\n|---|---|\n| Measured quantity | Reflection amplitude as a function of source-receiver offset, equivalently angle of incidence[1](https://faculty.kfupm.edu.sa/ES/ashuhail/Graduate/GEOP501/Ch2/Feng-2006.pdf) |\n| Properties constrained | Porosity, density, lithology, fluid content; via \\( V_{\\mathrm{p}}/V_{\\mathrm{s}} \\), also free gas[1](https://faculty.kfupm.edu.sa/ES/ashuhail/Graduate/GEOP501/Ch2/Feng-2006.pdf) • [2](https://www.kgs.ku.edu/Publications/Bulletins/237/Knapp1/) |\n| Theoretical basis | Zoeppritz plane-wave equations; the Aki-Richards linearization in changes in \\( V_{\\mathrm{p}} \\), \\( V_{\\mathrm{s}} \\) and density[1](https://faculty.kfupm.edu.sa/ES/ashuhail/Graduate/GEOP501/Ch2/Feng-2006.pdf) • [4](https://www.crewes.org/Documents/ResearchReports/2001/2001-24.pdf) |\n| Primary attributes | Intercept A, gradient B, curvature C; normal-incidence P- and S-wave reflectivities[5](https://cseg.ca/the-relationship-between-avo-and-petrophysics/) • [6](https://csim.kaust.edu.sa/files/erse210/fosterkeys.pdf) |\n| Angle validity | Roughly, the two-term Shuey form is invalid beyond about 30°, the Aki-Richards linearization is used below about 40°, and the three-term form is accurate to about 50°; these are approximate, model-dependent guidance rather than universal cutoffs[1](https://faculty.kfupm.edu.sa/ES/ashuhail/Graduate/GEOP501/Ch2/Feng-2006.pdf) • [4](https://www.crewes.org/Documents/ResearchReports/2001/2001-24.pdf) • [7](https://www.nature.com/articles/s41598-026-36501-6) |\n| Offset requirement | Ideally 0 to 40° incidence, far offsets about 1.6 times target depth; about 22° minimum for quantitative fitting[2](https://www.kgs.ku.edu/Publications/Bulletins/237/Knapp1/) • [8](https://cseg.ca/amplitude-vs-offset-and-seismic-rock-property-analysis-a-primer/) |\n| AVO classes | Classes I to IV, defined by intercept-gradient combinations[3](https://www.nature.com/articles/s41598-026-35935-2) |\n\n## How it works\n\nThe physical link between amplitude and offset is the Zoeppritz system of equations, which gives the plane-wave reflection amplitude as a function of incident angle from the P-wave and S-wave velocities and the densities of the two media bounding an interface.[1](https://faculty.kfupm.edu.sa/ES/ashuhail/Graduate/GEOP501/Ch2/Feng-2006.pdf) As offset increases, the incidence angle increases, so the reflection coefficient traces an angle-dependent curve unique to the elastic contrasts at the interface.\n\nTwo empirical results explain why the curve carries rock and fluid information. A change in [Poisson's ratio](https://www.edgepedia.org/poissons-ratio) across a reflecting interface causes a significant angle-dependent variation in the P-wave reflection coefficient, whereas models assuming a constant Poisson's ratio show little angle effect.[6](https://csim.kaust.edu.sa/files/erse210/fosterkeys.pdf) [Laboratory](https://www.edgepedia.org/laboratory) measurements on gas- and brine-saturated sandstones show that Poisson's ratio, or the related ratio \\( V_{\\mathrm{p}}/V_{\\mathrm{s}} \\), is significantly affected by pore fluid.[6](https://csim.kaust.edu.sa/files/erse210/fosterkeys.pdf) In a cited gas-sand/shale example, Poisson's ratio and density were 0.15 and 2.0 g/cm³ for the gas sand against 0.38 and 2.4 g/cm³ for the shale.[2](https://www.kgs.ku.edu/Publications/Bulletins/237/Knapp1/)\n\nBecause the exact Zoeppritz equations are awkward to invert, analysis relies on linearizations. The Aki-Richards approximation is parameterized simply in terms of the changes in density, P-wave velocity, and S-wave velocity across the interface.[4](https://www.crewes.org/Documents/ResearchReports/2001/2001-24.pdf) In the Shuey form the reflection coefficient is approximated as\n\n\\[ R(\\theta) \\approx A + B\\sin^{2}\\theta, \\]\n\nIn the general Shuey form this is \\( R(\\theta) \\approx A + B\\sin^{2}\\theta \\), where \\( A \\) is the normal-incidence reflection coefficient and \\( B \\) the AVO gradient, a combination of the contrasts in P-wave velocity, S-wave velocity, and density; only under additional assumptions does the gradient reduce to a form in the change in Poisson's ratio alone.