Braun, J., Van der Beek, P., and Batt, G. (2009). Quantitative Thermochronology. Cambridge: Cambridge University Press.Google Scholar

Carlson, W. D., Donelick, R. A., and Ketcham, R. A. (1999). Variability of apatite fission-track annealing kinetics: I. Experimental Results. American Mineralogist, 84, 1213–23Google Scholar

Cros, A., Gautheron, C., Pagel, M. et al. (2014). ⁴He behavior in calcite filling viewed by (U-Th)/He dating, ⁴He diffusion and grainlographic studies. Geochimica et Cosmochimica Acta, 125, 414–32.Google Scholar

Denison, D. G. T., Holmes, C. C., Mallick, B. K., and Smith, A. F. M. (2002). Bayesian Methods for Non-linear Classification and Regression. Chichester: John Wiley and Sons.Google Scholar

Dodson, M. H. (1973). Closure Temperature in Cooling Geochronological and Petrological Systems. Contributions to Mineralogy and Petrology, 40, 259–74.CrossRefGoogle Scholar

Donelick, R. A., Ketcham, R. A., and Carlson, W. D. (1999). Variability of apatite fission-track annealing kinetics II: Grainlographic orientation effects. American Mineralogist, 84, 1224–34.CrossRefGoogle Scholar

Ducassou, C. (2009). Age et origine des premiers reliefs de la chaîne hercynienne: le dévonocarbonifère du bassin d’Ancenis. Ph.D. thesis (in French), Université Rennes 1.Google Scholar

Duddy, I. R., Green, P. F., and Laslett, G. M. (1988). Thermal annealing of fission tracks in apatite 3. Variable temperature annealing. Chemical Geology: Isotope Geoscience Section, 73, 25–38.Google Scholar

Duddy, I. R., Green, P. F., Laslett, G. M. et al. (1989). Thermal annealing of fission tracks in apatite 4. Quantitative modelling techniques and extension to geological timescales. Chemical Geology: Isotope Geoscience Section, 79, 155–82.Google Scholar

Everitt, B.S., and Hand, D.J. (1981). Finite Mixture Distributions. New York: Chapman and Hall.CrossRefGoogle Scholar

Farley, K. A. (2000). Helium diffusion from apatite: General behavior as illustrated by Durango fluorapatite. Journal of Geophysical Research, 105(B2), 2903.CrossRefGoogle Scholar

Farley, K. A., and McKeon, R. (2015). Radiometric dating and temperature history of banded iron formation–associated hematite, Gogebic iron range, Michigan, USA. Geology 43(12), 1083–6. https://doi.org/10.1130/G37190.1.Google Scholar

Farley, K. A., Wolf, R. A., and Silver, L. T. (1996). The effects of long alpha-stopping distances on (U-Th)/He ages. Geochimica et Cosmochimica Acta, 60, 4223–9.Google Scholar

Flowers, R. M., Ketcham, R. A., Shuster, D. L., and Farley, K. A. (2009). Apatite (U-Th)/He thermochronometry using a radiation damage accumulation and annealing model. Geochimica et Cosmochimica Acta, 73, 2347–65Google Scholar

Friel, N., and Wyse, J. (2012). Estimating the evidence: A review. Statistica Neerlandica, 66, 288–308. https://doi.org/10.1111/j.1467-9574.2011.00515.x.CrossRefGoogle Scholar

Galbraith, R. (1988). Graphical display of estimates having differing standard errors. Technometrics, 30(3), 271–81. https://doi.org/10.2307/1270081.Google Scholar

Galbraith, R.F. (2005). Statistics for Fission-Track Analysis. New York: Chapman and Hall.CrossRefGoogle Scholar

Galbraith, R. F., and Green, P. F. (1990). Estimating the component ages in a finite mixture. Nuclear Tracks and Radiation Measurements, 17(3), 197–206.Google Scholar

Gallagher, K. (1995). Evolving thermal histories from fission track data. Earth Planetary Science Letters, 136, 421–35.Google Scholar

Gallagher, K. (2012). Transdimensional inverse thermal history modeling for quantitative thermochronology. Journal of Geophysical Research: Solid Earth, 117, B02408. https://doi.org/10.1029/2011JB00882.Google Scholar

Gallagher, K., Stephenson, J., Brown, R., Holmes, C., and Fitzgerald, P. (2005). Low temperature thermochronology and modelling strategies for multiple samples 1: Vertical profiles. Earth Planetary Science Letters, 237, 193–208.CrossRefGoogle Scholar

Gautheron, C., Tassan-Got, L., Barbarand, J., and Pagel, M. (2009). Effect of alpha-damage annealing on apatite (U-Th)/He thermochronology. Chemical Geology, 266, 157–70.CrossRefGoogle Scholar

Ginster, U., Reiners, P. W., Nasdala, L., and Chutimun Chanmuangg, N. (2019). Annealing kinetics of radiation damage in zircon. Geochimica et Cosmochimica Acta, 249, 235–46.Google Scholar

Goswami, J. N., Jha, R., and Lal, D. (1984). Quantitative treatment of annealing of charged particle tracks in common rock minerals. Earth Planetary Science Letters, 71, 120–8.Google Scholar

Green, P. F. (1988). The relationship between track shortening and fission track age reduction in apatite: Combined influences of inherent instability, annealing anisotropy, length bias and system calibration. Earth Planetary Science Letters, 89, 335–52.CrossRefGoogle Scholar

Green, P. F., Duddy, I. R., Gleadow, A. J. W., Tingate, P. R., and Laslett, G. M. (1986). Thermal annealing of fission tracks in apatite: 1. A qualitative description. Chemical Geology: Isotope Geoscience Section, 59, 237–53CrossRefGoogle Scholar

Guenthner, W. R., Reiners, P. W., Ketcham, R. A., Nasdala, L., and Giester, G. (2013). Helium diffusion in natural zircon: Radiation damage, anisotropy, and the interpretation of zircon (U- Th)/He thermochronology. American Journal of Science, 313, 145–98.Google Scholar

Herman, F., Seward, D., Valla, P. G. et al. (2013). Worldwide acceleration of mountain erosion under a cooling climate. Nature, 504(7480), 423–6. https://doi.org/10.1038/nature12877.CrossRefGoogle Scholar

Higson, E., Hadnley, W., Hobson, M, and Lasenby, A. (2019). Dynamic nested sampling: An improved algorithm for parameter estimation and evidence calculation. Statistics and Computing, 29, 891–913Google Scholar

Jasra, A., Stephens, D. A., Gallagher, K., and Holmes, C. C. (2006). Analysis of geochronological data with measurement error using Bayesian mixtures, Mathematical Geology, 38(3), 269-300.Google Scholar

Ketcham, R. A. (2005). Forward and inverse modeling of low-temperature thermochronometry data. In Reiners, P. W. and Ehlers, T. A., eds., Reviews in Mineralogy and Geochemistry. Vol 58: Low-Temperature Thermochronology: Techniques, Interpretations and Applications. Chantilly, VA: Mineralogical Society of America, pp. 275–314.CrossRefGoogle Scholar

Ketcham, R. A., Carter, A., Donelick, R. A., Barbarand, J., and Hurford, A. J. (2007). Improved modeling of fission-track annealing in apatite. American Mineralogist, 92, 799–810.Google Scholar

Ketcham, R. A., Donelick, R. A., and Carlson, W. D. (1999). Variability of apatite fission-track annealing kinetics. III. Extrapolation to geological timescales. American Mineralogist, 84, 1235–55.Google Scholar

Ketcham, R. A., Guenthner, W. R., and Reiners, P. W. (2013). Geometric analysis of radiation damage connectivity in zircon, and its implications for helium diffusion. American Mineralogist, 98, 350–60CrossRefGoogle Scholar

Lartillot, N., and Philippe, H. (2006). Computing Bayes factors using thermodynamic integration. Systematic Biology, 55, 195–207.Google Scholar

Laslett, G. M., Green, P. F., Duddy, I. R., and Gleadow, A. J. W. (1987). Thermal annealing of fission tracks, 2. A quantitative analysis. Chemical Geology: Isotope Geoscience Section, 65, 1–13.Google Scholar

Li, W., Wang, L., Lang, M., Trautmann, C., and Ewing, R. C. (2011). Thermal annealing mechanisms of latent fission tracks: Apatite vs. zircon. Earth and Planetary Science Letters, 203, 227–35.Google Scholar

Licciardi, A., Gallagher, K., and Clark, S. A. (2020). A Bayesian approach for thermal history reconstruction in basin modelling, Journal of Geophysical Research: Solid Earth, 125(7), e2020JB019384. https://doi.org/10.1029/2020JB019384.Google Scholar

Liu, P., Elshall, A. S., Ye, M. et al. (2016). Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods. Water Resources Research, 52(2), 734–58. https://doi.org/10.1002/2014WR016718.Google Scholar

Lovera, O. M., Richter, F. M, and Harrison, T. M. (1989). 40Ar/39Ar geothermometry for slowly cooled samples having a distribution of domain sizes. Journal of Geophysical Research, 94, 17917–35.Google Scholar

Malusa, M., and Fitzgerald, P. F. (2019). Fission-Track Thermochronology and its Application to Geology, Springer Textbooks in Earth Sciences. Cham: Springer International Publishing.Google Scholar

McDannell, K. T., and Issler, D. R. (2021). Simulating sedimentary burial cycles. Part 1: Investigating the role of apatite fission track annealing kinetics using synthetic data. Geochronology, 3, 321–35. https://doi.org/10.5194/gchron-3-321-2021.CrossRefGoogle Scholar

McDougall, I., and Harrison, T. M. (1988). Geochronology and Thermochronology by the 40Ar/39Ar method, 2nd ed. New York: Oxford University Press.Google Scholar

Meesters, A. G., and Dunai, T. J (2002a). Solving the production-diffusion equation for finite diffusion domains of various shapes. Part I: Implications for low-temperature (U-Th)/He-thermochronology. Chemical Geology, 186, 333–44Google Scholar

Meesters, A. G., and Dunai, T. J. (2002b). Solving the production-diffusion equation for finite diffusion domains of various shapes. Part II: Application to cases with -ejection and non-homogenous distribution of the source. Chemical Geology, 186, 347–63Google Scholar

Pooley, C. M., and Marion, G. (2018). Bayesian model evidence as a practical alternative to deviance information criterion. Royal Society Open Science, 5(3), 171519. http://dx.doi.org/10.1098/rsos.171519.Google Scholar

Recanati, A., Gautheron, C., Barbarand, J. et al. (2017). Helium trapping in apatite damage: Insights from (U-Th-Sm)/He dating of different granitoid lithologies. Chemical Geology 470, 116–31Google Scholar

Reiners, P. W., Carlson, R.W., Renne, P.R. et al. (2018). Geochronology and Thermochronology. Hoboken, NJ: Wiley.Google Scholar

