{ "id": "ep6n5sp9xy", "slug": "wavefield-separation", "title": "Wavefield separation", "updated": "2026-10-15", "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.geophysical-imaging-and-inversion", "label": "Geophysical imaging and inversion", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.earth.planet.geophysical-imaging-and-inversion" } ], "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": "Wavefield separation is a signal-processing method in seismology that decomposes recorded seismic data into components such as upgoing and downgoing waves or P- and S-waves, feeding migration and full-waveform inversion.", "snippet": "Wavefield separation is a signal-processing method in seismology that decomposes recorded seismic data into components such as upgoing and downgoing waves or P- and S-waves, feeding migration and full-waveform inversion.", "node": "physical.earth.planet.geophysical-imaging-and-inversion", "markdown": "# Wavefield separation\n\nWavefield separation is a signal-processing method in seismology that decomposes recorded seismic or acoustic data into components traveling in different directions or of different wave modes, such as upgoing and downgoing waves or P- and S-waves. A land surface recording contains the sum of upgoing, downgoing reflected, and downgoing mode-converted wavefields, but true-amplitude and phase imaging requires the upgoing wavefield alone.[1](https://www.earthdoc.org/content/papers/10.3997/2214-4609.201601357) Ocean-bottom cable (OBC) data are likewise a superposition of upgoing and downgoing P and S waves that must be decomposed before pre- or post-stack analysis.[2](https://academic.oup.com/gji/article/177/3/966/2107995) Its outputs feed acoustic migration, elastic reverse-time migration (RTM), and full-waveform inversion (FWI).[3](https://api.geophysical-press.com/uploads/file/asp/VOL28-5_art2.pdf)\n\n| Key fact | Detail |\n|---|---|\n| Inputs | Multicomponent data: pressure plus vertical particle velocity for up/down decomposition[4](https://pylops.readthedocs.io/en/v1.5.0/api/generated/pylops.waveeqprocessing.WavefieldDecomposition.html); three particle-velocity components plus pressure in OBC surveys[2](https://academic.oup.com/gji/article/177/3/966/2107995) |\n| Outputs | Upgoing and downgoing fields \\( p^-(x,t) \\) and \\( p^+(x,t) \\)[4](https://pylops.readthedocs.io/en/v1.5.0/api/generated/pylops.waveeqprocessing.WavefieldDecomposition.html), or P- and S-wave fields[3](https://api.geophysical-press.com/uploads/file/asp/VOL28-5_art2.pdf) |\n| Core principle | Linear combination of pressure and particle velocity in the frequency-wavenumber domain[5](https://pylops.readthedocs.io/en/v1.11.0/tutorials/wavefielddecomposition.html); at vertical incidence, summation scaled by the water-bottom acoustic impedance[6](https://www.geos.ed.ac.uk/~acurtis/assets/Papers/Robertsson_Curtis2002.pdf) |\n| Auxiliary data | For Wapenaar's procedure, only the medium parameters at the free surface; no subsurface knowledge[7](https://keeswapenaar.nl/4_Journals/Geophys.Prosp/GP_90c.pdf) |\n| Main geometries | VSP, OBC/OBS, land multicomponent, marine deghosting[2](https://academic.oup.com/gji/article/177/3/966/2107995) • [1](https://www.earthdoc.org/content/papers/10.3997/2214-4609.201601357) |\n| Known accuracy limit | Gradient-based land separation holds to roughly 25° (horizontal component) and 50° (vertical component) incidence[1](https://www.earthdoc.org/content/papers/10.3997/2214-4609.201601357) |\n| Status of AI variants | Efficient and independent of elastic parameters, but still described as exploratory[8](http://en.dzkx.org/article/doi/10.6038/pg2023GG0328) |\n\n## How it works\n\nThe physical basis is that differently directed or differently polarized wave components leave distinguishable signatures in combinations of the recorded fields. For up/down decomposition, at vertical incidence, summing the pressure and vertical recordings scaled by the acoustic impedance of the water bottom accomplishes the separation.