[4](https://www.crewes.org/Documents/ResearchReports/2001/2001-24.pdf) [Amplitude](https://www.edgepedia.org/amplitude) plotted against \\( \\sin^{2}\\theta \\) is then approximately a straight line whose intercept and gradient are the working attributes. Linearized forms are valid only for small and moderate incident angles, generally below 40°; for larger angles the exact Zoeppritz equation or higher-order approximations should be used.[7](https://www.nature.com/articles/s41598-026-36501-6)\n\n## How it is done\n\nA quantitative AVO workflow runs as follows.\n\n1. **Amplitude-preserving processing** of common depth point gathers: generalized amplitude corrections, signal-to-noise improvement, robust deconvolution, and prestack migration in structurally complex areas.[9](https://wiki.aapg.org/index.php?title=Amplitude_versus_offset_analysis)\n2. **Attribute fitting** on common-midpoint gathers, called Ostrander gathers in the AVO business: amplitudes are fitted against a function of incidence angle, yielding two attributes, essentially the slope and intercept of a straight line describing how amplitude behaves with angle.[8](https://cseg.ca/amplitude-vs-offset-and-seismic-rock-property-analysis-a-primer/)\n3. **Crossplotting** intercept against gradient to classify reflections into the AVO classes and flag anomalies.\n4. **Fluid displays**, which combine P and S reflectivities to highlight areas anomalous with respect to the regional \\( V_{\\mathrm{p}}/V_{\\mathrm{s}} \\) trend, the regional mudrock line.[8](https://cseg.ca/amplitude-vs-offset-and-seismic-rock-property-analysis-a-primer/)\n5. **Weighted stacking**, a methodology that transforms NMO-corrected gathers into estimates of rock properties by least-squares fitting a curve approximating the Zoeppritz equation.[1](https://faculty.kfupm.edu.sa/ES/ashuhail/Graduate/GEOP501/Ch2/Feng-2006.pdf)\n6. **Prestack inversion**, carried out by iteratively generating synthetic gathers with the Fatti equations and matching them to observed gathers, to derive P-wave impedance, S-wave impedance, and density volumes, from which \\( V_{\\mathrm{p}}/V_{\\mathrm{s}} \\), [bulk modulus](https://www.edgepedia.org/bulk-modulus) and Poisson's ratio are derived.[3](https://www.nature.com/articles/s41598-026-35935-2)\n7. **Layered-model inversion** of an anomaly, yielding compressional velocity, density, and Poisson's ratio used to predict the origin of the anomaly, pay-zone thickness, and the lithology, porosity and fluid content of a layer.[9](https://wiki.aapg.org/index.php?title=Amplitude_versus_offset_analysis)\n\nRelative amplitudes must be preserved throughout for any of these steps to mean anything.[1](https://faculty.kfupm.edu.sa/ES/ashuhail/Graduate/GEOP501/Ch2/Feng-2006.pdf)\n\n## Origin\n\nThe observational groundwork predates the method itself. Early work by Muskat and Meres in 1940 indicated that angle of incidence had little impact on P-wave reflections, because with limited information about sedimentary elastic properties they assumed a constant Poisson's ratio throughout their study.[6](https://csim.kaust.edu.sa/files/erse210/fosterkeys.pdf) Work published in 1955 investigated the effect of Poisson's ratio on the angle-dependent P-wave reflection coefficient and found that a change in Poisson's ratio at a reflecting interface can cause significant angle-dependent variation.[6](https://csim.kaust.edu.sa/files/erse210/fosterkeys.pdf) Laboratory measurements on gas- and brine-saturated sandstones reported in 1976 and 1977 then showed that pore fluid significantly affects Poisson's ratio and \\( V_{\\mathrm{p}}/V_{\\mathrm{s}} \\).