Reiners, P. W., and Ehlers, T. A., eds. (2005). Reviews in Mineralogy and Geochemistry. Vol. 58: Low-Temperature Thermochronology: Techniques, Interpretations and Applications. Chantilly, VA: Mineralogical Society of America.Google Scholar

Richardson, S., and Green, P. J. (1997). On Bayesian analysis of mixture models with an unknown number of components. Journal of the Royal Statistical Society Series B, 59(4), 731–92.Google Scholar

Richardson, S., Leblond, L., Jaussent, I., and Green, P. J. (2002). Mixture models in measurement error problems, with reference to epidemiological studies. Journal of the Royal Statistical Society Series A, 165(3), 549–66.Google Scholar

Sambridge, M. (2014). A parallel tempering algorithm for probabilistic sampling and multimodal optimization. Geophysical Journal International, 196, 357–74. https://doi.org/10.1093/gji/ggt342.Google Scholar

Sambridge, M. S., and Compston, W. (1994). Mixture modelling of multi-component data sets with application to ion-probe zircon ages. Earth Planetary Science Letters, 128, 373–90.CrossRefGoogle Scholar

Sambridge, M., Gallagher, K., Jackson, A., and Rickwood, P. (2006). Trans-dimensional inverse problems, Model Comparison and the Evidence. Geophysical Journal International, 167, 528–42.Google Scholar

Schildgen, T. F., van der Beek, P. A., Sinclair, H. D., and Thiede, R. C. (2018). Spatial correlation bias in late-Cenozoic erosion histories derived from thermochronology. Nature, 559(7712), 89–93. https://doi.org/10.1038/s41586-018-0260-6.Google Scholar

Schoene, B. (2014). U-Th-Pb Geochronology. In Holland, H. D. and Turekian, K. K., eds., Treatise on Geochemistry, 2nd ed. Amsterdam: Elsevier, pp. 341–78.Google Scholar

Shuster, D. L, Flowers, R. M., and Farley, K. A. (2006). The influence of natural radiation damage on helium diffusion kinetics in apatite. Earth and Planetary Science Letters. https://doi.org/10.1016/J.EPSL.2006.07.028.CrossRefGoogle Scholar

Stephenson, J., Gallagher, K., and Holmes, C. (2006). Low temperature thermochronology and modelling strategies for multiple samples 2: Partition modeling for 2D and 3D distributions with discontinuities. Earth and Planetary Science Letters, 241, 557–70.Google Scholar

Tagami, T., Galbraith, R., Yamada, R., and Laslett, G. (1998). Revised annealing kinetics of fission tracks in zircon and geological implications. In Van den Haute, P. and De Corte, F., eds., Advances in Fission-Track Geochronology. Dordrecht: Kluwer, pp. 99–112.Google Scholar

Titterington, D. M., Smith, A. F. M., and Makov, H. E. (1985). Statistical Analysis of Finite Mixture Distributions. Chichester: Wiley.Google Scholar

Trotta, R. (2008). Bayes in the sky: Bayesian inference and model selection in cosmology. Contemporary Physics, 49, 71–104Google Scholar

Willett, C. D., Fox, M., and Shuster, D.L. (2017). A helium-based model for the effects of radiation damage annealing on helium diffusion kinetics in apatite. Earth Planetary Science Letters, 477, 195–204Google Scholar

Willett, S. D., Herman, F., Fox, M. et al. (2021). Bias and error in modelling thermochronometric data: Resolving a potential increase in Plio-Pleistocene erosion rate. Earth Surface Dynamics, 9, 1153–221. https://doi.org/10.5194/esurf-9-1153-2021.Google Scholar

Yamada, R., Murakami, M., and Tagami, T. (2007). Statistical modelling of annealing kinetics of fission tracks in zircon; Reassessment of laboratory experiments. Chemical Geology 236, 75–91.Google Scholar

Branca, S., De Beni, E., and Proietti, C. (2013). The large and destructive 1669 AD eruption at Etna volcano: Reconstruction of the lava flow field evolution and effusion rate trend. Bulletin of Volcanology, 75, 694. https://doi.org/10.1007/s00445-013-0694-5.CrossRefGoogle Scholar

Bryant, E. (2005). Natural Hazards. Cambridge: Cambridge University Press.Google Scholar

Buttner, R., Zimanowski, B., Blumm, J., and Hagemann, L. (1998). Thermal conductivity of a volcanic rock material (olivine-melilinite) in the temperature range between 288 and 1470 K. Journal of Volcanology and Geothermal Research, 80, 293–302.CrossRefGoogle Scholar

Calder, E. S., Lavallée, Y., Kendrick, J. E., and Bernstein, M. (2015). Lava dome eruptions. In Sigurdsson, H., Houghton, B, Rymer, H, Stix, J, and McNutt, S, eds., Encyclopedia of Volcanoes, 2nd ed. San Diego, CA: Academic Press, pp. 343–62.CrossRefGoogle Scholar

Calvari, S., Spampinato, L., Lodato, L. et al. (2005). Chronology and complex volcanic processes during the 2002–2003 flank eruption at Stromboli volcano (Italy) reconstructed from direct observations and surveys with a handheld thermal camera. Journal of Geophysical Research, 110, B02201. https://doi.org/10.1029/2004JB003129.Google Scholar

Castruccio, A., and Contreras, M. A. (2016). The influence of effusion rate and rheology on lava flow dynamics and morphology: A case study from the 1971 and 1988–1990 eruptions at Villarrica and Lonquimay volcanoes, Southern Andes of Chile. Journal of Volcanology and Geothermal Research, 327, 469–83.Google Scholar

Chandrasekhar, S. (1961). Hydrodynamic and Hydromagnetic Stability. Oxford: Oxford University Press.Google Scholar

Chevrel, M. O., Platz, T., Hauber, E., Baratoux, D., Lavallée, Y., and Dingwell, D. B. (2013). Lava flow rheology: A comparison of morphological and petrological methods. Earth and Planetary Science Letters, 384, 109–20.Google Scholar

Christensen, U. R. (1992). An Eulerian technique for thermomechanical modeling of lithospheric extension. Journal of Geophysical Research, 97, 2015–36.Google Scholar

Cordonnier, B., Lev, E., and Garel, F. (2015). Benchmarking lava-flow models. In Harris, A. J. L., De Groeve, T., Garel, F., and Carn, S. A., eds., Detecting, Modelling and Responding to Effusive Eruptions, Special Publications, 426. London: Geological Society, pp. 425–45.Google Scholar

Costa, A., and Macedonio, G. (2005). Computational modeling of lava flows: A review. In Manga, M. and Ventura, G., eds., Kinematics and Dynamics of Lava Flows, Special Paper 396, Boulder, CO: Geological Society of America, pp. 209–18.Google Scholar

Costa, A., Caricchi, L., and Bagdassarov, N. (2009). A model for the rheology of particle-bearing suspensions and partially molten rocks. Geochemistry, Geophysics, Geosystems, 10, Q03010. https://doi.org/10.1029/2008Gc002138.Google Scholar

Cutter, S., Ismail-Zadeh, A., Alcántara-Ayala, I. et al. (2015). Global risk: Pool knowledge to stem losses from disasters. Nature, 522, 277–9.Google Scholar

Daag, A. S., Dolan, M. T., Laguerta, E. et al. (1996). Growth of a postclimactic lava dome at Pinatubo Volcano, July‒October 1992. In Newhall, C. and Punongbayan, R., eds., Fire and Mud: Eruptions and Lahars of Mount Pinatubo, Philippines. Seattle: University of Washington Press, pp. 647–64.Google Scholar

Dragoni, M. A. (1989). A dynamical model of lava flows cooling by radiation. Bulletin of Volcanology, 51, 88–95.Google Scholar

Flynn, L. P., Harris, A. J. L., and Wright, R. (2001). Improved identification of volcanic features using Landsat 7 ETM+. Remote Sensing of Environment, 78, 180–93.Google Scholar

Giordano, D., and Dingwell, D. B. (2003). Viscosity of hydrous Etna basalt: Implications for Plinian-style basaltic eruptions. Bulletin of Volcanology, 65, 8–14.Google Scholar

Griffiths, R. W. (2000). The dynamics of lava flows. Annual Review of Fluid Mechanics, 32, 477–518.Google Scholar

Harris, A. J. L., Flynn, L. P., Keszthelyi, L. et al. (1998). Calculation of lava effusion rates from Landsat TM data. Bulletin of Volcanology, 60, 52–71.Google Scholar

Harris, A. J. L., Flynn, L. P., Matias, O., Rose, W. I., and Cornejo, J. (2004). The evolution of an active silicic lava flow field: An ETM+ perspective. Journal of Volcanology and Geothermal Research, 135, 147–68.Google Scholar

Harris, A. J. L., Rose, W. I., and Flynn, L. P. (2003). Temporal trends in lava dome extrusion at Santiaguito 1922–2000. Bulletin of Volcanology, 65, 77–89.Google Scholar

Heap, M. J., Troll, V., Kushnir, A. R. L. et al. (2019). Hydrothermal alteration of andesitic lava domes can lead to explosive volcanic behaviour. Nature Communications, 10, 5063. https://doi.org/10.1038/s41467-019-13102-8.Google Scholar

Hidaka, M., Goto, A., Umino, S., and Fujita, E. (2005). VTFS project: Development of the lava flow simulation code LavaSIM with a model for three-dimensional convection, spreading, and solidification. Geochemistry, Geophysics, Geosystems, 6, Q07008. https://doi.org/10.1029/2004GC000869.Google Scholar

Ismail-Zadeh, A., and Tackley, P. (2010). Computational Methods for Geodynamics. Cambridge: Cambridge University Press.Google Scholar

Ismail-Zadeh, A., and Takeuchi, K. (2007). Preventive disaster management of extreme natural events. Natural Hazards, 42, 459–67.Google Scholar

Ismail-Zadeh, A., Korotkii, A., Schubert, G., and Tsepelev, I. (2007). Quasi-reversibility method for data assimilation in models of mantle dynamics. Geophysical Journal International, 170, 1381–98.Google Scholar

Ismail-Zadeh, A., Korotkii, A., and Tsepelev, I. (2016). Data-Driven Numerical Modeling in Geodynamics: Methods and Applications. Heidelberg: Springer.Google Scholar

Jeffrey, D., and Acrivos, A. (1976). The rheological properties of suspensions of rigid particles. AIChE Journal, 22, 417–32.Google Scholar

Kabanikhin, S. I. (2011). Inverse and Ill-Posed Problems: Theory and Applications. Berlin: De Gruyter.Google Scholar

Kelfoun, K., and Vargas, S. V. (2015). VolcFlow capabilities and potential development for the simulation of lava flows. In Harris, A. J. L., De Groeve, T., Farel, F., and Carn, S. A., eds., Detecting, Modelling and Responding to Effusive Eruptions, Special Publications 426. London: Geological Society, pp. 337–43.Google Scholar