[6](https://www.geos.ed.ac.uk/~acurtis/assets/Papers/Robertsson_Curtis2002.pdf) More generally, up- and down-going pressure components \\( p^-(x,t) \\) and \\( p^+(x,t) \\) are estimated by linearly combining measured pressure \\( p(x,t) \\) and vertical particle velocity \\( v_z(x,t) \\), a process also called data-based deghosting.[4](https://pylops.readthedocs.io/en/v1.5.0/api/generated/pylops.waveeqprocessing.WavefieldDecomposition.html)\n\nFor P/S separation, two mathematical routes dominate. The first is [Helmholtz decomposition](https://www.edgepedia.org/helmholtz-decomposition): a vector wavefield splits into a curl-free vector field, generated by a scalar potential, and a divergence-free vector field, generated by a vector potential, which in homogeneous isotropic media correspond to P and S motion.[9](https://www.ahay.org/RSF/book/cwp/geo2009VTIModeSeparation/paper_html/node2.html) The second uses the dispersion relation to compute normalized polarization vectors, which generalizes to transverse isotropy and 3D and handles lateral heterogeneity by splitting the near-surface into sections with smoothly varying velocities.[3](https://api.geophysical-press.com/uploads/file/asp/VOL28-5_art2.pdf)\n\n## How it is done\n\nA typical elastic separation workflow runs as follows[3](https://api.geophysical-press.com/uploads/file/asp/VOL28-5_art2.pdf):\n\n1. For each particle-velocity component of the input seismogram, perform a 3D [Fourier transform](https://www.edgepedia.org/fourier-transform) from the time-space domain to the frequency-wavenumber domain.\n2. Choose a dispersion relation and compute the normalized polarization vectors for each wavenumber-frequency sample.\n3. Apply the separation or decomposition equations in that domain.\n4. Inverse-transform back to time-space.\n\nFor acoustic up/down decomposition on streamer or seabed data, the same linear-combination idea is implemented in open-source software as `UpDownComposition2D`, combining pressure and particle velocity in the frequency-wavenumber domain.[5](https://pylops.readthedocs.io/en/v1.11.0/tutorials/wavefielddecomposition.html) • [4](https://pylops.readthedocs.io/en/v1.5.0/api/generated/pylops.waveeqprocessing.WavefieldDecomposition.html)\n\nFor OBC receiver-function work, decomposition is a two-step scheme: first estimate the upgoing wavefields (P up above the ocean bottom; P up and S up below it), then remove the remaining multiples from these upgoing fields by predictive deconvolution, for which the elastic decomposition acts as pre-conditioning.[2](https://academic.oup.com/gji/article/177/3/966/2107995) A notable feature of Wapenaar's decomposition procedure is that no knowledge of the subsurface is required; both decomposition and multiple elimination are fully determined by the medium parameters at the free surface.[7](https://keeswapenaar.nl/4_Journals/Geophys.Prosp/GP_90c.pdf) The gradient-based land method similarly needs only the P- and S-wave velocities exactly at the receiver locations.[1](https://www.earthdoc.org/content/papers/10.3997/2214-4609.201601357)\n\n## Origin\n\nFrequency-wavenumber-domain up/down separation was applied from the early 1960s (Embree et al., 1963; Treitel et al., 1967), and separation in the tau-p domain after a [Radon transform](https://www.edgepedia.org/radon-transform) was suggested.[10](https://www.sciencedirect.com/science/article/abs/pii/S0926985117309436) Acoustic decomposition began with the data-driven particle-velocity-to-pressure filter matching in P-Z summation; this was inexact and was followed by up-down decomposition for acoustic and elastic waves along horizontal recording surfaces developed by Frasier (1970), Aki and Richards (1980), Ursin (1983), Kennett (1984), Dankbaar (1985), and Wapenaar et al. (1990).