[6](https://csim.kaust.edu.sa/files/erse210/fosterkeys.pdf)\n\nCombining these observations, the AVO reflection response was shown to distinguish seismic amplitudes caused by gas sands from bright amplitudes caused by nonhydrocarbon-bearing rocks such as basalts.[6](https://csim.kaust.edu.sa/files/erse210/fosterkeys.pdf) • [10](https://csegrecorder.com/articles/view/avo-yesterday-today-and-a-peek-at-tomorrow)\n\n## Variants\n\nMost forms of AVO analysis derive from the Aki-Richards approximation to the Zoeppritz equations, expressed in P-wave velocity, S-wave velocity, and density.[5](https://cseg.ca/the-relationship-between-avo-and-petrophysics/) The named variants re-express the same physics in different variables:\n\n- **Shuey approximation.** Transforms the variables to display the change in Poisson's ratio.[11](https://www.crewes.org/Documents/ResearchReports/2010/CRR201002.pdf) It is the standard choice for two-term inversion but is invalid beyond about 30° of incidence.[1](https://faculty.kfupm.edu.sa/ES/ashuhail/Graduate/GEOP501/Ch2/Feng-2006.pdf) The most frequently used version is a modification of Shuey's equation using A, B, C terminology, where A is the intercept, B the AVO gradient, and C the curvature.[5](https://cseg.ca/the-relationship-between-avo-and-petrophysics/)\n- **Aki-Richards three-term form.** Solves for P-wave reflectivity, S-wave reflectivity, and density reflectivity, and generally honors the Zoeppritz response accurately to about 50°.[1](https://faculty.kfupm.edu.sa/ES/ashuhail/Graduate/GEOP501/Ch2/Feng-2006.pdf)\n- **Fatti approximation.** More accurate to higher angles of incidence than Shuey's, independent of any assumption of density, and yielding normal-incidence P and S impedance reflectivities.[8](https://cseg.ca/amplitude-vs-offset-and-seismic-rock-property-analysis-a-primer/)\n- **Verm-Hilterman form.** An angle-dependent expression in terms of normal-incidence attributes.[6](https://csim.kaust.edu.sa/files/erse210/fosterkeys.pdf)\n\n**AVO classes.** Large negative intercept and gradient values define Class III anomalies; a weak intercept combined with a large negative gradient indicates Class II; a positive intercept with a negative gradient defines Class I; and a negative intercept with a zero or positive gradient characterizes Class IV.[3](https://www.nature.com/articles/s41598-026-35935-2) Class IV describes low-impedance gas sands where reflection coefficients decrease with increasing offset, and classification of hydrocarbon-bearing sands has been recommended on intercept-versus-gradient crossplots rather than the NI-PR plot.[11](https://www.crewes.org/Documents/ResearchReports/2010/CRR201002.pdf) A later proposed classification reassigns parts of the class 3 and class 4 domains into a new Type 4 while keeping types 1 to 3 as before.[12](https://e-seis.com/wp-content/uploads/2014/11/A-Comprehensive-AVO-Clasification.pdf)\n\n## Applications\n\n**Gas-sand detection** is the classic use: distinguishing gas-related amplitude anomalies from other amplitude anomalies, and separating gas-sand bright spots from those caused by nonhydrocarbon rocks such as basalts.[11](https://www.crewes.org/Documents/ResearchReports/2010/CRR201002.pdf) • [6](https://csim.kaust.edu.sa/files/erse210/fosterkeys.pdf)\n\n**Gas hydrates.** Modeling of bottom-simulating reflectors with three-phase theory concludes that low and high concentrations of hydrate can be distinguished, since they give positive and negative anomalies respectively, and that the P-to-S reflection coefficient is a good indicator of high amounts of free gas and gas hydrate.[4](https://www.crewes.org/Documents/ResearchReports/2001/2001-24.pdf)\n\n**Marine reservoir characterization.** Bayesian AVO inversion of marine data estimates P- and S-wave impedances and density, from which [Young's modulus](https://www.edgepedia.org/youngs-modulus) and Poisson's ratio are derived indirectly.[13](https://www.mdpi.com/2077-1312/13/5/948)\n\n**Frequency-dependent AVO (FAVO)** uses spectral decomposition and a dispersion gradient as a hydrocarbon indicator, assuming frequency-dependent elastic parameters.