Abstract
Surface waves are widely used in near-surface geophysics and provide a noninvasive way to determine near-surface structures. By extracting and inverting dispersion curves to obtain local 1D S-wave velocity profiles, multichannel analysis of surface waves (MASW) has been proven as an efficient way to analyze shallow-seismic surface waves. By directly inverting the observed waveforms, full-waveform inversion (FWI) provides another feasible way to use surface waves in reconstructing near-surface structures. This paper provides a state of the art review of MASW and shallow-seismic FWI and a comparison of both methods. A two-parameter numerical test is performed to analyze the nonlinearity of MASW and FWI, including the classical, the multiscale, the envelope-based, and the amplitude-spectrum-based FWI approaches. A checkerboard model is used to compare the resolution of MASW and FWI. These numerical examples show that classical FWI has the highest nonlinearity and resolution among these methods, while MASW has the lowest nonlinearity and resolution. The modified FWI approaches have an intermediate nonlinearity and resolution between classical FWI and MASW. These features suggest that a sequential application of MASW and FWI could provide an efficient hierarchical way to delineate near-surface structures. We apply the sequential-inversion strategy to two field data sets acquired in Olathe, Kansas, USA, and Rheinstetten, Germany, respectively. We build a 1D initial model by using MASW and then apply the multiscale FWI to the data. High-resolution 2D S-wave velocity images are obtained in both cases, whose reliabilities are proven by borehole data and a GPR profile, respectively. It demonstrates the effectiveness of combining MASW and FWI for high-resolution imaging of near-surface structures.
Similar content being viewed by others
References
Aki K, Richards PG (2002) Quantitative seismology. University Science Books, Herndon
Aleardi M, Tognarelli A, Mazzotti A (2016) Characterisation of shallow marine sediments using high-resolution velocity analysis and genetic-algorithm-driven 1D elastic full-waveform inversion. Near Surf Geophys 14(5):449–460
Amrouche M, Yamanaka H (2015) Two-dimensional shallow soil profiling using time-domain waveform inversion. Geophysics 80(1):EN27–EN41
Askari R, Hejazi SH (2015) Estimation of surface-wave group velocity using slant stack in the generalized S-transform domain surface-wave group velocity estimation. Geophysics 80(4):EN83–EN92
Behura J, Snieder R (2013) Virtual real source: source signature estimation using seismic interferometry. Geophysics 78(5):Q57–Q68
Bergamo P, Socco LV (2014) Detection of sharp lateral discontinuities through the analysis of surface-wave propagation. Geophysics 79(4):EN77–EN90
Bergamo P, Boiero D, Socco LV (2012) Retrieving 2D structures from surface-wave data by means of space-varying spatial windowing. Geophysics 77(4):EN39–EN51
Boaga J, Vignoli G, Cassiani G (2011) Shear wave profiles from surface wave inversion: the impact of uncertainty on seismic site response analysis. J Geophys Eng 8(2):162
Boaga J, Cassiani G, Strobbia CL, Vignoli G (2013) Mode misidentification in Rayleigh waves: ellipticity as a cause and a cure. Geophysics 78(4):EN17–EN28
Bohlen T (2002) Parallel 3-D viscoelastic finite difference seismic modelling. Comput Geosci 28(8):887–899
Bohlen T, Kugler S, Klein G, Theilen F (2004) 1.5D inversion of lateral variation of Scholte wave dispersion. Geophysics 69(2):330–344
Boiero D, Socco LV (2010) Retrieving lateral variations from surface wave dispersion curves. Geophys Prospect 58(6):977–996
Boiero D, Bergamo P, Bruno Rege R, Socco LV (2011) Estimating surface-wave dispersion curves from 3D seismic acquisition schemes: part 11D models. Geophysics 76(6):G85–G93