[11](https://www.keeswapenaar.nl/4_Journals/Geophys.Prosp/GP_19a.pdf) Decomposing receiver data into upgoing P- and S-waves including slowness and amplitude variation with incidence angle was addressed, and the elastodynamic representation theorem was used to derive decomposition filters.[6](https://www.geos.ed.ac.uk/~acurtis/assets/Papers/Robertsson_Curtis2002.pdf)\n\nFor vertical well arrays, plane-wave up-down decomposition is followed by parametric decomposition by Leaney (1990).[11](https://www.keeswapenaar.nl/4_Journals/Geophys.Prosp/GP_19a.pdf) An algorithm derived from seafloor boundary conditions separates multicomponent data into upgoing and downgoing P- and S-waves.[3](https://api.geophysical-press.com/uploads/file/asp/VOL28-5_art2.pdf) Multicomponent decomposition is historically as old as the [Poynting vector](https://www.edgepedia.org/poynting-vector) (Poynting 1884).[11](https://www.keeswapenaar.nl/4_Journals/Geophys.Prosp/GP_19a.pdf) Richwalski, Roy-[Chowdhury](https://www.edgepedia.org/chowdhury), and Mondt (2000) examined a polarization-and-slowness method for two-component surface data in Geophysical Prospecting, presenting an iterative approach that separates waves differing in amplitude given only an estimate of the number of waves expected.[12](https://doi.org/10.1046/j.1365-2478.2000.00204.x)\n\n## Variants\n\nA review groups P/S separation into three principles: the Radon transform method, polarization filtering, and wavefield extrapolation.[8](http://en.dzkx.org/article/doi/10.6038/pg2023GG0328) Within these, several named distinctions matter.\n\n**PS separation versus PS decomposition.** PS separation, represented by divergence and curl operators, does not preserve amplitude and phase; PS decomposition uses the relations between wave propagation and polarization vectors and does preserve them.[3](https://api.geophysical-press.com/uploads/file/asp/VOL28-5_art2.pdf)\n\n**Domain-transform and wave-equation methods.** Besides f-k and tau-p implementations, the original dual-sensor summation was derived for normal incidence in the time-space domain, and later tau-p implementations made acoustic decomposition valid for all incidence angles.[2](https://academic.oup.com/gji/article/177/3/966/2107995)\n\n**Representation-theorem and gradient methods.** A spatial-wavefield-gradient approach based on the elastodynamic representation theorem isolates the upgoing wavefield for densely spaced receiver groups without assuming isolated arrivals.[1](https://www.earthdoc.org/content/papers/10.3997/2214-4609.201601357) Directional snapshot decomposition differs from conventional up-down decomposition in that the decomposition direction need not be normal to the recording surface, so the wavefield can be decomposed into any direction, which suits RTM snapshot processing.[11](https://www.keeswapenaar.nl/4_Journals/Geophys.Prosp/GP_19a.pdf)\n\n**Data-domain masking.** A structure-tensor local-dip estimate with a dip-masking filter separates upgoing and downgoing VSP wavefields while preserving amplitudes and producing a section free of fake events.[13](https://bgo.ogs.it/sites/default/files/pdf/bgta0303_Hashemi.pdf) An alternative marine approach records the pressure wavefield at two different constant depths, where the interference patterns of events differ between recordings.[14](https://www.tgs.com/hubfs/Technical%20Library/Technical%20Library%20Files/geophysics_vanborselen_etal_2013_wavefielddecomposition.pdf)\n\n## Applications\n\nSeparation is applied across acquisition geometries. In OBC surveys, a towed airgun array produces pressure only, yet the recorded data mix upgoing and downgoing P and S waves, so decomposition precedes analysis.[2](https://academic.oup.com/gji/article/177/3/966/2107995) On land, up/down separation extracts the true-amplitude upgoing wavefield and can significantly improve amplitude-versus-offset analysis and full-waveform inversion.