Continuous isolated noise sources induce repeating waves in the coda of ambient noise correlations


  • Sven Schippkus Institute of Geophysics, Centre for Earth System Research and Sustainability (CEN), Universität Hamburg, Hamburg
  • Mahsa Safarkhani Institute of Geophysics, Centre for Earth System Research and Sustainability (CEN), Universität Hamburg, Hamburg, Germany
  • Céline Hadziioannou Institute of Geophysics, Centre for Earth System Research and Sustainability (CEN), Universität Hamburg, Hamburg, Germany



Ambient seismic noise, Seismic interferometry, Correlations


Continuous excitation of isolated noise sources leads to repeating wave arrivals in cross correlations of ambient seismic noise, including throughout their coda. These waves propagate from the isolated sources. We observe this effect on correlation wavefields computed from two years of field data recorded at the Gräfenberg array in Germany and two master stations in Europe. Beamforming the correlation functions in the secondary microseism frequency band reveals repeating waves incoming from distinct directions to the West, which correspond to well-known dominant microseism source locations in the Northeastern Atlantic Ocean. These emerge in addition to the expected anti-causal and causal correlation wavefield contributions by boundary sources, which are converging onto and diverging from the master station, respectively. Numerical simulations reproduce this observation. We first model a source repeatedly exciting a wavelet, which helps illustrate the fundamental mechanism behind repeated wave generation. Second, we model continuously acting secondary microseism sources and find good agreement with our observations. Our observations and modelling have potentially significant implications for the understanding of correlation wavefields and monitoring of relative velocity changes in particular. Velocity monitoring commonly assumes that only multiply scattered waves, originating from the master station, are present in the coda of the correlation wavefield. We show that repeating waves propagating from isolated noise sources may dominate instead, including the very late coda. Our results imply that in the presence of continously acting noise sources, which we show is the case for ordinary recordings of ocean microseisms, velocity monitoring assuming scattered waves may be adversely affected with regard to measurement technique, spatial resolution, as well as temporal resolution. We further demonstrate that the very late coda of correlation functions contains useful signal, contrary to the common sentiment that it is dominated by instrument noise.


Ayala-Garcia, D., Curtis, A., & Branicki, M. (2021). Seismic Interferometry from Correlated Noise Sources. Remote Sensing, 13(14), 2703. doi:10.3390/rs13142703 DOI:

Bensen, G. D., Ritzwoller, M. H., Barmin, M. P., Levshin, A. L., Lin, F., Moschetti, M. P., … Yang, Y. (2007). Processing Seismic Ambient Noise Data to Obtain Reliable Broad-Band Surface Wave Dispersion Measurements. Geophysical Journal International, 169(3), 1239–1260. doi:10.1111/j.1365-246X.2007.03374.x DOI:

Bruland, C., & Hadziioannou, C. (2023). Gliding Tremors Associated with the 26 Second Microseism in the Gulf of Guinea. Communications Earth & Environment, 4(1), 1–9. doi:10.1038/s43247-023-00837-y DOI:

Chevrot, S., Sylvander, M., Benahmed, S., Ponsolles, C., Lefèvre, J. M., & Paradis, D. (2007). Source Locations of Secondary Microseisms in Western Europe: Evidence for Both Coastal and Pelagic Sources. Journal of Geophysical Research: Solid Earth, 112(B11). doi:10.1029/2007JB005059 DOI:

Crameri, F. (2021, September). Scientific Colour Maps. doi:10.5281/ZENODO.5501399

Friedrich, T., Zieger, T., Forbriger, T., & Ritter, J. R. R. (2018). Locating Wind Farms by Seismic Interferometry and Migration. Journal of Seismology, 22(6), 1469–1483. doi:10.1007/s10950-018-9779-0 DOI:

Friedrich, A., Krüger, F., Klinge, K., & 1998. (1998). Ocean-Generated Microseismic Noise Located with the Gräfenberg Array. Journal of Seismology, 2, 47–64. doi:10.1023/A:1009788904007 DOI:

Fuchs, F., Bokelmann, G., & the AlpArray Working Group. (2021, April). Persistent Monochromatic Seismic Signals across Central Europe: AlpArray Data Indicate a Man-Made Seismic Source for Regional Wave Propagation Studies. EGU General Assembly 2021. doi:10.5194/egusphere-egu21-11008 DOI:

Gouédard, P., Stehly, L., Brenguier, F., Campillo, M., Colin de Verdière, Y., Larose, E., … Weaver, R. L. (2008). Cross-Correlation of Random Fields: Mathematical Approach and Applications. Geophysical Prospecting, 56(3), 375–393. doi:10.1111/j.1365-2478.2007.00684.x DOI:

Gualtieri, L., Bachmann, E., Simons, F. J., & Tromp, J. (2020). The Origin of Secondary Microseism Love Waves. Proceedings of the National Academy of Sciences of the United States of America, 117(47), 29504–29511. doi:10.1073/pnas.2013806117 DOI:

Hadziioannou, C., Larose, E., Coutant, O., Roux, P., & Campillo, M. (2009). Stability of Monitoring Weak Changes in Multiply Scattering Media with Ambient Noise Correlation: Laboratory Experiments. The Journal of the Acoustical Society of America, 125(6), 3688–3695. doi:10.1121/1.3125345 DOI:

Harris, C. R., Millman, K. J., van der Walt, S. J., Gommers, R., Virtanen, P., Cournapeau, D., … Oliphant, T. E. (2020). Array Programming with NumPy. Nature, 585(7825), 357–362. doi:10.1038/s41586-020-2649-2 DOI:

Federal Institute for Geosciences and Natural Resources. (1976). German Regional Seismic Network (GRSN). doi:10.25928/MBX6-HR74

Hunter, J. D. (2007). Matplotlib: A 2D Graphics Environment. Computing in Science & Engineering, 9(3), 90–95. doi:10.1109/MCSE.2007.55 DOI:

Istituto Nazionale di Geofisica e Vulcanologia (INGV). (2005). Rete Sismica Nazionale (RSN). doi:10.13127/SD/X0FXNH7QFY DOI:

Juretzek, C., & Hadziioannou, C. (2016). Where Do Ocean Microseisms Come from? A Study of Love-to-Rayleigh Wave Ratios. Journal of Geophysical Research: Solid Earth, 121(9), 6741–6756. doi:10.1002/2016JB013017 DOI:

Krischer, L., Megies, T., Barsch, R., Beyreuther, M., Lecocq, T., Caudron, C., & Wassermann, J. (2015). ObsPy: A Bridge for Seismology into the Scientific Python Ecosystem. Computational Science & Discovery, 8(014003). doi:10.1088/1749-4699/8/1/014003 DOI:

Lobkis, O. I., & Weaver, R. L. (2003). Coda-Wave Interferometry in Finite Solids: Recovery of P -to- S Conversion Rates in an Elastodynamic Billiard. Physical Review Letters, 90(25), 254302. doi:10.1103/PhysRevLett.90.254302 DOI:

Lu, Y., Stehly, L., Paul, A., & the AlpArray Working Group. (2018). High-Resolution Surface Wave Tomography of the European Crust and Uppermost Mantle from Ambient Seismic Noise. Geophysical Journal International, 214(2), 1136–1150. doi:10.1093/gji/ggy188 DOI:

Mao, S., Lecointre, A., van der Hilst, R. D., & Campillo, M. (2022). Space-Time Monitoring of Groundwater Fluctuations with Passive Seismic Interferometry. Nature Communications, 13(1), 4643. doi:10.1038/s41467-022-32194-3 DOI:

Margerin, L., Planès, T., Mayor, J., & Calvet, M. (2016). Sensitivity Kernels for Coda-Wave Interferometry and Scattering Tomography: Theory and Numerical Evaluation in Two-Dimensional Anisotropically Scattering Media. Geophysical Journal International, 204(1), 650–666. doi:10.1093/gji/ggv470 DOI:

Met Office. (2010). Cartopy: A Cartographic Python Library with a Matplotlib Interface. Exeter, Devon.

Nagel, S., Zieger, T., Luhmann, B., Knödel, P., Ritter, J., & Ummenhofer, T. (2021). Ground Motions Induced by Wind Turbines. Civil Engineering Design, 3(3), 73–86. doi:10.1002/cend.202100015 DOI:

Obermann, A., Froment, B., Campillo, M., Larose, E., Planès, T., Valette, B., … Liu, Q. Y. (2014). Seismic Noise Correlations to Image Structural and Mechanical Changes Associated with the Mw 7.9 2008 Wenchuan Earthquake. Journal of Geophysical Research: Solid Earth, 119(4), 3155–3168. doi:10.1002/2013JB010932 DOI:

Petroff, M. A. (2021). Accessible Color Sequences for Data Visualization. doi:10.48550/arXiv.2107.02270

Planès, T., Larose, E., Margerin, L., Rossetto, V., & Sens-Schönfelder, C. (2014). Decorrelation and Phase-Shift of Coda Waves Induced by Local Changes: Multiple Scattering Approach and Numerical Validation. Waves in Random and Complex Media, 24(2), 99–125. doi:10.1080/17455030.2014.880821 DOI:

Polish Academy of Sciences (PAN) Polskiej Akademii Nauk. (1990). Polish Seismological Network. Polish Academy of Sciences (PAN) Polskiej Akademii Nauk.