Kelfoun, K., Santoso, A. B., Latchimy, T. et al. (2021). Growth and collapse of the 2018–2019 lava dome of Merapi volcano. Bulletin of Volcanology, 83, 8. https://doi.org/10.1007/s00445-020-01428-x.Google Scholar

Kilburn, C. R. J. (2000). Lava flow and flow fields. In Sigurdsson, H., ed., Encyclopedia of Volcanoes. San Diego, CA: Academic Press, pp.291–305.Google Scholar

Korotkii, A. I., and Kovtunov, D. A. (2006). Reconstruction of boundary regimes in an inverse problem of thermal convection of a high viscous fluid. Proceedings of the Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 12(2), 88–97.Google Scholar

Korotkii, A. I., and Starodubtseva, Y. V. (2014). Direct and inverse problems for models of stationary reactive-convective-diffusive flow. Proceedings of the Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 20(3), 98–113.Google Scholar

Korotkii, A., Kovtunov, D., Ismail-Zadeh, A., Tsepelev, I., and Melnik, O. (2016). Quantitative reconstruction of thermal and dynamic characteristics of lava from surface thermal measurements. Geophysical Journal International, 205, 1767–79.Google Scholar

Ladyzhenskaya, O. A. (1969). The Mathematical Theory of Viscous Incompressible Flow. New York: Gordon and Breach.Google Scholar

Lavallée, Y., Varley, N. R., Alatorre-Ibarguengoitia, M. A. et al. (2012). Magmatic architecture of dome building eruptions at Volcán de Colima, Mexico. Bulletin of Volcanology, 74, 249–60.Google Scholar

Lejeune, A., and Richet, P. (1995). Rheology of crystal-bearing silicate melts: An experimental study at high viscosity. Journal of Geophysical Research, 100, 4215–29.Google Scholar

Lions, J. L. (1971). Optimal Control of Systems Governed by Partial Differential Equations. Berlin: Springer.Google Scholar

Lombardo, V., Musacchio, M., and Buongiorno, M. F. (2012). Error analysis of subpixel lava temperature measurements using infrared remotely sensed data. Geophysical Journal International, 191, 112–25.Google Scholar

Loughlin, S. C., Sparks, S., Brown, S. K., Jenkins, S. F., and Vye-Brown, C., eds. (2015). Global Volcanic Hazards and Risk. Cambridge: Cambridge University Press.Google Scholar

Mardles, E. (1940). Viscosity of suspensions and the Einstein equation. Nature, 145, 970. https://doi.org/10.1038/145970a0.Google Scholar

Marsh, B. D. (1981). On the crystallinity, probability of occurrence, and rheology of lava and magma. Contributions to Mineralogy and Petrology, 78, 85–98.Google Scholar

Melnik, O., and Sparks, R. S. J. (1999). Nonlinear dynamics of lava dome extrusion. Nature, 402, 37–41.Google Scholar

Naimark, B. M., and Ismail-Zadeh, A. T. (1995). Numerical models of subsidence mechanism in intracratonic basin: Application to North American basins. Geophysical Journal International, 123, 149–60.Google Scholar

Naimark, B. M., Ismail-Zadeh, A. T., and Jacoby, W. R. (1998). Numerical approach to problems of gravitational instability of geostructures with advected material boundaries. Geophysical Journal International, 134, 473–83.Google Scholar

Nakada, S., Shimizu, H., and Ohta, K. (1999). Overview of the 1990‒1995 eruption at Unzen Volcano. Journal of Volcanology and Geothermal Research, 89, 1–22.Google Scholar

Nakada, S., Zaennudin, A., Yoshimoto, M. et al. (2019). Growth process of the lava dome/flow complex at Sinabung volcano during 2013‒2016. Journal of Volcanology and Geothermal Research, 382, 120–36.Google Scholar

Navon, I. M., Zou, X., Derber, J. and Sela, J. (1992). Variational data assimilation with an adiabatic version of the NMC spectral model. Monthly Weather Review, 120, 1433–46.Google Scholar

Papale, P., ed. (2014). Volcanic Hazards, Risks and Disasters. Amsterdam: Elsevier.Google Scholar

Patankar, S. V., and Spalding, D. B. (1972). A calculation procedure for heat and mass transfer in three-dimensional parabolic flows. International Journal of Heat and Mass Transfer, 15, 1787–806.Google Scholar

Poland, M. P., and Anderson, K. R. (2020). Partly cloudy with a chance of lava flows: Forecasting volcanic eruptions in the twenty‐first century. Journal of Geophysical Research, 125, e2018JB016974. https://doi.org/10.1029/2018JB016974.Google Scholar

Polak, E., and Ribière, G. (1969). Note on the convergence of methods of conjugate directions. Revue Francaise d’Informatique et de Recherche Operationnelle, 3(16), 35–43.Google Scholar

Rumpf, M. E., Lev, E. and Wysocki, R. (2018). The influence of topographic roughness on lava flow emplacement. Bulletin of Volcanology, 80, 63. https://doi.org/10.1007/s00445-018-1238-9.Google Scholar

Salomon, D. (2007). Data Compression: The Complete Reference. London: Springer.Google Scholar

Sheldrake, T. E., Sparks, R. S. J., Cashman, K. V., Wadge, G., and Aspinall, W. P. (2016). Similarities and differences in the historical records of lava dome-building volcanoes: Implications for understanding magmatic processes and eruption forecasting. Earth-Science Reviews, 160, 240–63.Google Scholar

Short, N. M., and Stuart, L. M. (1983). The Heat Capacity Mapping Mission (HCMM) Anthology. Washington, DC: NASA Scientific and Technical Information Branch.Google Scholar

Starodubtseva, Y., Starodubtsev, I., Ismail-Zadeh, A. et al. (2021). A method for magma viscosity assessment by lava dome morphology. Journal of Volcanology and Seismology, 15, 159–68. https://doi.org/10.1134/S0742046321030064.Google Scholar

Swanson, D. A., Dzurisin, D., Holcomb, R. T. et al. (1987). Growth of the lava dome at Mount St Helens, Washington, (USA) 1981‒1983. In Fink, J. H., ed., The Emplacement of Silicic Domes and Lava Flows, Special Paper 212. Boulder, CO: Geological Society of America, pp. 1–16.Google Scholar

Takeuchi, S. (2011). Preeruptive magma viscosity: An important measure of magma eruptibility. Journal of Geophysical Research, 116, B10201. https://doi.org/10.1029/2011JB008243.Google Scholar

Temam, R. (1977). Navier–Stokes Equations: Theory and Numerical Analysis. Amsterdam: North-Holland.Google Scholar

Tikhonov, A. N. (1963). Solution of incorrectly formulated problems and the regularization method, Soviet Mathematics Doklady 4, 1035–8.Google Scholar

Tikhonov, A. N., and Arsenin, V. Y. (1977). Solution of Ill-Posed Problems. Washington, DC: Winston.Google Scholar

Tikhonov, A. N., and Samarskii, A. A. (1990). Equations of Mathematical Physics. New York: Dover Publications.Google Scholar

Tsepelev, I., Ismail-Zadeh, A., Melnik, O., and Korotkii, A. (2016). Numerical modelling of fluid flow with rafts: An application to lava flows. Journal of Geodynamics, 97, 31–41.Google Scholar

Tsepelev, I., Ismail-Zadeh, A., Starodubtseva, Y., Korotkii, A., and Melnik, O. (2019). Crust development inferred from numerical models of lava flow and its surface thermal measurements. Annals of Geophysics, 62(2), VO226. https://doi.org/10.4401/ag-7745.Google Scholar

Tsepelev, I., Ismail-Zadeh, A., and Melnik, O. (2020). Lava dome morphology inferred from numerical modelling. Geophysical Journal International, 223(3), 1597–609.Google Scholar

Tsepelev, I., Ismail-Zadeh, A., and Melnik, O. (2021). Lava dome evolution at Volcán de Colima, México during 2013: Insights from numerical modeling. Journal of Volcanology and Seismology, 15, 491–501. https://doi.org/10.1134/S0742046321060117.Google Scholar

Turcotte, D. L., and Schubert, G. (2002). Geodynamics, 2nd ed. Cambridge: Cambridge University Press.Google Scholar

Voight, B., and Elsworth, D. (2000). Instability and collapse of hazardous gas-pressurized lava domes. Geophysical Research Letters, 27(1), 1–4.Google Scholar

Wadge, G., Robertson, R. E. A., and Voight, B., eds. (2014). The Eruption of Soufrière Hills Volcano, Montserrat, from 2000 to 2010. GSL Memoirs, vol. 39. London: Geological Society. https://doi.org/10.1144/M39.Google Scholar

Wang, Z., Bovik, A. C., Sheikh, H. R., and Simoncelli, E. P. (2004). Image quality assessment: From error visibility to structural similarity. IEEE Transactions on Image Processing, 13(4), 600–12.Google Scholar

Walker, G. P. L. (1973). Lengths of lava flows. Philosophical Transactions of the Royal Society, 274, 107–18.Google Scholar

Watts, R. B., Herd, R. A., Sparks, R. S. J., and Young, S. R. (2002). Growth patterns and emplacement of the andesitic lava dome at Soufrière Hills Volcano, Montserrat. In Druitt, T. H., and Kokelaar, B. P., eds., The Eruption of Soufrière Hills Volcano, Montserrat, from 1995 to 1999. GLS Memoirs, vol. 21. London: Geological Society, pp. 115–52.Google Scholar

Wright, R., Garbeil, H., and Davies, A. G. (2010). Cooling rate of some active lavas determined using an orbital imaging spectrometer. Journal of Geophysical Research, 115, B06205. https://doi.org/10.1029/2009JB006536.Google Scholar

Wright, T. L., and Okamura, R. T. (1977). Cooling and crystallization of tholeiitic basalt, 1965 Makaopuhi lava lake, Hawaii. US Geological Survey Professional Paper 1004.Google Scholar

Zakšek, K., Hort, M., and Lorenz, E. (2015). Satellite and ground based thermal observation of the 2014 effusive eruption at Stromboli volcano. Remote Sensing, 7, 17190–211.Google Scholar

Zeinalova, N., Ismail-Zadeh, A., Melnik, O. E., Tsepelev, I., and Zobin, V. M. (2021). Lava dome morphology and viscosity inferred from data-driven numerical modeling of dome growth at Volcán de Colima, Mexico during 2007–2009. Frontiers in Earth Science, 9, 735914. https://doi.org/10.3389/feart.2021.735914.Google Scholar

Zobin, V. M., Arámbula, R., Bretón, M. et al. (2015). Dynamics of the January 2013–June 2014 explosive-effusive episode in the eruption of Volcán de Colima, México: Insights from seismic and video monitoring. Bulletin of Volcanology, 77, 31. https://doi.org/10.1007/s00445-015-0917-z.Google Scholar

Asano, K., and Iwata, T. (2012). Source model for strong ground motion generation in the frequency range 0.1–10 Hz during the 2011 Tohoku earthquake. Earth Planets Space, 64, 1111–23. https://doi.org/10.5047/eps.2012.05.003.Google Scholar