[14](https://www.sciopen.com/article/10.1016/j.petsci.2023.02.011)\n\n## Limitations and alternatives\n\n**Geometric and wavelet errors.** Five sources of error affect intercept and slope estimates, including NMO stretch (frequency distortion from normal-moveout correction of seismic gathers) and thin-bed tuning (wave interference when layers approach quarter-wavelength thickness); a detectability analysis gives the tuning-plus-stretching condition \\( \\delta_{\\gamma}^{2} > 0.41 \\).[4](https://www.crewes.org/Documents/ResearchReports/2001/2001-24.pdf)\n\n**Noise.** A correlated noise trend in intercept-gradient crossplots typically lies at an angle of approximately 15° and is commonly cited as a factor limiting the power of AVA to resolve hydrocarbon anomalies in time-windowed crossplots.[15](https://info.tgs.com/hubfs/2021%20Articles/Went%202021%20tle_40060454.1%20hires_seg.pdf) One analysis concluded that in most real data sets the gradient and intercept are statistically correlated as a result of seismic noise, rendering attributes like the Fluid Factor essentially meaningless.[10](https://csegrecorder.com/articles/view/avo-yesterday-today-and-a-peek-at-tomorrow)\n\n**False positives.** Fluid Factor sections show negative or false-positive anomalies resulting from errors or assumptions in the AVO method, including that the pre-processed seismic data has a \"true\" AVO response, noise, and multiple interference.[16](https://geoconvention.com/wp-content/uploads/abstracts/2022/73399-the-use-and-abuse-of-avo_-value-analysis-errors.pdf) A long list of factors degrades robustness: tuning and interference, poor S/N, inadequate offset, bandwidth or fold, unbalanced channels, coherent noise, complex structure and stratigraphy, geometric spreading, focusing, scattering, dip, Fresnel-zone effects, fault shadows, anisotropy, attenuation and dispersion, lateral velocity variations, improper processing, and inversion non-uniqueness.[16](https://geoconvention.com/wp-content/uploads/abstracts/2022/73399-the-use-and-abuse-of-avo_-value-analysis-errors.pdf) Migration choice matters: a 40° incident-angle PSTM section can show an isolated bright-spot-like AVO amplitude that the corresponding PSDM section does not show.[16](https://geoconvention.com/wp-content/uploads/abstracts/2022/73399-the-use-and-abuse-of-avo_-value-analysis-errors.pdf) In FAVO work, non-reservoir strong reflection interfaces can cause significant false dispersion, so logging and geological data should be used to guard against it.[14](https://www.sciopen.com/article/10.1016/j.petsci.2023.02.011)\n\n**Parameter uncertainty.** Inverted density carries inherent uncertainty when the offset of the seismic data is not long enough, and calculating parameters indirectly by multiplication, division or squaring enlarges inversion error.[13](https://www.mdpi.com/2077-1312/13/5/948) Inversion can, however, separate overburden effects on reflection coefficients from reservoir effects.[5](https://cseg.ca/the-relationship-between-avo-and-petrophysics/)\n\n**Alternatives.** Fatti P and S impedance attributes, or equivalents such as the Shuey normal-incidence attribute and gradient, can be combined with post-stack impedance inversion to estimate layer impedances.[8](https://cseg.ca/amplitude-vs-offset-and-seismic-rock-property-analysis-a-primer/) For data with large incidence angles, the exact Zoeppritz equation or higher-order approximations should replace linearized forms.[7](https://www.nature.com/articles/s41598-026-36501-6) Recent published work extends the linearized toolbox toward nonlinear, probabilistic, and learning-based inversion, including hybrid quantum ant colony optimization with the exact Zoeppritz equation for nonlinear amplitude-versus-angle inversion[17](https://www.frontiersin.org/journals/earth-science/articles/10.3389/feart.2024.1483776/full) and a semi-supervised deep-learning framework using a time-frequency joint CNN with exact-Zoeppritz forward modeling.