Borisov D, Modrak R, Gao F, Tromp J (2017) 3D elastic full-waveform inversion of surface waves in the presence of irregular topography using an envelope-based misfit function. Geophysics 83(1):1–45
Bozdağ E, Trampert J, Tromp J (2011) Misfit functions for full waveform inversion based on instantaneous phase and envelope measurements. Geophys J Int 185(2):845–870
Bretaudeau F, Brossier R, Leparoux D, Abraham O, Virieux J (2013) 2D elastic full-waveform imaging of the near-surface: application to synthetic and physical modelling data sets. Near Surf Geophys 11(3):307–316
Brossier R, Operto S, Virieux J (2009) Seismic imaging of complex onshore structures by 2D elastic frequency-domain full-waveform inversion. Geophysics 74(6):WCC105–WCC118
Brossier R, Operto S, Virieux J (2010) Which data residual norm for robust elastic frequency-domain full waveform inversion? Geophysics 75(3):R37–R46
Bunks C, Saleck FM, Zaleski S, Chavent G (1995) Multiscale seismic waveform inversion. Geophysics 60(5):1457–1473
Cercato M (2009) Addressing non-uniqueness in linearized multichannel surface wave inversion. Geophys Prospect 57(1):27–47
Chai HY, Phoon KK, Goh SH, Wei CF (2012) Some theoretical and numerical observations on scattering of Rayleigh waves in media containing shallow rectangular cavities. J Appl Geophys 83:107–119
Chen X (1993) A systematic and efficient method of computing normal modes for multilayered half-space. Geophys J Int 115(2):391–409
Dal Moro G, Moura RMM, Moustafa SS (2015) Multi-component joint analysis of surface waves. J Appl Geophys 119:128–138
Dal Moro G, Moustafa SS, Al-Arifi NS (2018) Improved holistic analysis of Rayleigh waves for single-and multi-offset data: joint inversion of Rayleigh-wave particle motion and vertical-and radial-component velocity spectra. Pure Appl Geophys 175(1):67–88
De Nil D (2005) Characteristics of surface waves in media with significant vertical variations in elasto-dynamic properties. J Environ Eng Geophys 10(3):263–274
Di Fiore V, Cavuoto G, Tarallo D, Punzo M, Evangelista L (2016) Multichannel analysis of surface waves and down-hole tests in the archeological Palatine Hill area (Rome, Italy): evaluation and influence of 2D effects on the shear wave velocity. Surv Geophys 37(3):625–642
Dokter E, Köhn D, Wilken D, Nil D, Rabbel W (2017) Full-waveform inversion of SH- and Love-wave data in near-surface prospecting. Geophys Prospect 65:216–236
Dou S, Ajo-Franklin JB (2014) Full-wavefield inversion of surface waves for mapping embedded low-velocity zones in permafrost. Geophysics 79(6):EN107–EN124
Fichtner A, Kennett BL, Igel H, Bunge HP (2008) Theoretical background for continental- and global-scale full-waveform inversion in the time-frequency domain. Geophys J Int 175(2):665–685
Forbriger T (2003) Inversion of shallow-seismic wavefields: I. Wavefield transformation. Geophys J Int 153(3):719–734
Forbriger T, Groos L, Schäfer M (2014) Line-source simulation for shallow-seismic data. Part 1: theoretical background. Geophys J Int 198(3):1387–1404
Foti S, Comina C, Boiero D, Socco L (2009) Non-uniqueness in surface-wave inversion and consequences on seismic site response analyses. Soil Dyn Earthq Eng 29(6):982–993
Foti S, Parolai S, Albarello D, Picozzi M (2011) Application of surface-wave methods for seismic site characterization. Surv Geophys 32(6):777–825
Foti S, Lai CG, Rix GJ, Strobbia C (2014) Surface wave methods for near-surface site characterization. CRC Press, Boca Raton
Gao L, Pan Y (2016) Acquisition and processing pitfall with clipped traces in surface-wave analysis. J Appl Geophys 125:1–6
Gao L, Pan Y (2018) Source signature estimation from multimode surface waves via mode-separated virtual real source method. Geophys J Int 213(2):1177–1186
Gao L, Xia J, Pan Y (2014) Misidentification caused by leaky surface wave in high-frequency surface wave method. Geophys J Int 199(3):1452–1462