Awaji, T., Kamachi, M., Ikeda, M., and Ishikawa, Y. (2009). Data Assimilation: Innovation Combining Observation and Model (in Japanese). Kyoto: Kyoto University Press.Google Scholar

Böse, M., Smith, D. E., Felizardo, C. et al. (2018). FinDer v.2: Improved real-time ground-motion predictions forM2–M9 with seismic finite-source characterization. Geophysical Journal International, 212, 725–42. https://doi.org/10.1093/gji/ggx430.Google Scholar

Chen, D. Y., Hsiao, N. C., and Wu, Y. M. (2015). The earthworm-based earthquake alarm reporting system in Taiwan. Bulletin of the Seismological Society of America, 105, 568–79. https://doi.org/10.1785/0120140147.Google Scholar

Cochran, E. S., Bunn, J., Minson, S. E. et al. (2019). Event detection performance of the PLUM earthquake early warning algorithm in southern California. Bulletin of the Seismological Society of America, 109, 1524–41. https://doi.org/10.1785/0120180326.Google Scholar

Cuellar, A., Espinosa-Aranda, J. M., Suárez, G. (2014). The Mexican Seismic Alert System (SASMEX): Its alert signals, broadcast results and performance during the M 7.4 Punta Maldonado earthquake of March 20th, 2012. In Wenzel, F. and Zschau, J., eds., Early Warning for Geological Disasters. Berlin: Springer, pp. 71–87.Google Scholar

Erdik, M., Fahjan, Y., Ozel, O. et al. (2003). Istanbul earthquake rapid response and the early warning system, Bulletin of Earthquake Engineering, 1, 157–63. https://doi.org/10.1023/A:1024813612271.Google Scholar

Furumura, T., and Maeda, T. (2021). High-resolution source imaging based on time-reversal wave propagation simulations using assimilated dense seismic records. Geophysical Journal International, 225, 140–57. https://doi.org/10.1093/gji/ggaa586.Google Scholar

Furumura, T., Maeda, T., and Oba, A. (2019). Early forecast of long‐period ground motions via data assimilation of observed ground motions and wave propagation simulations. Geophysical Research Letters, 46(1), 139–47. https://doi.org/10.1029/2018GL081163.Google Scholar

Gasparini, P., and Manfredi, G. (2014). Development of earthquake early warning systems in the European Union. In Zschau, J. and Wenzel, F., eds., Early Warning for Geological Disasters: Scientific Methods and Current Practice, Berlin: Springer, pp. 89–101. https://doi.org/10.1007/978-3-642-12233-0_5.Google Scholar

Gusev, A. A., and Abubakirov, I. R. (1987). Monte-Carlo simulation of record envelope of a near earthquake. Physics of the Earth and Planetary Interiors, 49, 30–6.Google Scholar

Hoshiba, M. (1991). Simulation of multiple scattered coda wave excitation based on the energy conservation law. Physics of the Earth and Planetary Interiors, 67, 123–6.Google Scholar

Hoshiba, M. (2013a). Real-time prediction of ground motion by Kirchhoff–Fresnel boundary integral equation method: Extended front detection method for earthquake early warning. Journal of Geophysical Research: Solid Earth, 118, 1038–50. https://doi.org/10.1002/jgrb.50119.Google Scholar

Hoshiba, M. (2013b). Real-time correction of frequency-dependent site amplification factors for application to earthquake early warning. Bulletin of the Seismological Society of America, 103, 3179–88. https://doi.org/10.1785/0120130060.Google Scholar

Hoshiba, M. (2020). Too-late warnings by estimating Mw: earthquake early warning in the near-fault region. Bulletin of the Seismological Society of America, 110, 1276–88. https://doi.org/10.1785/0120190306.Google Scholar

Hoshiba, M. (2021), Real-time prediction of impending ground shaking: Review of wavefield-based (ground-motion-based) method for earthquake early warning. Frontier in Earth Sciences, 22. https://doi.org/10.3389/feart.2021.722784.Google Scholar

Hoshiba, M., and Aoki, S. (2015). Numerical shake prediction for earthquake early warning: Data assimilation, real‐time shake mapping, and simulation of wave propagation. Bulletin of the Seismological Society of America, 105, 1324–38. https://doi.org/10.1785/0120140280.Google Scholar

Hoshiba, M., and Ozaki, T. (2014). Earthquake early warning and tsunami warning of the Japan Meteorological Agency, and their performance in the 2011 off the Pacific Coast of Tohoku Earthquake (Mw9.0). In Wenzel, F. and Zschau, J., eds., Early Warning for Geological Disasters: Scientific Methods and Current Practice. Berlin: Springer, pp. 1–28. https://doi.org/10.1007/978-3-642-12233-0_1.Google Scholar

Hoshiba, M., Iwakiri, K., Hayashimoto, N. et al. (2011). Outline of the 2011 off the Pacific Coast of Tohoku Earthquake (Mw 9.0): Earthquake Early Warning and observed seismic intensity. Earth Planets Space, 63, 547–51. https://doi.org/10.5047/eps.2011.05.031.Google Scholar

Hoshiba, M., Kamigaichi, O., Saito, M., Tsukada, S. Y., and Hamada, N. (2008). Earthquake early warning starts nationwide in Japan. Eos, Transactions, American Geophysical Union, 89, 73–4. https://doi.org/10.1029/2008EO080001.Google Scholar

Japan Meteorological Agency. (2012). Report of the 2011 off the Pacific Coast of Tohoku earthquake by Japan Meteorological Agency (in Japanese), Japan Meteorological Agency.Google Scholar

Kalnay, E. (2003). Atmospheric Modeling, Data Assimilation and Predictability. Cambridge: Cambridge University Press.Google Scholar

Kurahashi, S. and Irikura, K. (2013). Short-period source model of the 2011 Mw 9.0 Off the Pacific Coast of Tohoku earthquake. Bulletin of the Seismological Society of America, 103, 1373–93. https://doi.org/10.1785/0120120157.Google Scholar

Kurzon, I., Nof, R. N., Laporte, M. et al. (2020). The ‘TRUAA’ seismic network: Upgrading the Israel seismic network – Toward national earthquake early warning system. Seismological Research Letters, 91, 3236–3255. https://doi.org/10.1785/0220200169.Google Scholar

Oba, A., Furumura, T., and Maeda, T. (2020). Data assimilation‐based early forecasting of long‐period ground motions for large earthquakes along the Nankai Trough. Journal of Geophysical Research: Solid Earth, 125(6), e2019JB019047. https://doi.org/10.1029/2019JB019047.Google Scholar

Ogiso, M., Aoki, S., and Hoshiba, M. (2016). Real-time seismic intensity prediction using frequency-dependent site amplification factors. Earth Planets Space 68, 83. https://doi.org/10.1186/s40623-016-0467-4.Google Scholar

Ogiso, M., Hoshiba, M., Shito, A., and Matsumoto, S.(2018). Numerical shake prediction for earthquake early warning incorporating heterogeneous attenuation structure: The case of the 2016 Kumamoto earthquake. Bulletin of the Seismological Society of America, 108, 3457–68. https://doi.org/10.1785/0120180063.Google Scholar

Peng, H., Wu, Z., Wu, Y. M. et al. (2011). Developing a prototype earthquake early warning system in the Beijing Capital Region. Seismological Research Letters, 82, 394–403. https://doi.org/10.1785/gssrl.82.3.394.Google Scholar

Sato, H., Fehler, M. C., and Maeda, T. (2012). Seismic Wave Propagation and Scattering in the Heterogeneous Earth, 2nd ed. Berlin: Springer. https://doi.org/10.1007/978-3-642-23029-5.Google Scholar

Sheen, D. H., Park, J. H., Chi, H. C. et al. (2017). The first stage of an earthquake early warning system in South Korea. Seismological Research Letters, 88, 1491–98. https://doi.org/10.1785/0220170062Google Scholar

Suzuki, W., Aoi, S., Kunugi, T. et al. (2017). Strong motions observed by K-NET and KiK-net during the 2016 Kumamoto earthquake sequence. Earth Planets Space, 69, 19. https://doi.org/10.1186/s40623-017-0604-8.Google Scholar

Tamaribuchi, K., Yamada, M., and Wu, S. (2014). A new approach to identify multiple concurrent events for improvements of earthquake early warning. Zisin, 67(2), 41–55. https://doi.org/10.4294/zisin67.41 (in Japanese with English abstract).Google Scholar

Wald, D. J., Worden, B. C., Quitoriano, V., and Pankow, K. L. (2005). ShakeMap manual: Technical manual, user’s guide, and software guide, Techniques and Methods 12-A1. https://doi.org/10.3133/tm12A1.Google Scholar

Wang, T., Jin, X., Wei, Y. and Huang, Y. (2017a). Real-time numerical shake prediction and updating for earthquake early warning. Earthquake Science, 30, 251–67. https://doi.org/10.1007/s11589-017-0195-2Google Scholar

Wang, T., Jin, X., Huang, Y. and Wei, Y. (2017b). Real-time three-dimensional space numerical shake prediction for earthquake early warning. Earthquake Science, 30, 269–81. https://doi.org/10.1007/s11589-017-0196-1.Google Scholar

Wessel, P., and Smith, W. H. F. (1995). New version of the generic mapping tool released. Eos, Transactions, American Geophysical Union, 76, 329.Google Scholar

Yoshimoto, K. (2000). Monte Carlo simulation of seismogram envelopes in scattering medium. Journal of Geophysical Research: Solid Earth, 105, 6153–61. https://doi.org/10.1029/1999JB900437.Google Scholar

EEW: Earthquake early warning. Warning of strong shaking before its arrival.Google Scholar

GMPE: Ground-motion prediction equation. Strength of ground motion is empirically estimated from the equation, in which earthquake magnitude and distance (hypocentral distance, epicentral distance, or fault distance) are usually used.Google Scholar

JMA: Japan Meteorological Agency. A national governmental organization in Japan.Google Scholar

K-NET, KiK-net: Observation networks of strong ground motion operated by National Research Institute for Earth Science and Disaster Resilience (NIED) in Japan.Google Scholar

RTT: Radiative transfer theory. A model of wave propagation based on ray theoretical approach, in which scattering and attenuation are included.Google Scholar

Adourian, S., Lyu, C., Masson, Y., Munch, F., and Romanowicz, B. (2023). Combining different 3-D global and regional seismic wave propagation solvers towards box tomography in the deep Earth. Geophysical Journal International, 232(2), 1340–56.Google Scholar

Aki, K., Christofferson, A., and Husebye, E. S. (1977). Determination of the three-dimensional seismic structure of the lithosphere. Journal of Geophysical Research, 82, 277–96.Google Scholar

Al-Attar, D., Woodhouse, J. H., and Deuss, A. (2012). Calculation of normal mode spectra in laterally heterogeneous earth models using an iterative direct solution method. Geophysical Journal International, 189, 1038–46.Google Scholar