Retailleau, L., Boué, P., Stehly, L., & Campillo, M. (2017). Locating Microseism Sources Using Spurious Arrivals in Intercontinental Noise Correlations. Journal of Geophysical Research: Solid Earth, 122(10), 8107–8120. doi:10.1002/2017JB014593 DOI:

Rost, S., & Thomas, C. (2002). Array Seismology: Methods and Applications. Reviews of Geophysics, 40(3), 2-1-2–27. doi:10.1029/2000RG000100 DOI:

Schippkus, S., Zigone, D., Bokelmann, G. H. R., & the AlpArray Working Group. (2018). Ambient-Noise Tomography of the Wider Vienna Basin Region. Geophysical Journal International, 215(1), 102–117. doi:10.1093/gji/ggy259 DOI:

Schippkus, S., Garden, M., & Bokelmann, G. (2020). Characteristics of the Ambient Seismic Field on a Large-N Seismic Array in the Vienna Basin. Seismological Research Letters, 91(5), 2803–2816. doi:10.1785/0220200153 DOI:

Schippkus, S., & Hadziioannou, C. (2022). Matched Field Processing Accounting for Complex Earth Structure: Method and Review. Geophysical Journal International, 231(2), 1268–1282. doi:10.1093/gji/ggac240 DOI:

Schippkus, S. (2023). Schipp/Repeating_direct_waves. doi:10.5281/zenodo.7643286

Schippkus, S., Snieder, R., & Hadziioannou, C. (2022). Seismic Interferometry in the Presence of an Isolated Noise Source. Seismica, 1(1). doi:10.26443/seismica.v1i1.195 DOI:

Sens-Schönfelder, C., & Larose, E. (2010). Lunar Noise Correlation, Imaging and Monitoring. Earthquake Science, 23(5), 519–530. doi:10.1007/s11589-010-0750-6 DOI:

Sheng, Y., Mordret, A., Brenguier, F., Boué, P., Vernon, F., Takeda, T., … Ben-Zion, Y. (2023). Seeking Repeating Anthropogenic Seismic Sources: Implications for Seismic Velocity Monitoring at Fault Zones. Journal of Geophysical Research: Solid Earth, 128(1). doi:10.1029/2022JB024725 DOI:

Snieder, R., Wapenaar, K., & Larner, K. (2006). Spurious Multiples in Seismic Interferometry of Primaries. GEOPHYSICS, 71(4), SI111–SI124. doi:10.1190/1.2211507 DOI:

Soergel, D., Pedersen, H. A., Bodin, T., Paul, A., Stehly, L., AlpArray Working Group, … Egdorf, S. (2022). Bayesian Analysis of Azimuthal Anisotropy in the Alpine Lithosphere from Beamforming of Ambient Noise Cross-Correlations. Geophysical Journal International, 232(1), 429–450. doi:10.1093/gji/ggac349 DOI:

Sollberger, D., Bradley, N., Edme, P., & Robertsson, J. O. A. (2023). Efficient Wave Type Fingerprinting and Filtering by Six-Component Polarization Analysis. Geophysical Journal International, 234(1), 25–39. doi:10.1093/gji/ggad071 DOI:

van Dinther, C., Margerin, L., & Campillo, M. (2021). Implications of Laterally Varying Scattering Properties for Subsurface Monitoring With Coda Wave Sensitivity Kernels: Application to Volcanic and Fault Zone Setting. Journal of Geophysical Research: Solid Earth, 126(12). doi:10.1029/2021JB022554 DOI:

Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., … SciPy 1.0 Contributors. (2020). SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods, 17, 261–272. doi:10.1038/s41592-019-0686-2 DOI:

Wapenaar, K., Fokkema, J., & Snieder, R. (2005). Retrieving the Green’s Function in an Open System by Cross Correlation: A Comparison of Approaches (L). The Journal of the Acoustical Society of America, 118(5), 2783–2786. doi:10.1121/1.2046847 DOI:

Wapenaar, K., Draganov, D., Snieder, R., Campman, X., & Verdel, A. (2010). Tutorial on Seismic Interferometry: Part 1 textemdash Basic Principles and Applications. GEOPHYSICS, 75(5), 75A195-75A209. doi:10.1190/1.3457445 DOI:

Wegler, U., & Sens-Schönfelder, C. (2007). Fault Zone Monitoring with Passive Image Interferometry. Geophysical Journal International, 168(3), 1029–1033. doi:10.1111/j.1365-246X.2006.03284.x DOI:

Yates, A., Caudron, C., Lesage, P., Mordret, A., Lecocq, T., & Soubestre, J. (2022). Assessing Similarity in Continuous Seismic Cross-Correlation Functions Using Hierarchical Clustering: Application to Ruapehu and Piton de La Fournaise Volcanoes. Geophysical Journal International, 233(1), 472–489. doi:10.1093/gji/ggac469 DOI:

Zeng, X., & Ni, S. (2010). A Persistent Localized Microseismic Source near the Kyushu Island, Japan. Geophysical Research Letters, 37(24). doi:10.1029/2010GL045774 DOI:

Additional Files



How to Cite

Schippkus, S., Safarkhani, M., & Hadziioannou, C. (2023). Continuous isolated noise sources induce repeating waves in the coda of ambient noise correlations. Seismica, 2(2).




Funding data