[1](https://www.earthdoc.org/content/papers/10.3997/2214-4609.201601357) In vector processing of multicomponent data, separation reduces data complexity, aiding analysis of fast and slow S-waves and increasing imaging quality.[15](https://www.mdpi.com/2076-3417/9/9/1770)\n\nIts downstream roles are threefold. It is a prerequisite step before imaging the subsurface, or directly part of the imaging condition, and the removed receiver ghost can be reused as an additional source wavefield.[11](https://www.keeswapenaar.nl/4_Journals/Geophys.Prosp/GP_19a.pdf) It suppresses P- and S-wave cross-talk noise in elastic-wave migration and waveform inversion, improving imaging quality and inversion accuracy.[16](https://www.sciencedirect.com/science/article/abs/pii/S0926985126001023)\n\n## Limitations and alternatives\n\nSeveral failure modes are documented. Early VSP separation filters assume depth-stationarity of the signal on all traces used, which fails when the depth window grows to about 100-200 m.[17](https://ogst.ifpenergiesnouvelles.fr/articles/ogst/abs/1990/02/vol45n2p181/vol45n2p181.html) Common VSP tools have characteristic artifacts: median filtering suffers an averaging effect that generates artifacts and modifies amplitudes, and 2D Fourier methods suffer spectral leakage and edge effects after the inverse transform.[13](https://bgo.ogs.it/sites/default/files/pdf/bgta0303_Hashemi.pdf) With sparse seabed stations, complete decomposition is possible only if the data contain no down-going reflections from the sea surface or other arrivals overlapping recorded events.[6](https://www.geos.ed.ac.uk/~acurtis/assets/Papers/Robertsson_Curtis2002.pdf) Acoustic decomposition is of limited interest when the ocean-bottom [reflection coefficient](https://www.edgepedia.org/reflection-coefficient) is close to 0.5, and elastic decomposition requires the elastic properties at the ocean bottom.[2](https://academic.oup.com/gji/article/177/3/966/2107995) The gradient-based land method improves separation up to about 25° and 50° incidence for the horizontal and vertical components, beyond which the traditional vertical-propagation assumption degrades.[1](https://www.earthdoc.org/content/papers/10.3997/2214-4609.201601357)\n\n**Deep-learning separation** is the main recent development. A deep neural network treats P/S separation in isotropic media as nonlinear point-by-point prediction, outperforming the classical polarization projection method while removing dependence on surface elastic parameters.[18](http://www.dzkx.org/en/article/doi/10.6038/cjg2022Q0049) SeparationPINN, a physics-informed neural network for P- and S-wave mode separation motivated by eliminating wave-mode interference during imaging or inversion, was proposed by Mu, Cheng, and Alkhalifah and published in IEEE Transactions on Geoscience and Remote Sensing, vol. 63, pp. 1-10, 2025. A 2023 review nonetheless describes intelligent P/S separation as still at an exploratory stage.[8](http://en.dzkx.org/article/doi/10.6038/pg2023GG0328)\n\n## References\n\n1. [Wavefield Separation of Multicomponent Land Seismic Data Using Spatial Wavefield Gradients (EAGE)](https://www.earthdoc.org/content/papers/10.3997/2214-4609.201601357)\n2. [Receiver function decomposition of OBC data: theory (Geophysical Journal International)](https://academic.oup.com/gji/article/177/3/966/2107995)\n3. [P- and S-wave separation and decomposition of two- and three-component elastic seismograms (Geophysical Prospecting)](https://api.geophysical-press.com/uploads/file/asp/VOL28-5_art2.pdf)\n4. [pylops.waveeqprocessing.WavefieldDecomposition](https://pylops.readthedocs.io/en/v1.5.0/api/generated/pylops.waveeqprocessing.WavefieldDecomposition.html)\n5. [PyLops wavefield decomposition