INITIAL MODEL DESIgN FOR FuLL-wAvEFORM INvERSION ... · Full-Waveform Inversion (FWI) is a high resolution seismic tomograph technique ased on the numerical solution of the waves

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INITIAL MODEL DESIgN FOR FuLL-wAvEFORM INvERSION - PRELIMINARy ELASTIC MODELLINg FROM SuRFACE wAvES DATA ANALySISD. Teodor1, C. Comina1, L.V. Socco2, R. Brossier3, P.T. Trinh3, J. Virieux3

1 Dipartimento di Scienze della Terra, Università degli Studi di Torino, Italy 2 Dipartimento di Ingegneria dell’Ambiente, del Territorio e delle Infrastrutture (DIATI), Politecnico di Torino, Italy 3 Institut des Sciences de la Terre (IsTerre), Université Grenoble Alpes, Grenoble, France

Introduction. Full-Waveform Inversion (FWI) is a high resolution seismic tomograph� technique �ased on the numerical solution of the waves equation proposed �� �arantola in 1984 (Fichtner, 2011� for a recent text�ook)� it is defined �� Virieux and �perto (2009) as “a data-fitting procedure that uses the full-wavefield to extract quantitative information from seismograms”. Various FWI techniques, �oth in the time and in the frequenc� domain, are

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availa�le in literature. Considering the significant computational resources required �� a pro�a�ilistic approach, for the majorit� of cases local optimization (gradient-�ased) methods are used. �hus, there are man� examples in literature regarding successful deterministic FWI on s�nthetic models, �oth in the elastic and in the acoustic approximation. However, when moving from s�nthetic to real-data, deterministic FWI still remains challenging mainl� due to c�cle-skipping issues and local minima pro�lems. In order to overcome this limit it is necessar� to start the inversion process from an initial model sufficientl� close to the glo�al minimum or, at least, located in its “main valle�”.

�he aim of the work is to assess the required qualit� of the initial model for FWI, in the frame of near-surface targets. In this note we focus on the first preliminar� results regarding the forward modelling part� we investigate differences and similarities �etween a ver� well-controlled real acquisition and the corresponding numerical simulations. �he case stud� is an area where a perfectl� well-known low densit� sand-�od� is surrounded �� denser geological formations. An initial near-surface model was retrieved from the laterall� constrained inversion (LCI) of the dispersion curves (DCs) along a testing line. 3D forward modelling of wave propagation on this model compare promisingl� well with experimental data and suggests that this initial model is accurate enough for making FWI converging to the glo�al minimum we are interested in.

Field case. �he real-dataset was o�tained from a dedicated seismic acquisition in the CNR experimental area in �urin (Ital�). In particular, we performed two acquisitions (Fig. 1) following respectivel� a 3D and a 2D pattern. For �oth acquisitions we used a 8 kg sledgehammer vertical point source and a total of 72 vertical receivers (4.5 Hz) connected to 3 �eode - seismic modules� the time sampling was set to 0.125 ms and the acquisition time to 0.512 s (with a pre-trig of 0.1 s).

For the 3D acquisition (Fig. 1 - left side upper corner) we energized in 83 points, stacking from 8 to 10 shots for each source-position. �he in line distance �etween the source-points was 0.75 m, while the receivers interval was 0.5 m. For the 2D acquisition (Fig. 1 - left side lower corner) we energized in 11 positions (stacking again from 8 to 10 shots for each point)� 4 of the

Fig. 1 - �he CNR acquisition geometr�. Left side upper corner: the 3D acquisition scheme and the position of the 2D line (not in scale)� left side lower corner: the 2D line with the outlined position of 2nd shot (green circle)� right side upper corner: photo of the area with the scheme of the receivers position for the 3D and 2D acquisition� right side lower corner: simple 3D scheme of the model.

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11 shots were located outside the receivers line (2 of them at -2 m and 2 m from its extremities and the other two at -4 m and 4 m, respectivel�)� the other source-points were placed inside the receivers line, evenl� spaced at a distance of a�out 2.7 m. �he geophone-interval for the 2D acquisition was 0.3 m.

In the present work we refer onl� to the seismograms �elonging to the 2D acquisition. In Fig. 2a we show an example of a field seismogram referred to the 2nd shot (placed at -2 m left side from the first receiver - Fig. 1 - left side lower corner). �he wave propagation along the line clearl� evidences the presence of the sand �od�.

Methodology. For the numerical simulations, we used the spectral elements code developed in the frame of the �EI�C�PE Consortium (http://seiscope2.osug.fr). �he code is written in Fortran 95. It has two levels of MPI parallelization (the domain decomposition and the possi�ilit� to run multiple shots simultaneousl�). It is �ased on non-overlapping hexahedra spectral elements in a deformed Cartesian-�ased mesh automaticall� �uilt-up. Moreover, viscoelastic time-domain modelling can �e considered as well as the misfit gradient with respect to densit�, stiffness coefficients and attenuation factors, in the frame of the FWI whole machiner�. More details a�out the code and methods �ehind for modeling and inversion can �e found in �rinh et al. (2017a, 2017�, 2017c).

�he method used to o�tain the initial model from the surface-waves data involves two steps: the extraction of the dispersion curves (DCs), together with their uncertainties, from the experimental seismograms and the laterall� constrained inversion of the DCs.

