Estimation of an acoustic velocity model for the CROP M12A seismic line using a

gradient-based Full Waveform Inversion

B. Galuzzi, Department of Informatics, University of Milan-Bicocca

E. Stucchi, Department of Earth Sciences, University of Pisa

A. Tognarelli, Department of Earth Sciences, University of Pisa

19 November 2018

GNGTS 2018, BolognaSessione3.1: Geofisica applicata per le georisorse e le strutture profonde

Outline

➢ Full Waveform Inversion

➢The CROP M12A seismic profile

➢ Setting of the modelling, the misfit function, and the optimization procedure

➢Preliminary results

Full Waveform Inversion➢ Estimation of a geological macro-model of subsurface from active seismic data by means of:

1) Modelling algorithm

2) Misfit function

3) Optimization algorithm

Numerical solution of the wave equation (2D acoustic)

Difference between predicted and observed data (seismograms)

Iterative procedure to minimize the misfit function

▪ Virieux J., Operto S.; (2009): An overview of full waveform inversion in exploration geophysics. Geophysics.

Starting model𝑣0

Observed data𝑑0Starting

data

Iterative scheme

Modelling

Predicted data𝑑 𝑣𝑘

Misfit evaluation𝐹(𝑣𝑘) = 𝑑 𝑣𝑘 − 𝑑0

New predicted model𝑣𝑘

Modelling

Are the optimization criteria met?

No: k=k+1

yes

Final modelҧ𝑣

▪ Louboutin, M. et Al.; (2017): Full-waveform inversion, Part 1: forward modelling. The Leading Edge

▪ Louboutin, M. et Al.; (2018): Full-waveform inversion, Part 2: Adjoint modelling. The Leading Edge

▪ Witte, P. et Al.; (2018): Full-waveform inversion, Part 3: Optimization. The Leading Edge

▪ Tarantola A . (1984): Inversion of seismic reflection data in the acoustic approximation. Geophysics.

Optimization

Misfit

The CROP M12A seismic profile▪ 1500 marine seismic shots

▪ Source and receivers (180 channels) located at a depth of 8m and 14m respectively, with offset between 125m and 4.5km

▪ 𝑑𝑡 = 4𝑚𝑠, and 𝑇 = 3𝑠 − 4𝑠 (enough for structures located at shallow depth)

Original dataset

▪ 100 shots gathers evenly distributed in 22 km towards the end of the line

Dataset considered for FWI

Shots 6198Map of acquisition

▪ Scrocca D. et Al. (2003): CROP ATLAS:seismic reflection profiles of the Italian crust. Memorie Descrittive Carta Geoliche Italiane.

Modelling

➢ Explicit, 2nd order in time, finite difference code to solve the 2D acoustic wave equation:

▪ d𝑥 = 𝑑𝑧 = 25𝑚, 𝑛𝑥 = 981, 𝑛𝑧 = 80

▪ 𝑑𝑡 = 4𝑚𝑠, 𝑇 = 2.5𝑠

▪ 𝑣 Ԧ𝑥 is the 2D acoustic model

▪ 𝑓 Ԧ𝑥, 𝑡 is the seismic source, whose wavelet is estimated from seabed reflection

ሷ𝑝 Ԧ𝑥, 𝑡 = 𝑣 Ԧ𝑥 2∆𝑝 Ԧ𝑥, 𝑡 + 𝑓 Ԧ𝑥, 𝑡

Modelling gridWavelet24.5 km

2 k

m

nx▪ Galuzzi B., Zampieri E., Stucchi E.; 2017: A local adaptive method for the numerical approximation in seismic wave modelling. Communications in Applied

and Industrial Mathematics.