Backus, G. (1962). Long-wave elastic anisotropy produced by horizontal layering. Journal of Geophysical Research, 67(11), 4427–40.Google Scholar

Bassin, C., Laske, G., and Masters, G. (2000). The current limits of resolution for surface wave tomography in North America. EOS Transactions American Geophysical Union, 81, 1351–75.Google Scholar

Borgeaud, A. F. E., Kawai, K., and Geller, R. J. (2019). Three-dimensional S velocity structure of the mantle transition zone beneath Central America and the Gulf of Mexico inferred using waveform inversion. Journal of Geophysical Research: Solid Earth, 124, 9664–81.Google Scholar

Boschi, L., Becker, T. W., Soldati, G., and Dziewonski, A. M. (2006). On the relevance of Born theory in global seismic tomography. Geophysical Research Letters, 33, L06302.Google Scholar

Bozdag, E., and Trampert, J. (2008). On crustal corrections in surface wave tomography. Geophysical Journal International, 172, 1066–82.Google Scholar

Bozdag, E., Trampert, J., and Tromp, J. (2011). Misfit functions for full waveform inversion based on instantaneous phase and envelope measurements. Geophysical Journal International, 185, 845–70.Google Scholar

Bozdag, E., Peter, D., Lefebvre, M., et al. (2016). Global adjoint tomography: First generation model. Geophysical Journal International, 207(3), 1739–66.Google Scholar

Bozdag, E., Orsvuran, R., Ciardelli, C., Peter, D., and Wang, Y. (2021). Upper mantle anisotropy from global adjoint tomography. AGU Fall Meeting 2021, New Orleans, LA, 13–17 December 2021, abstract DI42A-08.Google Scholar

Capdeville, Y., and Marigo, J. J. (2007). Second order homogenization of the elastic wave equation for non-periodic layered media. Geophysical Journal International, 170, 823–38.Google Scholar

Capdeville, Y., Chaljub, E., Vilotte, J. P., and Montagner, J. P. (2003a). Coupling the spectral element method with a modal solution for elastic wave propagation in global Earth models. Geophysical Journal International, 152, 34–66.Google Scholar

Capdeville, Y., Gung, Y., and Romanowicz, B. (2005). Towards global Earth tomography using the spectral element method: A technique based on source stacking. Geophysical Journal International, 162, 541–54.Google Scholar

Capdeville, Y., To, A., and Romanowicz, B. A. (2003b). Coupling spectral elements and modes in a spherical Earth: An extension to the ‘sandwich’ case. Geophysical Journal International, 154, 44–57.Google Scholar

Chaljub, E., and Valette, B., B. (2004). Spectral element modelling of three-dimensional wave propagation in a self-gravitating Earth with an arbitrarily stratified outer core, Geophysical Journal International, 158, 131–41.Google Scholar

Chang, S.-J., Ferreira, A. M., Ritsema, J., van Heijst, H. J., and Woodhouse, J. H. (2014). Global radially anisotropic mantle structure from multiple datasets: a review, current challenges, and outlook. Tectonophysics, 617, 1–19.Google Scholar

Chen, P., Zhao, L., and Jordan, T. H. (2007). Full three-dimensional tomography: A comparison between the scattering-integral and adjoint-wavefield methods. Bulletin of the Seismological Society of America, 97, 1094–120.Google Scholar

Clévédé, E., and Lognonné, P. (1996). Fréchet derivatives of coupled seismograms with respect to an anelastic rotating Earth. Geophysical Journal International, 124, 456–82.Google Scholar

Clouzet, P., Masson, Y., and Romanowicz, B. (2018). Box tomography: First application to the imaging of upper mantle shear velocity and radial anisotropy structure beneath the North American continent. Geophysical Journal International, 213, 1849–75. doi: 10.1093/gji/ggy078Google Scholar

COSOD-II (1987). Report of the Second Conference on Scientific Ocean Drilling (Cosod II): Strasbourg, 6–8 July, 1987, Joint Oceanographic Institutions for Deep Earth Sampling. https://archives.eui.eu/en/fonds/476326?item=ESF-1224.Google Scholar

Cupillard, P., Delavaud, E., Burgos, G. et al. (2012). RegSEM: a versatile code based on the spectral element method to compute seismic wave propagation at the regional scale. Geophysical Journal International, 188, 1203–20.Google Scholar

Dahlen, F. A., Hung, S.-H., and Nolet, G. (2000). Fréchet kernels for finite-frequency traveltimes – I. Theory. Geophysical Journal International, 141, 157–74.Google Scholar

Davaille, A., and Romanowicz, B. (2020). Deflating the LLSVPs: Bundles of mantle thermochemical plumes, rather than thick ‘stagnant’ piles. Tectonics, 39, e2020TC006265. https://doi.org/10.1029/2020TC006265.Google Scholar

Durek, J. J., and Ekström, G. (1996). A radial model of anelasticity consistent with long-period surface-wave attenuation. Bulletin of the Seismological Society of America, 86, 144–58.Google Scholar

Dziewonski, A., and Anderson, D. (1981). Preliminary reference Earth model. Physics of the Earth and Planetary Interiors, 25, 297–356.Google Scholar

Dziewonski, A., Hager, B., and O’Connell, R. (1977). Large-scale heterogeneities in the lower mantle. Journal of Geophysical Research, 82, 239–55.Google Scholar

Efron, B., and Stein, C. (1981). The jackknife estimate of variance. Annals of Statistics, 9(3), 586–96.Google Scholar

Efron, B., and Tibishirani, R. J. (1991). An Introduction to the Bootstrap. Boca Raton, FL: Chapman and Hall.Google Scholar

Ferreira, A. M., Woodhouse, J. H., Visser, K., and Trampert, J. (2010). On the robustness of global radially anisotropic surface wave tomography. Journal of Geophysical Research, 115, B04313. https://doi.org/:10.1029/2009JB006716.Google Scholar

Fichtner, A. (2011). Full Seismic Waveform Modelling and Inversion. Cham: Springer.Google Scholar

Fichtner, A., and Igel, H. (2008). Efficient numerical surface wave propagation through the optimization of discrete crustal models: A technique based on non-linear dispersion curve matching (DCM). Geophysical Journal International, 173, 519–33.Google Scholar

Fichtner, A., and Trampert, J. (2011a). Hessian kernels of seismic data functionals based upon adjoint techniques. Geophysical Journal International, 185, 775–98.Google Scholar

Fichtner, A., and Trampert, J. (2011b). Resolution analysis in full waveform inversion. Geophysical Journal International, 187, 1604–24. https://doi.org/10.1111/j.1365-246X.2011.05218.x.Google Scholar

Fichtner, A., Kennett, B. L. N., Igel, H., and Bunge, H.-P. (2008). Theoretical background for continental- and global-scale full-waveform inversion in the time-frequency domain. Geophysical Journal International, 175, 665–85.Google Scholar

Fichtner, A., Kennett, B. L. N., Igel, H., and Bunge, H. P. (2009). Full seismic waveform tomography for upper-mantle structure in the Australasian region using adjoint methods. Geophysical Journal International, 179, 1703–25.Google Scholar

Fichtner, A., Kennett, B. L. N., Igel, H., and Bunge, H.-P. (2010). Full waveform tomography for radially anisotropic structure: New insights into present and past states of the Australasian upper mantle. Earth and Planetary Science Letters, 290, 270–80.Google Scholar

French, S., Lekic, V., and Romanowicz, B. (2013). Waveform tomography reveals channeled flow at the base of the oceanic asthenosphere. Science, 342, 227–30.Google Scholar

French, S. W. & Romanowicz, B. (2014). Whole-mantle radially anisotropic shear velocity structure from spectral-element waveform tomography. Geophysical Journal International, 199(3), 1303–27.Google Scholar

French, S. W., Zheng, Y., Romanowicz, B., and Yelick, K. (2015). Parallel Hessian assembly for Seismic Waveform inversion using Global updates, Proceedings of the 29th IEEE International Parallel and Distributed Processing Symposium (2015). https://doi.org/10.1109/IPDPS.2015.58.Google Scholar

Fukao, Y., and Obayashi, M. (2013). Subducted slabs stagnant above, penetrating through, and trapped below the 660 km discontinuity. Journal of Geophysical Research, 118(11), 5920–38.Google Scholar

Gharti, H. N., Tromp, J., and Zampini, S. (2018). Spectral-infinite-element simulations of gravity anomalies, Geophysical Journal International, 215, 1098–117. https://doi.org/10.1093/gji/ggy324.Google Scholar

Geller, R. J., and Ohminato, T (1994). Computation of synthetic seismograms and their partial derivatives for heterogeneous media with arbitrary natural boundary conditions using the direct solution method. Geophysical Journal International, 116, 421–46.Google Scholar

Gung, Y., and Romanowicz, B. (2004). Q tomography of the upper mantle using three-component long-period waveforms. Geophysical Journal International, 157(2), 813–30.Google Scholar

Gung, Y., Panning, M., and Romanowicz, B. (2003). Global anisotropy and the thickness of continents. Nature, 422(6933), 707–11.Google Scholar

Hello, Y., Ogé, A. Sukhovich, , A., and Nolet, G. (2011). Modern mermaids: New floats image the Deep Earth. EOS Transactions American Geophysical Union, 92, 337–48.Google Scholar

Houser, C., Masters, G., Shearer, P., and Laske, G. (2008). Shear and compressional velocity models of the mantle from cluster analysis of long period waveforms. Geophysical Journal International, 174, 195–212.Google Scholar

Karaoglu, H., and Romanowicz, B. (2017). Global seismic attenuation imaging using full-waveform inversion: a comparative assessment of different choices of misfit functionals. Geophysical Journal International, 212, 807–26.Google Scholar

Karaoglu, H., and Romanowicz, B. (2018). Inferring global upper-mantle shear attenuation structure by waveform tomography using the spectral element method. Geophysical Journal International, 213, 1536–58.Google Scholar

Kawai, K., Konishi, K., Geller, R. J., and Fuji, N. (2014). Methods for inversion of body‐wave waveforms for localized three‐dimensional seismic structure and an application to D″ structure beneath Central America. Geophysical Journal International, 197(1), 495–524. https://doi.org/10.1093/gji/ggt520.Google Scholar

Komatitsch, D., and Tromp, J. (2002a). Spectral-element simulations of global seismic wave propagation – I. Validation. Geophysical Journal International, 149, 390–412.Google Scholar

Komatitsch, D., and Tromp, J. (2002b). Spectral-element simulations of global seismic wave propagation – II. Three-dimensional models, oceans, rotation and self-gravitation. Geophysical Journal International, 150, 303–18.Google Scholar

Komatitsch, D., and Vilotte, J. P. (1998).The spectral element method: an efficient tool to simulate the seismic response of 2D and 3D geological structures. Bulletin of the Seismological Society of America, 88, 368–92.Google Scholar