�he extraction of DCs has �een performed using a space-var�ing �aussian windowing approach (Bergamo et al., 2012). �his technique allows to o�tain a set of DCs, each one in correspondence of the moving �aussian window maxima and each one referring to a different su�surface portion. �he num�er of the DCs for a given seismic line depends on a parameter related to the width of the window. �his parameter is inversel� proportional to the �aussian-window standard deviation� its value is chosen as a trade-off �etween the width of the window in the time domain and the spectral resolution in the frequenc�-wavenum�er (f-k) domain. After appropriate selection of these parameters, for each window position several shots are considered and the picking of the DCs is performed over the stacked f-k spectrum of several source positions.

�nce all the DCs are extracted from the field data, the� are inverted in a LCI approach (�occo et al., 2009). �his is a deterministic inversion in which all the DCs along the profile are linked together �� mutual constraints, referring to the variance allowed for the same parameter �etween adjacent models. In particular, small values of variance are required for rigid constraints and �igger values for weak constraints. �he final result of the inversion is a pseudo-2D model of the shear-waves velocities (Vs) distri�ution along the line.

�his pseudo-2D model is later interpolated to o�tain a smooth 2D Vs model, more suita�le for the forward modelling code. �tarting from this model we associated an appropriate Vp model �� assuming a constant Poisson value. �he 2D models are then extended in 3D in order to respect the input format required �� the �EM3D code and perform the 3D numerical simulations of wave propagation. In this particular case, after the 2D to 3D conversion, it was preserved for the y direction the same geometr� as for the x direction.

Elastic modelling tests and results. For the numerical simulations we used an element size (i.e. distance �etween two adjacent points of the 3D mesh) of 0.2 m to satisf� the volume condition for 4th order �EM simulation (�rinh et al., 2017a). �he CFL sta�ilit� condition leads us to use a 1e-5 s time-step value and 51200 time-samples to reach the same duration as the registration length used during the field acquisition (0.512 s).

For the first series of simulations we used a Ricker source with a central frequenc� of 60 Hz and a maximum frequenc� of 150 Hz, in order to reproduce the frequenc� content of the field data. In Fig. 2� we show the results of the simulation performed, for the same shot position where we have shown experimental data, using this Ricker wavelet. In order to �etter reproduce

the real-data source frequenc� content, we also attempted a source-wavelet estimation. �he signature of the real source was o�tained using a matching-filter estimation of the simulated and real data (e.g. Pratt, 1999). In Fig. 2c we show the results o�tained with this new estimated source.

Discussion, conclusions and perspectives. �he comparison �etween the real-data and the s�nthetic seismograms o�tained �� propagating the Ricker source in the model deduced from the DCs anal�sis shows a good similarit� among the two datasets� there is an even greater similarit� �etween the field seismogram and the one o�tained from the numerical simulation when recovering the source time function. �his shows that the initial model o�tained from LCI of DCs appears to �e a good candidate for further FWI. �herefore, according to these preliminar� o�servations, we could send out a positive prediction regarding the possi�ilit� to o�tain accurate results from the FWI of this near-surface target� nevertheless, managing high amplitudes variations �etween surface and �od� waves will �e a challenge.

As a short-time perspective, we are planning to perform the estimation of the first FWI gradient �efore inverting the 2D data using the full 3D elastic FWI. Long-time perspectives will involve the anal�sis of the 3D field data and FWI.Acknowledgements We would like to thank the �EI�C�PE consortium for providing the �EM3D code and the CIMEN� mesocentre for allowing the access to the computational resources.

ReferencesBergamo, P., Boiero, D. and �occo, L.V. (2012): Retrieving 2D structures from surface-waves data by means of space-

varying windowing. �eoph�sics, 77(4), EN39-EN51. Fichtner, A. (2011): Full �eismic Waveform modelling and Inversion. �pringer �cience & Business Media, 343 pp.Pratt, R.�. (1999): Seismic waveform inversion in the frequency domain, Part 1: Theory and verification in a physical

scale model. �eoph�sics, 64 (3):888-901.�occo, L.V., Boiero, D., Foti, �. and Wisén, R. (2009): Laterally constrained inversion of ground roll from seismic

reflection records. �eoph�sics, 74(6): �35-�45.�arantola, A. (2005): Inverse problem theory and methods for model parameter estimation, 2nd edn. �ociet� for

Industrial and Applied Mathematics, Philadelphia, PA (2005).�rinh, P. �., Brossier, R., Métivier, L., �avard, L. and Virieux, J. (2017a): Efficient 3D elastic FWI using a spectral-

element method. In 87th �E� Conference and Exhi�ition 2017, Houston. �rinh, P. �., Brossier, R., Métivier, L., Virieux, J. and Wellington, P. (2017�): Bessel smoothing filter for spectral

element mesh. �eoph�sical Journal International, 209 (3): 1489-1512.�rinh, P. �., Brossier, R., Métivier, L., Virieux, J. and Wellington, P. (2017c): Structure-smoothing Bessel filter for

finite element mesh: Application on 3D elastic FWI. In 79th EA�E Conference and Exhi�ition 2017, Paris. Virieux, J. and �perto, �. (2009): An overview of full-waveform inversion in exploration geophysics. �eoph�sics,

74(6): WCC1-WCC26.

Fig. 2 - �eismograms related to the �hot nr. 2. a: field data� �:s�nthetic data o�tained �� propagating the Ricker source� c:s�nthetic data o�tained �� propagating the real (estimated) source.

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