Processing on seismic data

Before the processing After the processing

➢ The seismograms must be processed:

▪ to increase the S/N ratio

▪ To reduce the non-linearity of the misfit function

▪ because the modelling is 2D acoustic

1.muting mask

2.low-pass filter up to 15Hz

3.trace envelope

4.trace normalization

Processing operations

Design of a robust misfit function➢ Mean of all the 𝐿2-norm difference between the observed and the synthetic seismograms

➢ Dedicated processing operator is to reduce the cycle skipping effect and the non-linearity of the optimization problem

𝐹 𝑣 =

𝑠=

𝑛𝑠

𝑟=1

𝑛°𝑐ℎ𝑎𝑛

𝑘=1

𝑛𝑡

𝐺 𝑝 𝑣, 𝑡𝑘 , 𝑥𝑠, 𝑥𝑟,𝑠 − 𝐺 𝑝0 𝑣, 𝑡𝑘 , 𝑥

𝑠, 𝑥𝑟,𝑠2

where:

▪ 𝑝 𝑣, 𝑡𝑘 , 𝑥𝑠, 𝑥𝑟,𝑠 are the observed seismograms

▪ 𝑝𝑜 𝑣, 𝑡𝑘 , 𝑥𝑠, 𝑥𝑟,𝑠 are the synthetic seismograms

▪ 𝐺 correspons to the following processing operations (Galuzzi et al., 2018):

1. Mute on the diving waves and the shallow reflections

2. Filtering [5𝐻𝑧 − 15𝐻𝑧]

3. Trace envelope

4. Trace normalization

▪ Galuzzi B., Tognarelli A., Stucchi E.M.; 2018: A Global-Local Experience of 2D Acoustic FWI on a Real Data Set. EAGE Technical Program Expanded Abstracts.

Inversion procedure➢ The inversion grid is the modelling grid without the first four rows (a total of 819X76 unknowns)

➢ The optimization algorithm used is the steepest descent algorithm

𝑣𝑘+1 = 𝑣𝑘 + 𝛾𝑘ℎ𝑘

▪ ℎ𝑘 = −∇𝑣𝐹(𝑣𝑘) is the descent direction, computed by means of the adjoint method (Plessix, 2006)

▪ 𝛾𝑘 > 0 is the step length

➢ The initial model 𝑣0 is obtained from a Migration Velocity Analysis (MVA) (Tognarelli et. Al., 2010)

nx=981nz=762

km

24,5 km

➢ Due to the non-linearity of the misfit function, the starting model in the FWI procedure plays an important role

▪ Tognarelli A., Stucchi E.M., Masumeci F., Mazzarini F., Sani F.; 2010: Reprocessing of the CROP M12A seismic line focused on shallow-depth geological structures in the northern

Tyrrhenian Sea. Bollettino di Geofisica Teorica ed Applicata.Final model

Velocity [km/s]

24,5 km

Shot 27Shot 3

▪ Plessix R.; 2006: A review of the adjoint-state method for computing the gradient of a functional with geophysical applications. Geophysical Journal International.

Updated model

After 50 iterations of the minimization procedure…

Final modelVelocity [km/s]

➢ The long-wavelength structure is not significantly changed

➢ The upper part shows the updated velocity values

Value of the misfit function

24,5 km

Shot 27Shot 3

Difference between MVA and FWI modelVelocity [km/s]

24,5 km

2 k

m

Shot 27Shot 3

MVA SeismogramsPredicted data

…and difference between the observed and predicted data

Shot 3 Shot 27

FWI SeismogramsPredicted data

…and difference between the observed and predicted data

Shot 3 Shot 27

0.5

1.0

1.5

Dep

th (

km

)

0.5

1.0

1.5

Dep

th (

km

)

5000 5200 5400 5600 5800 6000 6200

Pre Stack Depth Migrated SectionCDP

MVA Common image gathers

125

CIG

500 875 1250

5490offset

125 500 875 1250

5640

125 500 875 1250

5730

125 500 875 1250

5765

125 500 875 1250

5913

125 500 875 1250

5970

0.5

1.0

1.5

Dep

th (

km

)