Koroni, M., and Trampert, J. (2021). Imaging global mantle discontinuities: a test using full-waveforms and adjoint kernels. Geophysical Journal International, 226, 1498–15.Google Scholar

Krebs, J., Anderson, J., Hinkley, D. et al. (2009). Fast full-wavefield seismic inversion using encoded sources. Geophysics, 74, WCC177–WCC188.Google Scholar

Kustowski, B., Ekström, G., and Dziewonski, A.M. (2008). Anisotropic shear-wave velocity structure of the Earth’s mantle: A global model. Journal of Geophysical Research: Solid Earth, 113(B6), 2156–202.Google Scholar

Laske, G., Collins, J. A., Wolfe, C. J. et al. (2009). Probing the Hawaiian hotspot with new broadband ocean bottom instruments, Eos, Transactions, American Geophysical. Union, 90(41), 362–636.Google Scholar

Lee, E.-J., Chen, P., Jordan, T. H. et al. (2014). Full‐3‐D tomography for crustal structure in southern California based on the scattering‐integral and the adjoint‐wavefield methods. Journal of Geophysical Research, 119, 6421–51.Google Scholar

Lei, W., Ruan, Y., Bozdag, E. et al. (2020). Global adjoint tomography: model GLAD-M25. Geophysical Journal International 223, 1–21.Google Scholar

Lekic, V., and Romanowicz, B. (2011). Inferring upper-mantle structure by full waveform tomography with the spectral element method. Geophysical Journal International, 185, 799–831.Google Scholar

Lekic, V., Panning, M., and Romanowicz, B. (2010). A simple method for improving crustal corrections in waveform tomography. Geophysical Journal International, 182, 265–78.Google Scholar

Lerner-Lam, A.L., and, Jordan, T. H. (1983). Earth structure from fundamental and higher mode waveform analysis. Geophysical Journal of the Royal Astronomical Society, 75(3), 759–97.Google Scholar

Lévêque, J. J., Rivera, L., and Wittlinger, G. (1993). On the use o the checker-board test to assess the resolution of tomographic inversions. Geophysical Journal International, 115, 313–18Google Scholar

Li, X.-D., and Romanowicz, B. (1995). Comparison of global waveform inversions with and without considering cross-branch modal coupling. Geophysical Journal International, 121(3), 695–709.Google Scholar

Li, X.-D., and Romanowicz, B. (1996). Global mantle shear velocity model developed using non-linear asymptotic coupling theory. Journal of Geophysical Research, 101, 22245–72.Google Scholar

Li, X.-D., and Tanimoto, T. (1993). Waveforms of long-period body waves in a slightly aspherical Earth model. Geophysical Journal International, 112, 92–102.Google Scholar

Lin, C., Monteiller, V., Wang, K., Liu, T., Tong, P., and Liu, Q. (2019). High-frequency seismic wave modelling of the Deep Earth based on hybrid methods and spectral-element simulations: a conceptual study. Geophysical Journal International, 219, 1948–69.Google Scholar

Liu, Q., Beller, S., Lei, W., Peter, D., and Tromp, J. (2022). Pre-conditioned BFGS-based uncertainty quantification in elastic full-waveform inversion. Geophysical Journal International, 228(2), 796–815.Google Scholar

Maggi, A., Tape, C., Chen, M., Chao, D., and Tromp, J. (2009). An automated time-window selection algorithm for seismic tomography. Geophysical Journal International, 178, 257–81.Google Scholar

Marquering, H., Nolet, G., and Dahlen, F. A. (1998). Three-dimensional waveform sensitivity kernels. Geophysical Journal International, 132, 521–34.Google Scholar

Marone, F., and Romanowicz, B. (2007). Non-linear crustal corrections in high-resolution regional waveform seismic tomography. Geophysical Journal International, 170, 460–67.Google Scholar

Masson, Y. (2023). Distributed finited difference modelling of seismic waves, Geophysical Journal International , 233, 264–96.Google Scholar

Masson, Y., Cupillard, P., Capdeville, Y., and Romanowicz, B. (2014). On the numerical implementation of time reversal mirrors for tomographic imaging. Geophysical Journal International, 196, 1580–99. https://doi.org/10.1093/gji/ggt459.Google Scholar

Masson, Y., and Romanowicz, B. (2017a). Fast computation of synthetic seismograms within a medium containing remote localized perturbations: a numerical solution to the scattering problem. Geophysical Journal International, 208(2), 674–92.Google Scholar

Masson, Y., and Romanowicz, B. (2017b). Box tomography: localized imaging of remote targets buried in an unknown medium, a step forward for understanding key structures in the deep Earth. Geophysical Journal International, 211(1), 141–63.Google Scholar

Mégnin, C., and Romanowicz, B. (2000). The three-dimensional shear velocity structure of the mantle from the inversion of body, surface and highermode waveforms. Geophysical Journal International, 143, 709–28.Google Scholar

Meier, U., Curtis, A., and Trampert, J. (2007). Fully nonlinear inversion of fundamental mode surface waves for a global crustal model. Geophysical Research Letters, 34, L16304. https://doi.org/10.1029/2007GL030989.Google Scholar

Mochizuki, E. (1986). Free oscillations and surface waves of an aspherical Earth. Geophysical Research Letters, 13, 1478–81.Google Scholar

Moczo, P., Kristek, J., and Halada, L. (2004). The Finite-Difference Method for Seismologists. Bratislava: Comenius University. www.spice-rtn.org.Google Scholar

Modrak, R., and Tromp, J. (2016). Seismic waveform inversion best practices: Regional, global and exploration test cases. Geophysical Journal International, 206, 1864–89.Google Scholar

Montagner, J., and Anderson, D. (1989). Petrological constraints on seismic anisotropy. Physics of the Earth and Planetary Interiors, 54, 82–105.Google Scholar

Monteiller, V., Chevrot, S., Komatitsch, D., and Wang, Y. (2015). Three-dimensional full waveform inversion of short period teleseismic wavefields based upon the SEM-DSM hybrid method. Geophysical Journal International, 202, 811–27.Google Scholar

Montelli, R., Nolet, G., Dahlen, F.A. et al. (2004a). Finite-frequency tomography reveals a variety of plumes in the mantle. Science, 303(5656), 338–43.Google Scholar

Nocedal, J., and Wright, S. J. (2017). Numerical Optimization, 2nd ed. New York: Springer.Google Scholar

Nolet, G. (1990). Partitioned waveform inversion and two-dimensional structure under the network of autonomously recording seismograph. Journal of Geophysical Research, 95, 8499–8512.Google Scholar

Nolet, G., and Dahlen, F. A. (2000). Wave front healing and the evolution of seismic delay times. Journal of Geophysical Research, 105, 19043–54.Google Scholar

Nolet, G., Hello, Y., van der Lee, S. et al. (2019). Imaging the Galapagos mantle plume with an unconventional application of floating seismometers. Scientific Reports, 9, 1326.Google Scholar

Panning, M., and Romanowicz, B. (2006). A three-dimensional radially anisotropic model of shear velocity in the whole mantle. Geophysical Journal International, 167, 361–79.Google Scholar

Park, J. (1987). Asymptotic coupled-mode expressions for multiplet amplitude anomalies and frequency shifts on an aspherical earth. Geophysical Journal of the Royal Astronomical Society, 90(1), 129–69.Google Scholar

Pasyanos, M., and Nyblade, A. (2007). A top to bottom lithospheric study of Africa and Arabia. Tectonophysics, 444(1–4), 27–44.Google Scholar

Pienkowska, M., Monteiller, V., and Nissen-Meyer, T. (2020). High-frequency global wavefields for local 3-D structures by wavefield injection and extrapolation. Geophysical Journal International, 225, 1782–98.Google Scholar

Pipatprathanporn, P., and Simons, F. J. (2022). One year of sound recorded by a MERMAID float in the Pacific: hydroacoustic earthquake signals and infrasonic ambient noise. Geophysical Journal International, 228(1), 193–212.Google Scholar

Obayashi, M., Yoshimitsu, J., Sugioka, H. et al. (2016). Mantle plumes beneath the South Pacific Superswell revealed by finite frequency P tomography using regional seafloor and island data. Geophysical Research Letters, 43(11), 628–11634.Google Scholar

Rawlinson, N., Fichtner, A., Sambridge, M., and Young, M. K. (2014). Seismic tomography and the assessment of uncertainty. Advances in Geophysics, 55, 1–76.Google Scholar

Replumaz, A., Karason, H., van der Hilst, R. D., Besse, J., and Tapponnier, P. (2004). 4-D evolution of SE Asia’s mantle from geological reconstructions and seismic tomography. Earth and Planetary Science Letters, 221, 103–15.Google Scholar

Richards, M. A., and Engebretson, D. C. (1992). Large scale mantle convection and the history of subduction. Nature, 355, 437–40.Google Scholar

Rickers, F., Fichtner, A., and Trampert, J. (2013). The Iceland–Jan Mayen plume system and its impact on mantle dynamics in the North Atlantic region: Evidence from full-waveform inversion. Earth and Planetary Science Letters, 367, 39–51.Google Scholar

Ritsema, J., and Lekic, V. (2020). Heterogeneity of seismic wave velocity in Earth’s mantle. Annual Review of Earth and Planetary Sciences, 48, 377–401Google Scholar

Ritsema, J., Deuss, A., van Heijst, H. J., and Woodhouse, J. H. (2011). S40RTS: A degree-40 shear-velocity model for the mantle from new Rayleigh wave dispersion, teleseismic traveltime and normal-mode splitting function measurements. Geophysical Journal International, 184(3), 1223–36.Google Scholar

Ritsema, J., van Heijst, H. J., and Woodhouse, J. H. (1999). Complex shear velocity structure imaged beneath Africa and Iceland. Science, 286, 1925–8.Google Scholar

Ritsema, J., van Heijst, H.J., and Woodhouse, J.H. (2004). Global transition zone tomography. Journal of Geophysical Research, 109. https://doi.org/10.1029/2003JB002610.Google Scholar

Romanowicz, B. (1987). Multiplet-multiplet coupling due to lateral heterogeneity: Asymptotic effects on the amplitude and frequency of the Earth’s normal modes. Geophysical Journal of the Royal Astronomical Society, 90(1), 75–100.Google Scholar

Romanowicz, B. (2003). Global mantle tomography: Progress status in the last 10 years. Annual Review of Earth and Planetary Sciences, 31(1), 303–28.Google Scholar

Romanowicz, B. (2020). Seismic tomography of the Earth’s mantle. In Alderton, D. and Elias, S. A., eds., Encyclopedia of Geology, vol. 1, 2nd ed. Cambridge, MA: Academic Press, pp. 587–609.Google Scholar

Romanowicz, B., and Suyehiro, K. (2001). History of the International Ocean Network. http://eri-ndc.eri.u-tokyo.ac.jp/OHP-sympo2/report/index.html.Google Scholar