[18](https://www.earthdoc.org/content/journals/10.1111/1365-2478.70145)\n\n## References\n\n1. [AVO principles, processing and inversion](https://faculty.kfupm.edu.sa/ES/ashuhail/Graduate/GEOP501/Ch2/Feng-2006.pdf)\n2. [KGS--Bulletin 237--Amplitude Variation with Offset](https://www.kgs.ku.edu/Publications/Bulletins/237/Knapp1/)\n3. [Geological controls on reservoir seismic responses | Scientific Reports](https://www.nature.com/articles/s41598-026-35935-2)\n4. [A review of AVO analysis (CREWES Research Report 2001-24)](https://www.crewes.org/Documents/ResearchReports/2001/2001-24.pdf)\n5. [The Relationship between AVO and Petrophysics](https://cseg.ca/the-relationship-between-avo-and-petrophysics/)\n6. [Interpretation of AVO anomalies (Foster & Keys)](https://csim.kaust.edu.sa/files/erse210/fosterkeys.pdf)\n7. [Integrating physics and machine learning for unified seismic forward modeling and reservoir property inversion](https://www.nature.com/articles/s41598-026-36501-6)\n8. [Amplitude-vs-Offset and Seismic Rock Property Analysis: A Primer - CSEG](https://cseg.ca/amplitude-vs-offset-and-seismic-rock-property-analysis-a-primer/)\n9. [Amplitude versus offset (AVO) analysis - AAPG Wiki](https://wiki.aapg.org/index.php?title=Amplitude_versus_offset_analysis)\n10. [AVO: Yesterday, today, and (a peek at) tomorrow | CSEG RECORDER](https://csegrecorder.com/articles/view/avo-yesterday-today-and-a-peek-at-tomorrow)\n11. [Tutorial: AVO inversion (CREWES Research Report 2010)](https://www.crewes.org/Documents/ResearchReports/2010/CRR201002.pdf)\n12. [A comprehensive AVO classification](https://e-seis.com/wp-content/uploads/2014/11/A-Comprehensive-AVO-Clasification.pdf)\n13. [Reservoir Characterization Based on Bayesian Amplitude Versus Offset Inversion of Marine Seismic Data](https://www.mdpi.com/2077-1312/13/5/948)\n14. [The applicability and underlying factors of frequency-dependent amplitude-versus-offset (AVO) inversion](https://www.sciopen.com/article/10.1016/j.petsci.2023.02.011)\n15. [Practical application of global siliciclastic rock-property trends to AVA interpretation in frontier basins (TGS / The Leading Edge)](https://info.tgs.com/hubfs/2021%20Articles/Went%202021%20tle_40060454.1%20hires_seg.pdf)\n16. [The Use and Abuse of AVO: Value, Analysis, Errors and Pitfalls (GeoConvention 2022)](https://geoconvention.com/wp-content/uploads/abstracts/2022/73399-the-use-and-abuse-of-avo_-value-analysis-errors.pdf)\n17. [Nonlinear amplitude versus angle inversion using hybrid quantum ant colony optimization and the exact Zoeppritz equation](https://www.frontiersin.org/journals/earth-science/articles/10.3389/feart.2024.1483776/full)\n18. [Semi-Supervised Amplitude-Variation-With-Offset Inversion With Time-Frequency Feature Fusion and Geological Constraints](https://www.earthdoc.org/content/journals/10.1111/1365-2478.70145)\n\n---\n*Topic: Encyclopedia › Physical world and mathematics › Earth sciences › Earth systems and geophysics › Seismic survey and processing*\n\n*Initially written Sep 29, 2026 · Reviewed: Sep 30, 2026 · Edited: Sep 30, 2026 · Last review: Sep 30, 2026*\n\n*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*\n\nLicense: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license\n", "same_as": [], "url": "https://www.edgepedia.org/amplitude-versus-offset-analysis", "markdown_url": "https://www.edgepedia.org/amplitude-versus-offset-analysis.md", "license": { "name": "Edgepedia Community License 1.0", "url": "https://www.edgepedia.org/edgepedia/license", "summary": "Free with credit, commercial use included. AI training is open to everyone. 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Edgepedia Community License 1.0.", "speakable": "Amplitude versus offset analysis measures how seismic reflection amplitude changes with source-receiver offset, and uses that variation to constrain subsurface rock properties and fluid content, notably free gas." }