Gao L, Xia J, Pan Y, Xu Y (2016) Reason and condition for mode kissing in MASW method. Pure Appl Geophys 173(5):1627–1638
Garofalo F, Foti S, Hollender F, Bard P, Cornou C, Cox BR, Ohrnberger M, Sicilia D, Asten M, Di Giulio G et al (2016) Interpacific project: comparison of invasive and non-invasive methods for seismic site characterization. Part I: intra-comparison of surface wave methods. Soil Dyn Earthq Eng 82:222–240
Gélis C, Virieux J, Grandjean G (2007) Two-dimensional elastic full waveform inversion using Born and Rytov formulations in the frequency domain. Geophys J Int 168(2):605–633
Gilbert JC, Nocedal J (1992) Global convergence properties of conjugate gradient methods for optimization. SIAM J Optim 2(1):21–42
Groos L, Schäfer M, Forbriger T, Bohlen T (2014) The role of attenuation in 2D full-waveform inversion of shallow-seismic body and Rayleigh waves. Geophysics 79(6):R247–R261
Groos L, Schäfer M, Forbriger T, Bohlen T (2017) Application of a complete workflow for 2D elastic full-waveform inversion to recorded shallow-seismic Rayleigh waves. Geophysics 82(2):R109–R117
Haskell NA (1953) The dispersion of surface waves on multilayered media. Bull Seismol Soc Am 43(1):17–34
Hayashi K, Suzuki H (2004) CMP cross-correlation analysis of multi-channel surface-wave data. Explor Geophys 35:7–13
Hestenes MR, Stiefel E (1952) Methods of conjugate gradients for solving linear systems. J Res Natl Bur Stand 49(6):409–436
Ikeda T, Tsuji T (2015) Advanced surface-wave analysis for 3D ocean bottom cable data to detect localized heterogeneity in shallow geological formation of a CO2 storage site. Int J Greenh Gas Control 39:107–118
Ikeda T, Tsuji T, Matsuoka T (2013) Window-controlled CMP crosscorrelation analysis for surface waves in laterally heterogeneous media. Geophysics 78(6):EN95–EN105
Ikeda T, Matsuoka T, Tsuji T, Nakayama T (2014) Characteristics of the horizontal component of Rayleigh waves in multimode analysis of surface waves. Geophysics 80(1):EN1–EN11
Ivanov J, Miller RD, Xia J, Steeples D, Park CB (2006) Joint analysis of refractions with surface waves: an inverse solution to the refraction-traveltime problem. Geophysics 71(6):R131–R138
Kallivokas L, Fathi A, Kucukcoban S, Stokoe K II, Bielak J, Ghattas O (2013) Site characterization using full waveform inversion. Soil Dyn Earthq Eng 47:62–82
Ke G, Dong H, Kristensen Å, Thompson M (2011) Modified Thomson–Haskell matrix methods for surface-wave dispersion-curve calculation and their accelerated root-searching schemes. Bull Seismol Soc Am 101(4):1692–1703
Kennett B (1974) Reflections, rays, and reverberations. Bull Seismol Soc Am 64(6):1685–1696
Knopoff L (1964) A matrix method for elastic wave problems. Bull Seismol Soc Am 54(1):431–438
Köhn D, Meier T, Fehr M, Nil D, Auras M (2016) Application of 2D elastic Rayleigh waveform inversion to ultrasonic laboratory and field data. Near Surf Geophys 14(5):461–476
Kumar J, Naskar T (2017) Resolving phase wrapping by using sliding transform for generation of dispersion curves. Geophysics 82(3):V127–V136
Lin CP, Chang TS (2004) Multi-station analysis of surface wave dispersion. Soil Dyn Earthq Eng 24(11):877–886
Lin CP, Lin CH, Chien CJ (2017) Dispersion analysis of surface wave testing: SASW versus MASW. J Appl Geophys 143:223–230
Liu Y, Teng J, Xu T, Badal J, Liu Q, Zhou B (2017) Effects of conjugate gradient methods and step-length formulas on the multiscale full waveform inversion in time domain: numerical experiments. Pure Appl Geophys 174(5):1983–2006
Lu L, Wang C, Zhang B (2007) Inversion of multimode Rayleigh waves in the presence of a low-velocity layer: numerical and laboratory study. Geophys J Int 168(3):1235–1246
Luo Y, Xia J, Miller R, Xu Y, Liu J, Liu Q (2008) Rayleigh-wave dispersive energy imaging using a high-resolution linear Radon transform. Pure Appl Geophys 165(5):903–922