Romanowicz, B., and Wenk, R. (2017). Anisotropy in the Deep Earth. Physics of the Earth and Planetary Interiors, 269, 58–90. https://doiorg/10.1016/j.pepi.2017.05.005.Google Scholar

Romanowicz, B., Chen, L.-W., and French, S. W. (2019). Accelerating full waveform inversion via source stacking and cross-correlations. Geophysical Journal International, 220(1), 308–22.Google Scholar

Romanowicz, B., Panning, M., Gung, Y., and Capdeville, Y. (2008). On the computation of long period seismograms in a 3-D Earth using normal mode based approximations. Geophysical Journal International, 175, 520–36.Google Scholar

Romanowicz, B. A., French, S. W., Rickers, F., and Yuan, H. (2013). Source stacking for numerical wavefield computations: Application to continental and global scale seismic mantle tomography, in American Geophysical Union, Fall Meeting 2013, abstract S21E-05.Google Scholar

Ruan, Y., Lei, W., Modrak, R. et al. (2019). Balancing unevenly distributed data in seismic tomography: a global adjoint tomography example. Geophysical Journal International, 219(2), 1225–36Google Scholar

Schaeffer, A. J., and Lebedev, S. (2013). Global shear speed structure of the upper mantle and transition zone. Geophysical Journal International, 194(1), 417–49.Google Scholar

Schaeffer, A. J., and Lebedev, S. (2014). Imaging the North American continent using waveform inversion of global and USArray data. Earth and Planetary Science Letters, 402, 26–41.Google Scholar

Shapiro, N., and Ritzwoller, M. (2002). Monte-Carlo inversion for a global shear-velocity model of the crust and upper mantle. Geophysical Journal International, 151, 88–105.Google Scholar

Sigloch, K., McQuarrie, N., and Nolet, G. (2008). Two-stage subduction history under North America inferred from multiple-frequency tomography. Nature Geoscience, 1, 458–63.Google Scholar

Su, W.-J., Woodward, R. L., and Dziewonski, A. M. (1994). Degree-12 model of shear velocity heterogeneity in the mantle. Journal of Geophysical Research, 99(4), 4945–80.Google Scholar

Suetsugu, D., Isse, T., Tanaka, S. et al. (2009). South Pacific mantle plumes imaged by seismic observation on islands and seafloor. G-Cubed, 10, Q11014.Google Scholar

Sukhovich, A., Bonnieux, S., Hello, Y. et al. (2015). Seismic monitoring in the oceans by autonomous floats. Nature Communications, 6, 8027–33.Google Scholar

Suzuki, Y., Kawai, K., Geller, R. J., Borgeaud, A. F. E., and Konishi, K. (2016). Waveform inversion for 3‐D S‐velocity structure of D″ beneath the Northern Pacific: Possible evidence for a remnant slab and a passive plume. Earth, Planets and Space, 68(1). https://doi.org/10.1186/s40623‐016‐0576‐0.Google Scholar

Suzuki, Y., Kawai, K., Geller, R. J. et al. (2020). High-resolution 3-D S-velocity structure in the D’ region at the western margin of the Pacific LLSVP: Evidence for small-scale plumes and paleoslabs. Physics of the Earth and Planetary Interiors, 307, 106544.Google Scholar

Tanimoto, T. (1987). The three-dimensional shear wave structure in the mantle by overtone waveform inversion – I. Radial seismogram inversion. Geophysical Journal of the Royal Astronomical Society, 89(2), 713–40.Google Scholar

Tape, C., Liu, Q., Maggi, A., and Tromp, J. (2010). Seismic tomography of the southern California crust based upon spectral-element and adjoint methods. Geophysical Journal International, 180, 433–62.Google Scholar

Tarantola, A. (1984). Inversion of seismic reflection data in the acoustic approximation. Geophysics, 49, 1259–66.Google Scholar

Tarantola, A. (2005). Inverse Problem Theory and Methods for Model Parameter Estimation. Philadelphia, PA: Society for Industrial and Applied Mathematics.Google Scholar

Tarantola, A., and Valette, B. (1982). Generalized nonlinear inverse problems solved using the least squares criterion. Reviews of Geophysics, 20(2), 219–232.Google Scholar

Thrastarson, S., van Driel, M., Krischer, L. et al. (2020). Accelerating numerical wave propagation by wavefield adapted meshes. Part II: Full-waveform inversion. Geophysical Journal International, 221, 1591–604.Google Scholar

Thurber, C., and Ritsema, J. (2015). Theory and Observations- Seismic Tomography and Inverse Methods. In Schubert, G., ed., Treatise on Geophysics, vol. 1. Amsterdam: Elsevier, pp. 307–37.Google Scholar

Tromp, J. (2015). 1.07 – Theory and Observations: Forward Modeling and Synthetic Seismograms, 3D Numerical Methods. In Schubert, G., ed., Treatise on Geophysics. Amsterdam: Elsevier, pp. 231–51.Google Scholar

Tromp, J. (2020). Seismic wavefield imaging of earth’s interior across scales. Nature Reviews Earth and Environment, 1, 40–53.Google Scholar

Tromp, J., and Bachmann, E. (2019). Source encoding for adjoint tomography. Geophysical Journal International, 218, 2019–44.Google Scholar

Tromp, J., Tape, C. & Liu, Q. Y. (2005). Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels. Geophysical Journal International, 160, 195–216.Google Scholar

Tromp, J., Komatitsch, D., Hjörleifsdóttir, V. et al. (2010). Near real-time simulations of global CMT earthquakes. Geophysical Journal International, 183(1), 381–9.Google Scholar

Valentine, A. P., and Trampert, J. (2016). The impact of approximations and arbitrary choices on geophysical images. Geophysical Journal International, 204, 59–73.Google Scholar

van der Hilst, R., and de Hoop, M. V. (2005). Banana-doughnut kernels and mantle tomography. Geophysical Journal International, 163, 956–61.Google Scholar

van der Lee, S., and Nolet, G. (1997). Upper mantle S velocity structure of North America. Journal of Geophysical Research: Solid Earth, 102, 22815–38.Google Scholar

van der Meer, D. G., Spakman, W., van Hinsbergen, D. J. J, Amaru, M. L., and Torsvik, T. H. (2010). Towards absolute plate motions constrained by lower-mantle slab remnants. Nature Geoscience, 3, 36–40.Google Scholar

van Driel, M., Krischer, L., Stähler, S. C., Hosseini, K., and Nissen-Meyer, T. (2015). Instaseis: instant global seismograms based on a broadband waveform database. Solid Earth, 6(2), 701–17.Google Scholar

van Driel, M., Kemper, J., and Boehm, C. (2021). On the modelling of self-gravitation for full 3-D global seismic wave propagation. Geophysical Journal International, 227, 632–43.Google Scholar

van Herwaarden, D. P., Boehm, C., Afanasiev, M. et al. (2020). Accelerated full-waveform inversion using dynamic mini-batches. Geophysical Journal International, 221, 1427–38.Google Scholar

Virieux, J., and Operto, S. (2009). An overview of full-waveform inversion in exploration geophysics. Geophysics, 74, WCC127–WCC152.Google Scholar

Virieux, J., Asnaashari, A., Brossier, R. et al. (2014). 6. An introduction to full waveform inversion. In Encyclopedia of Exploration Geophysics, Geophysical References Series: R1-1-R1-40. Tulsa, OK: Society of Exploration Geophysicists.Google Scholar

Wang, Z., and Dahlen, F.A. (1995). Spherical-spline parameterization of three-dimensional Earth models. Geophysical Research Letters, 22, 3099–102.Google Scholar

Wen, L., and Helmberger, D.V. (1998). A two-dimensional P-SV hybrid method and its application to modeling localized structures near the core-mantle boundary. Journal of Geophysical Research, 103, 17901–18.Google Scholar

Woodhouse, J. H., and Dziewonski, A. M. (1984). Mapping the upper mantle: Three dimensional modeling of Earth structure by inversion of seismic waveforms. Journal of Geophysical Research, 89, 5953–86.Google Scholar

Woodhouse, J. H., and Deuss, A. (2015). 1.03 – Theory and Observations: Earth’s Free Oscillations. In Schubert, G., ed., Treatise on Geophysics. Amsterdam: Elsevier, pp. 31–65.Google Scholar

Yang, H., and Tromp, J. (2015). Synthetic free-oscillation spectra: an appraisal of various mode-coupling methods. Geophysical Journal International, 203, 1179–92.Google Scholar

Zhang, Q., Mao, W., Zhou, H., Zhang, H., and Chen, Y. (2018). Hybrid-domain simultaneous-source full waveform inversion without crosstalk noise. Geophysical Journal International, 215(3), 1659–81.Google Scholar

Zhu, H., Bozdag, E., and Tromp, J. (2015). Seismic structure of the European upper mantle based on adjoint tomography. Geophysical Journal International, 201(1), 18–52.Google Scholar

Afanasiev, M., Boehm, C., van Driel, M. et al. (2019). Modular and flexible spectral-element waveform modelling in two and three dimensions. Geophysical Journal International, 216, 1675–92.Google Scholar

Afanasiev, M. V., Pratt, R. G., Kamei, R., and McDowell, G. (2014). Waveform-based simulated annealing of crosshole transmission data: A semi-global method for estimating seismic anisotropy. Geophysical Journal International, 199, 1586–607.Google Scholar

Ajo-Franklin, J. B. (2009). Optimal experiment design for time-lapse traveltime tomography. Geophysics, 74, Q27–Q40.Google Scholar

Backus, G. E., and Gilbert, F. (1968). The resolving power of gross Earth data. Geophysical Journal of the Royal Astronomical Society, 16, 169–205.Google Scholar

Backus, G. E., and Gilbert, F. (1970). Uniqueness in the inversion of inaccurate gross Earth data. Philosophical Transactions of the Royal Society A, 266(1173), 123–92.Google Scholar

Bamberger, A., Chavent, G., and Lailly, P. (1977). Une application de la théorie du contrôle à un problème inverse sismique. Annales Geophysicae, 33, 183–200.Google Scholar

Bamberger, A., Chavent, G., Hemons, C., and Lailly, P. (1982). Inversion of normal incidence seismograms. Geophysics, 47, 757–70.Google Scholar

Bayes, T. (1764). An essay toward solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London, 53, 370-418.Google Scholar

Bernauer, M., Fichtner, A., and Igel, H. (2014). Optimal observables for multi-parameter seismic tomography. Geophysical Journal International, 198, 1241–54.Google Scholar

Betancourt, M. (2017). A conceptual introduction to Hamiltonian Monte Carlo. arXiv:1701.02434 [stat.ME].Google Scholar

Blom, N., Boehm, C., and Fichtner, A. (2017). Synthetic inversion for density using seismic and gravity data. Geophysical Journal International, 209, 1204–20.Google Scholar

Bodin, T., Sambridge, M., Rawlinson, N., and Arroucau, P. (2012). Transdimensional tomography with unknown data noise. Geophysical Journal International, 189, 1536–56.Google Scholar