tutorial](https://pylops.readthedocs.io/en/v1.11.0/tutorials/wavefielddecomposition.html)\n6. [Land Seismic Wavefield Separation (Robertsson & Curtis, 2002)](https://www.geos.ed.ac.uk/~acurtis/assets/Papers/Robertsson_Curtis2002.pdf)\n7. [Decomposition of multicomponent seismic data into primary P- and S-wave responses (Wapenaar, Geophysical Prospecting 1990)](https://keeswapenaar.nl/4_Journals/Geophys.Prosp/GP_90c.pdf)\n8. [Review of seismic P-and S-wavefields separation methods (Applied Geophysics, 2023)](http://en.dzkx.org/article/doi/10.6038/pg2023GG0328)\n9. [Separation method (Madagascar/RSF VTI mode separation documentation)](https://www.ahay.org/RSF/book/cwp/geo2009VTIModeSeparation/paper_html/node2.html)\n10. [Up- and downgoing borehole wavefield retrieval using single component borehole and reflection data (Journal of Applied Geophysics)](https://www.sciencedirect.com/science/article/abs/pii/S0926985117309436)\n11. [Acoustic directional snapshot wavefield decomposition (Geophysical Prospecting)](https://www.keeswapenaar.nl/4_Journals/Geophys.Prosp/GP_19a.pdf)\n12. [Sandra Richwalski, Kabir Roy‐Chowdhury, Jaap C. Mondt (2000). Practical aspects of wavefield separation of two‐component surface seismic data based on polarization and slowness estimates. Geophysical Prospecting.](https://doi.org/10.1046/j.1365-2478.2000.00204.x)\n13. [Structure-tensor / local-dip masking filter for VSP wavefield separation (Bollettino di Geofisica Teorica ed Applicata)](https://bgo.ogs.it/sites/default/files/pdf/bgta0303_Hashemi.pdf)\n14. [Wavefield decomposition based on acoustic reciprocity: Theory and applications to marine acquisition (Van Borselen et al. 2013, Geophysics)](https://www.tgs.com/hubfs/Technical%20Library/Technical%20Library%20Files/geophysics_vanborselen_etal_2013_wavefielddecomposition.pdf)\n15. [Discussions on the Processing of the Multi-Component Seismic Vector Field (Applied Sciences, MDPI)](https://www.mdpi.com/2076-3417/9/9/1770)\n16. [Elastic wavefield separation based on the modified pseudo-Helmholtz operator in TTI media (Journal of Applied Geophysics)](https://www.sciencedirect.com/science/article/abs/pii/S0926985126001023)\n17. [Trace Pair Filtering for Separation of Upgoing and Downgoing Waves in VSP (Oil & Gas Science and Technology, 1990)](https://ogst.ifpenergiesnouvelles.fr/articles/ogst/abs/1990/02/vol45n2p181/vol45n2p181.html)\n18. [P/S separation of multi-component seismograms using a deep learning method (Chinese Journal of Geophysics)](http://www.dzkx.org/en/article/doi/10.6038/cjg2022Q0049)\n\n---\n*Topic: Encyclopedia › Physical world and mathematics › Earth sciences › Earth systems and geophysics › Geophysical imaging and inversion*\n\n*Initially written Sep 29, 2026 · Edited: Oct 15, 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/wavefield-separation", "markdown_url": "https://www.edgepedia.org/wavefield-separation.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. For other uses, organizations over USD 100M in revenue or 100M monthly users license separately.", "spdx": "LicenseRef-Edgepedia-Community-1.0" }, "credit": "\"Wavefield separation\", Edgepedia (EdgeChat), https://www.edgepedia.org/wavefield-separation. Edgepedia Community License 1.0.", "credit_md": "\"[Wavefield separation](https://www.edgepedia.org/wavefield-separation)\", Edgepedia (EdgeChat), [https://www.edgepedia.org/wavefield-separation](https://www.edgepedia.org/wavefield-separation). [Edgepedia Community License 1.0](https://www.edgepedia.org/edgepedia/license).", "credit_html": "\"Wavefield separation\", Edgepedia (EdgeChat), https://www.edgepedia.org/wavefield-separation. Edgepedia Community License 1.0.", "speakable": "Wavefield separation is a signal-processing method in seismology that decomposes recorded seismic data into components such as upgoing and downgoing waves or P- and S-waves, feeding migration and full-waveform inversion." }