Luo Y, Xia J, Liu J, Xu Y, Liu Q (2009) Research on the middle-of-receiver-spread assumption of the MASW method. Soil Dyn Earthq Eng 29(1):71–79
Maraschini M, Foti S (2010) A monte carlo multimodal inversion of surface waves. Geophys J Int 182(3):1557–1566
Masoni I, Brossier R, Virieux J, Boelle J (2013a) Alternative misfit functions for FWI applied to surface waves. In: 75th EAGE conference and exhibition incorporating SPE EUROPEC 2013
Masoni I, Valensi R, Brossier R, Virieux J, Boelle J, Leparoux D, Cote P (2013b) Toward a better full waveform inversion of surface waves. In: 19th European meeting of environmental and engineering geophysics, EAGE, expanded abstracts, vol 19200
Maurer H, Curtis A, Boerner DE (2010) Recent advances in optimized geophysical survey design. Geophysics 75(5):75A177–75A194
Menke W (2017) The uniqueness of single data function, multiple model functions, inverse problems including the Rayleigh wave dispersion problem. Pure Appl Geophys 174(4):1699–1710
Métivier L, Brossier R (2016) The SEISCOPE optimization toolbox: a large-scale nonlinear optimization library based on reverse communicationthe seiscope optimization toolbox. Geophysics 81(2):F1–F15
Métivier L, Brossier R, Virieux J, Operto S (2013) Full waveform inversion and the truncated Newton method. SIAM J Sci Comput 35(2):B401–B437
Mi B, Xia J, Shen C, Wang L, Hu Y, Cheng F (2017) Horizontal resolution of multichannel analysis of surface waves. Geophysics 82(3):EN51–EN66
Mi B, Xia J, Shen C, Wang L (2018) Dispersion energy analysis of Rayleigh and Love waves in the presence of low-velocity layers in near-surface seismic surveys. Surv Geophys 39(2):271–288
Miller R, Xia J, Park C, Ivanov J (1999) Multichannel analysis of surface waves to map bedrock. Lead Edge 18(12):1392–1396
Mun S, Bao Y, Li H (2015) Generation of Rayleigh-wave dispersion images from multichannel seismic data using sparse signal reconstruction. Geophys J Int 203(2):818–827
Nazarian S, Stokoe I, Kenneth H, Hudson W (1983) Use of spectral analysis of surface waves method for determination of moduli and thicknesses of pavement systems. Transp Res Rec 930:38–45
Nguyen TD, Tran KT, McVay M (2016) Evaluation of unknown foundations using surface-based full waveform tomography. J Bridge Eng 21(5):04016013
Nocedal J, Wright S (2006) Numerical optimization. Springer, Berlin
Nuber A, Manukyan E, Maurer H (2017) Optimizing measurement geometry for seismic near-surface full waveform inversion. Geophys J Int 210(3):1909–1921
Pan Y, Xia J, Gao L, Shen C, Zeng C (2013a) Calculation of Rayleigh-wave phase velocities due to models with a high-velocity surface layer. J Appl Geophys 96:1–6
Pan Y, Xia J, Zeng C (2013b) Verification of correctness of using real part of complex root as Rayleigh-wave phase velocity with synthetic data. J Appl Geophys 88:94–100
Pan Y, Xia J, Xu Y, Gao L (2016a) Multichannel analysis of Love waves in a 3D seismic acquisition system. Geophysics 81(5):EN67–EN74
Pan Y, Xia J, Xu Y, Gao L, Xu Z (2016b) Love-wave waveform inversion for shallow shear-wave velocity using a conjugate gradient algorithm. Geophysics 81(1):R1–R14
Pan Y, Gao L, Bohlen T (2017) Sequential phase-velocity and waveform inversion of shallow-seismic surface waves—a field example for bedrock mapping. In: 23rd European meeting of environmental and engineering geophysics
Pan Y, Gao L, Bohlen T (2018a) Time-domain full-waveform inversion of Rayleigh and Love waves in presence of free-surface topography. J Appl Geophys 152:77–85
Pan Y, Schaneng S, Steinweg T, Bohlen T (2018b) Estimating S-wave velocities from 3D 9-component shallow seismic data using local Rayleigh-wave dispersion curves—a field study. J Appl Geophys 159:532–539
Park CB, Miller RD, Xia J, et al (1998) Imaging dispersion curves of surface waves on multi-channel record. In: 1998 SEG annual meeting, society of exploration geophysicists