Bozdag, E., Peter, D., Lefebvre, M. et al. (2016). Global adjoint tomography: First-generation model. Geophysical Journal International, 207, 1739–66.Google Scholar

Bui-Thanh, T., Ghattas, O., Martin, J., and Stadler, G. (2013). A computational framework for infinite-dimensional Bayesian inverse problems. Part I: The linearized case, with application to global seismic inversion. SIAM Journal on Scientific Computing, 35, A2494–A2523.Google Scholar

Calvetti, D., and Somersalo, E. (2017). Inverse problems: From regularization to Bayesian inference. Computational Statistics, 10(3). http://doi.org/10.1002/wics.1427.Google Scholar

Capdeville, Y., Guillot, L., and Marigo, J. J. (2010). 2-D non-periodic homogenization to upscale elastic media for P–SV waves. Geophysical Journal International, 182, 903–22.Google Scholar

Capdeville, Y., Gung, Y., and Romanowicz, B. (2005). Towards global Earth tomography using the spectral element method: A technique based on source stacking. Geophysical Journal International, 162, 541–54.Google Scholar

Chen, P., Jordan, T. H., and Zhao, L. (2007a). Full 3D waveform tomography: A comparison between the scattering-integral and adjoint-wavefield methods. Geophysical Journal International, 170, 175–81.Google Scholar

Chen, P., Zhao, L., and Jordan, T. H. (2007b). Full 3D tomography for the crustal structure of the Los Angeles region. Bulletin of the Seismological Society of America, 97, 1094–120.Google Scholar

Chib, S., and Greenberg, E. (1995). Understanding the Metropolis-Hastings algorithm. American Statistician, 49, 327–35.Google Scholar

Choi, Y., and Alkhalifah, T. (2011). Source-independent time-domain waveform inversion using convolved wavefields: Application to the encoded multisource waveform inversion. Geophysics, 76, R125–R134.Google Scholar

Clouzet, P., Masson, Y., and Romanowicz, B. (2018). Box tomography: First application to the imaging of upper mantle shear velocity and radial anisotropy structure beneath the north American continent. Geophysical Journal International, 213, 1849–75.Google Scholar

Curtis, A. (1999). Optimal experiment design: Cross-borehole tomographic examples. Geophysical Journal International, 136, 637–50.Google Scholar

de la Puente, J., Dumbser, M., Käser, M., and Igel, H. (2007). An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured methods. IV. Anisotropy. Geophysical Journal International, 169, 1210–28.Google Scholar

Djikpesse, H. A., Khodja, M. R., Prange, M. D., Duchenne, S., and Menkiti, H. (2012). Bayesian survey design to optimize resolution in waveform inversion. Geophysics, 77, R81–R93.Google Scholar

Duane, S., Kennedy, A. D., Pendleton, B. J., and Roweth, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195, 216–22.Google Scholar

Dziewonski, A. M., and Anderson, D. L. (1981). Preliminary reference Earth model. Physics of the Earth and Planetary Interiors, 25, 297–356.Google Scholar

Fichtner, A., Bunge, H.-P., and Igel, H. (2006). The adjoint method in seismology – I. Theory. Physics of the Earth and Planetary Interiors, 157, 105–23.Google Scholar

Fichtner, A., Kennett, B. L. N., Igel, H., and Bunge, H.-P. (2009). Full seismic waveform tomography for upper-mantle structure in the Australasian region using adjoint methods. Geophysical Journal International, 179, 1703–25.Google Scholar

Fichtner, A. (2010). Full seismic waveform modeling and inversion. Heidelberg: Springer.Google Scholar

Fichtner, A., and Trampert, J. (2011). Resolution analysis in full waveform inversion. Geophysical Journal International, 187, 1604–24.Google Scholar

Fichtner, A. (2021). Lecture Notes on Inverse Theory. Cambridge: Cambridge Open Engage, http://doi.org/10.33774/coe-2021-qpq2j.Google Scholar

Fichtner, A., van Herwaarden, D.-P., Afanasiev, M. et al. (2018). The Collaborative Seismic Earth Model: Generation I. Geophysical Research Letters, 45, 4007–16.Google Scholar

Fichtner, A., and van Leeuwen, T. (2015). Resolution analysis by random probing. Journal of Geophysical Research: Solid Earth, 120, 5549–73.Google Scholar

Gebraad, L., Boehm, C., and Fichtner, A. (2020). Bayesian elastic full‐waveform inversion using Hamiltonian Monte Carlo. Journal of Geophysical Research: Solid Earth, 125, e2019JB018428.Google Scholar

Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82, 711–32.Google Scholar

Hardt, M., and Scherbaum, F. (1994). The design of optimum networks for aftershock recordings. Geophysical Journal International, 117, 716–26.Google Scholar

Huang, Y., and Schuster, G. T. (2018). Full‐waveform inversion with multisource frequency selection of marine streamer data. Geophysical Prospecting, 66, 1243–57.Google Scholar

Hunziker, J., Laloy, E., and Linde, N. (2019). Bayesian full-waveform tomography with application to crosshole ground penetrating radar data. Geophysical Journal International, 218, 913–31.Google Scholar

Igel, H. (2016). Computational Seismology: A Practical Introduction. Cambridge: Cambridge University Press.Google Scholar

Kijko, A. (1977). An algorithm for the optimum distribution of a regional seismic network – I. Pure and Applied Geophysics, 115, 999–1009.Google Scholar

Komatitsch, D., and Vilotte, J.-P. (1998). The spectral element method: An effective tool to simulate the seismic response of 2D and 3D geological structures. Bulletin of the Seismological Society of America, 88, 368–92.Google Scholar

Käufl, P., Fichtner, A., and Igel, H. (2013). Probabilistic full waveform inversion based on tectonic regionalisation: Development and application to the Australian upper mantle. Geophysical Journal International, 193, 437–51.Google Scholar

Kotsi, P., Malcolm, A., and Ely, G. (2020). Time-lapse full-waveform inversion using Hamiltonian Monte Carlo: A proof of concept. SEG Technical Program Expanded Abstracts, 845–49.Google Scholar

Krampe, V., Edme, P., and Maurer, H. (2021). Optimized experimental design for seismic full waveform inversion: A computationally efficient method including a flexible implementation of acquisition costs. Geophysical Prospecting, 69, 152–66.Google Scholar

Krebs, J. R., Anderson, J. E., Hinkley, D. et al. (2009). Fast full-wavefield seismic inversion using encoded sources. Geophysics, 74, WCC177–WCC188.Google Scholar

Krebs, J. R., Cha, Y. H., Lee, S. et al. ExxonMobil Upstream Research Co (2018). Orthogonal Source and Receiver Encoding. U.S. Patent 10,012,745.Google Scholar

Kullback, S., and Leibler, R. A. (1951). On information and sufficiency. Annals of Mathematical Statistics, 22, 79–86.Google Scholar

Kuo, C., and Romanowicz, B. (2002). On the resolution of density anomalies in the Earth’s mantle using spectral fitting of normal mode data. Geophysical Journal International, 150, 162–79.Google Scholar

Leng, K., Nissen-Meyer, T., and van Driel, M. (2016). Efficient global wave propagation adapted to 3-D structural complexity: A pseudospectral/spectral-element approach. Geophysical Journal International, 207, 1700–21.Google Scholar

Liu, Q., and Gu, Y. (2012). Seismic imaging: From classical to adjoint tomography. Tectonophysics, 566–567, 31–66.Google Scholar

Liu, Q., and Peter, D. (2019). Square-root variable metric based elastic full-waveform inversion. Part 2: Uncertainty estimation. Geophysical Journal International, 218(2), 1100–20.Google Scholar

Liu, Q., and Wang, D. (2016). Stein variational gradient descent: A general purpose Bayesian inference algorithm. Advances in Neural Information Processing Systems, 2378–86. arXiv:1608.04471.Google Scholar

Liu, Q., Peter, D., and Tape, C. (2019). Square-root variable metric based elastic full-waveform inversion. Part 1: Theory and validation. Geophysical Journal International, 218(2), 1121–35.Google Scholar

Masson, Y., and Romanowicz, B. (2017). Fast computation of synthetic seismograms within a medium containing remote localized perturbations: A numerical solution to the scattering problem. Geophysical Journal International, 218, 674–92.Google Scholar

Maurer, H., Nuber, A., Martiartu, N. K. et al. (2017). Optimized experimental design in the context of seismic full waveform inversion and seismic waveform imaging. In Nielsen, L., ed., Advances in Geophysics, vol. 58. Cambridge, MA: Academic Press, pp. 1–45.Google Scholar

Malinverno, A. (2002). Parsimonious Bayesian Markov chain Monte Carlo inversion in a nonlinear geophysical problem. Geophysical Journal International, 151, 675–88.Google Scholar

Moczo, P., Kristek, J., Vavrycuk, V., Archuleta, R., and Halada, L. (2002). 3D heterogeneous staggered-grid finite-difference modeling of seismic motion with volume harmonic and arithmetic averaging of elastic moduli. Bulletin of the Seismological Society of America, 92, 3042–66.Google Scholar

Mosegaard, K. (2012). Limits to nonlinear inversion. In Jónasson, K., ed., Applied Parallel and Scientific Computing, Berlin: Springer, pp. 11–21.Google Scholar

Neal, R. M. (2011). MCMC using Hamiltonian dynamics. In Brooks, S., Gelman, A., Jones, G., and Meng, X.-L., eds., Handbook of Markov chain Monte Carlo. New York: Chapman and Hall, pp. 113–62.Google Scholar

Plessix, R.-E. (2006). A review of the adjoint-state method for computing the gradient of a functional with geophysical applications. Geophysical Journal International, 167, 495–503.Google Scholar

Rabinowitz, N., and Steinberg, D. M. (1990). Optimal configuration of a seismographic network: A statistical approach. Bulletin of the Seismological Society of America, 80, 187–96.Google Scholar

Resovsky, J., and Trampert, J. (2002). Reliable mantle density error bars: An application of the Neighbourhood Algorithm to normal-mode and surface wave data. Geophysical Journal International, 150, 665–72.Google Scholar

Romero, L. A., Ghiglia, D. C., Ober, C. C., and Morton, S. A. (2000). Phase encoding of shot records in prestack migration. Geophysics, 65, 426–36.Google Scholar

Ronchi, C., Iacono, R., and Paolucci, P. S. (1996). The ‘cubed sphere’: A new method for the solution of partial differential equations in spherical geometry. Journal of Computational Physics, 124, 93–114.Google Scholar

Sambridge, M. S., Bodin, T., Gallagher, K., and Tkalcic, H. (2013). Transdimensional inference in the geosciences. Philosophical Transactions of the Royal Society A, 371, 20110547.Google Scholar

Sambridge, M. S., Gallagher, K., Jackson, A., and Rickwood, P. (2006). Trans-dimensional inverse problems, model comparison, and the evidence. Geophysical Journal International, 167, 528–42.Google Scholar