0.5

1.0

1.5

Dep

th (

km

)

125

CIG

500 875 1250

5490offset

125 500 875 1250

5640

125 500 875 1250

5730

125 500 875 1250

5765

125 500 875 1250

5913

125 500 875 1250

5970

0.5

1.0

1.5

Dep

th (

km

)

0.5

1.0

1.5

Dep

th (

km

)

FWI Common image gathers

125

CIG

500 875 1250

6004offset

125 500 875 1250

6040

125 500 875 1250

6043

125 500 875 1250

6062

125 500 875 1250

6100

125 500 875 1250

6128

0.5

1.0

1.5

Dep

th (

km

)

0.5

1.0

1.5

Dep

th (

km

)

MVA Common image gathers

125

CIG

500 875 1250

6004offset

125 500 875 1250

6040

125 500 875 1250

6043

125 500 875 1250

6062

125 500 875 1250

6100

125 500 875 1250

6128

0.5

1.0

1.5

Dep

th (

km

)

0.5

1.0

1.5

Dep

th (

km

)

FWI Common image gathers

Conclusions

➢ An acoustic FWI experience was carried out on a portion of the CROP M12A marine seismic profile acquired in the framework of the Italian Deep Crust Project.

➢ The processing sequence applied to the data is an important step to reduce the non-linearity of the misfit function

➢ Using the gradient-based FWI method we were able to update the velocity model previously obtained by a MVA procedure

➢ The quality of the final model is assessed by a better horizontal alignment of the events in the CIGs

➢ Use of the full-wavelet for improving the resolution of the estimated velocity model

...and future works

Ackownledgments

...thank you for the attention!

➢ We gratefully acknowledge the support of Landmark/Halliburton for the use of the seismic software ProMAX at theDepartment of Earth Science of the University of Pisa.

➢ We would like to thank the “Banca Dati CROP” at the Institute of Marine Sciences of Bologna for providing the seismicdata and for their invaluable efforts to guarantee CROP data preservation for the scientific community.

➢ We wish to thank Prof. Mazzotti of University of Pisa for its continued support in the research

ReferencesBozdag E., Trampert J., Tromp J.; 2011: Misfit functions for full waveform inversion based on instantaneous phase and envelope

measurements. Geophysical Journal International..

Fichtner A.; 2010: Full Seismic Waveform Modelling and Inversion. Berlin: Springer-Verlag.

Galuzzi B., Zampieri E., Stucchi E.; 2017: A local adaptive method for the numerical approximation in seismic wave modelling.

Communications in Applied and Industrial Mathematics.

Galuzzi B., Tognarelli A., Stucchi E.M.; 2018: A Global-Local Experience of 2D Acoustic FWI on a Real Data Set. EAGE Technical

Program Expanded Abstracts.

Mazzotti A., Bienati N., Stucchi E., Tognarelli A., Aleardi M., Sajeva A.; 2016: Two-grid genetic algorithm full waveform inversion. The

Leading Edge.

Plessix R.; 2006: A review of the adjoint-state method for computing the gradient of a functional with geophysical applications.

Geophysical Journal International.

Pratt, R. G.; 2008: Waveform tomography—successes, cautionary tales, and future directions. In 70th EAGE Conference & Exhibition.

Scrocca D., Doglioni C., Innocenti F., Manetti P., Mazzotti A., Bertelli L., Burbi L., D’Offizi S.; 2003: CROP ATLAS:seismic reflection

profiles of the Italian crust. Mem. Descr. Carta Geol. It.

Tognarelli A., Stucchi E.M., Masumeci F., Mazzarini F., Sani F.; 2010: Reprocessing of the CROP M12A seismic line focused on

shallow-depth geological structures in the northern Tyrrhenian Sea. Bollettino di Geofisica Teorica ed Applicata.

Virieux J., Operto S.; 2009: An overview of full waveform inversion in exploration geophysics. Geophysics.