Park CB, Miller RD, Xia J (1999) Multichannel analysis of surface waves. Geophysics 64(3):800–808
Parolai S (2009) Determination of dispersive phase velocities by complex seismic trace analysis of surface waves (CASW). Soil Dyn Earthq Eng 29(3):517–524
Pei D, Louie JN, Pullammanappallil SK (2008) Improvements on computation of phase velocities of Rayleigh waves based on the generalized R/T coefficient method. Bull Seismol Soc Am 98(1):280–287
Pérez Solano C, Donno D, Chauris H (2014) Alternative waveform inversion for surface wave analysis in 2-D media. Geophys J Int 198(3):1359–1372
Piatti C, Socco L, Boiero D, Foti S (2013) Constrained 1D joint inversion of seismic surface waves and P-refraction traveltimes. Geophys Prospect 61(1):77–93
Plessix R (2006) A review of the adjoint-state method for computing the gradient of a functional with geophysical applications. Geophys J Int 167(2):495–503
Plessix R, Mulder W (2004) Frequency-domain finite-difference amplitude-preserving migration. Geophys J Int 157(1):957–987
Renalier F, Jongmans D, Savvaidis A, Wathelet M, Endrun B, Cornou C (2010) Influence of parameterization on inversion of surface wave dispersion curves and definition of an inversion strategy for sites with a strong versus contrast. Geophysics 75(6):B197–B209
Romdhane A, Grandjean G, Brossier R, Rejiba F, Operto S, Virieux J (2011) Shallow-structure characterization by 2D elastic full waveform inversion. Geophysics 76(3):R81–R93
Ryden N, Park CB (2006) Fast simulated annealing inversion of surface waves on pavement using phase-velocity spectra. Geophysics 71(4):R49–R58
Schwab F, Knopoff L (1970) Surface-wave dispersion computations. Bull Seismol Soc Am 61:321–344
Shen C, Wang A, Wang L, Xu Z, Cheng F (2015) Resolution equivalence of dispersion-imaging methods for noise-free high-frequency surface-wave data. J Appl Geophys 122:167–171
Sloan SD, Peterie SL, Miller RD, Ivanov J, Schwenk JT, McKenna JR (2015) Detecting clandestine tunnels using near-surface seismic techniques. Geophysics 80(5):EN127–EN135
Socco L, Boiero D (2008) Improved monte carlo inversion of surface wave data. Geophys Prospect 56(3):357–371
Socco L, Boiero D, Foti S, Wisn R (2009) Laterally constrained inversion of ground roll from seismic reflection records. Geophysics 74(6):G35–G45
Socco L, Foti S, Boiero D (2010) Surface wave analysis for building near surface velocity models: established approaches and new perspectives. Geophysics 75(5):A83–A102
Song X, Tang L, Lv X, Fang H, Gu H (2012) Application of particle swarm optimization to interpret Rayleigh wave dispersion curves. J Appl Geophys 84:1–13
Strobbia C, Foti S (2006) Multi-offset phase analysis of surface wave data (MOPA). J Appl Geophys 59(4):300–313
Strobbia C, Laake A, Vermeer P, Glushchenko A (2011) Surface waves: use them then lose them. surface-wave analysis, inversion and attenuation in land reflection seismic surveying. Near Surf Geophys 9(6):503–514
Tarantola A (1986) A strategy for nonlinear elastic inversion of seismic reflection data. Geophysics 51(10):1893–1903
Tarantola A (1988) Theoretical background for the inversion of seismic waveforms including elasticity and attenuation. Pure Appl Geophys 128(1–2):365–399
Tarantola A (2005) Inverse problem theory and methods for model parameter estimation, vol 89. SIAM, Bangkok
Thomson WT (1950) Transmission of elastic waves through a stratified solid medium. J Appl Phys 21(2):89–93
Tran K, McVay M, Faraone M, Horhota D (2013) Sinkhole detection using 2D full seismic waveform tomography. Geophysics 78(5):R175–R183
Tran KT, Sperry J (2018) Application of 2-D full waveform tomography on land-streamer data for assessment of roadway subsidence. Geophysics 83(3):1–42
Tsuji T, Johansen TA, Ruud BO, Ikeda T, Matsuoka T (2012) Surface-wave analysis for identifying unfrozen zones in subglacial sediments S-wave velocity in subglacial sediment. Geophysics 77(3):EN17–EN27
Verachtert R, Lombaert G, Degrande G (2017) Multimodal determination of Rayleigh dispersion and attenuation curves using the circle fit method. Geophys J Int 212(3):2143–2158
Vignoli G, Cassiani G (2010) Identification of lateral discontinuities via multi-offset phase analysis of surface wave data. Geophys Prospect 58(3):389–413
Vignoli G, Strobbia C, Cassiani G, Vermeer P (2011) Statistical multioffset phase analysis for surface-wave processing in laterally varying media. Geophysics 76(2):U1–U11
Virieux J (1986) P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method. Geophysics 51(4):889–901
Virieux J, Operto S (2009) An overview of full-waveform inversion in exploration geophysics. Geophysics 74(6):WCC1–WCC26
Wang L, Xu Y, Xia J, Luo Y (2015) Effect of near-surface topography on high-frequency Rayleigh-wave propagation. J Appl Geophys 116:93–103
Watson T (1970) A note on fast computation of Rayleigh wave dispersion in the multilayered elastic half-space. Bull Seismol Soc Am 60(1):161–166
Wu RS, Luo J, Wu B (2014) Seismic envelope inversion and modulation signal model. Geophysics 79(3):WA13–WA24
Xia J (2014) Estimation of near-surface shear-wave velocities and quality factors using multichannel analysis of surface-wave methods. J Appl Geophys 103:140–151
Xia J, Miller R, Park C (1999) Estimation of near-surface shear-wave velocity by inversion of Rayleigh wave. Geophysics 64(4):691–700
Xia J, Miller RD, Park CB, Tian G (2003) Inversion of high frequency surface waves with fundamental and higher modes. J Appl Geophys 52(1):45–57
Xia J, Xu Y, Miller RD (2007) Generating an image of dispersive energy by frequency decomposition and slant stacking. Pure Appl Geophys 164(5):941–956
Xia J, Xu Y, Miller RD, Zeng C (2010) A trade-off solution between model resolution and covariance in surface-wave inversion. Pure Appl Geophys 167(12):1537–1547
Xia J, Xu Y, Luo Y, Miller R, Cakir C, Zeng C (2012) Advantages of using multichannel analysis of Love waves (MALW) to estimate near-surface shear-wave velocity. Surv Geophys 33:841–860
Xing Z, Mazzotti A (2018) Two-grid genetic algorithm full waveform inversion of surface waves: two actual data examples. In: 80th EAGE conference and exhibition 2018
Yamanaka H, Ishida H (1996) Application of genetic algorithms to an inversion of surface-wave dispersion data. Bull Seismol Soc Am 86(2):436–444
Yuan YO, Simons FJ, Bozdağ E (2015) Multiscale adjoint waveform tomography for surface and body waves. Geophysics 80(5):R281–R302
Zeng C, Xia J, Miller R, Tsoflias GP (2011a) Feasibility of waveform inversion of Rayleigh waves for shallow shear-wave velocity using a genetic algorithm. J Appl Geophys 75:655–684
Zeng C, Xia J, Miller RD, Tsoflias GP (2011b) Application of the multiaxial perfectly matched layer (M-PML) to near-surface seismic modeling with Rayleigh waves. Geophysics 76(3):T43–T52
Zeng C, Xia J, Miller RD, Tsoflias GP, Wang Z (2012) Numerical investigation of MASW applications in presence of surface topography. J Appl Geophys 84:52–60
Zhang SX, Chan LS (2003) Possible effects of misidentified mode number on Rayleigh wave inversion. J Appl Geophys 53(1):17–29
Acknowledgements
The authors would like to thank Dr. Thomas Hertweck for an internal review and Prof. Jianghai Xia for providing the first field data set. The authors also appropriate the editor Prof. Michael J. Rycroft and two anonymous reviewers for their helpful and constructive comments. We gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG) through CRC 1173.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Pan, Y., Gao, L. & Bohlen, T. High-Resolution Characterization of Near-Surface Structures by Surface-Wave Inversions: From Dispersion Curve to Full Waveform. Surv Geophys 40, 167–195 (2019). https://doi.org/10.1007/s10712-019-09508-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10712-019-09508-0