Surface wave analysis for P- and S-wave velocity models

Distinguished Lectures in Earth Sciences, Napoli, 24 Maggio 2018 Surface wave analysis for P- and S-wave velocity models Laura Valentina Socco, Farbod Khosro Anjom, Cesare Comina, Daniela Teodor POLITECNICO DI TORINO UNIVERSITA DI TORINO

What am I going to talk about Surface wave propagation in layered systems and the concept of geometrical dispersion; The inversion of surface wave dispersion curves for 1D VS model estimation: potentials and limitations; Some examples of applications in laterally varying sites; A change in paradigm: from interval velocity to time-average velocity; A new approach to subsurface characterization: from inversion to data transform; Sensitivity to Poisson s ratio and VP estimation.

Surface waves: definitions There are many kinds of surface waves (guided waves) that can be exploited in geophysics: Rayleigh waves (1885): land data, ground surface, in line polarization, always generated; Scholte waves (1947): marine data, seabed, in line polarization, always generated; P guided waves: land data, ground surface, in line polarization; Love waves (1911): land/marine data, ground surface/seabed, horizontal cross line polarization; Lamb waves (1904): on solid plates; Stoneley waves (1924): in boreholes, along borehole walls;

Surface wave propagation in the homogeneous medium Rayleigh waves travel in a limited layer close to the free surface; The thickness of the layer depends on the wavelength of the propagating harmonics; Hence in a homogeneous medium high frequencies (short l) propagate close to the surface while low frequencies (long l) reach greater depth. Low frequency High frequency

Surface wave propagation in the homogeneous medium In a homogeneous halfspace, the different frequency components of the seismic signal produce different wavelengths, which propagates at different depths, at the Rayleigh wave velocity of the medium.

Surface wave propagation in the layered medium geometrical dispersion In a layered halfspace, the different frequency components of the seismic signal produce different wavelengths, which propagates at different depths, with different velocities depending from the depth.

Surface wave propagation in the layered medium

Surface wave propagation in the layered medium Rayleigh waves appear as high energy (amplitude) signals; body waves The effect of geometrical dispersion in time domain is the tipycal cone shape of the wavelength; The velocity of propagation is lower than body waves and varies for the different harmonics. Surface waves

Surface wave propagation in the layered medium Surface wave propagation can be modeled by for a stack of linear homogenous elastic layers. Layer parameters are: S-wave velocity, Poisson s ratio (or P-wave velocity), density and thickness. When we solve the forward problem we have to find the zeros of the Rayleigh secular function and they provides couple or f-v (or f-k) values which are possible solutions of the propagation.

Surface wave propagation in the layered medium V S =100m/s V P =200m/s V S =300m/s V P =600m/s 300 H = 5m Cut-off f-v frequencies f-k wavenumber [rad/m] 4 3 2 1 0 0 10 20 30 40 50 60 frequency [Hz] phase velocity [m/s] 250 200 150 100 Dispersion curve 10 20 30 40 50 60 frequency [Hz] Higher modes Fundamental mode

Characterization : inversion of geometrical dispersion A brief introduction Vertical particle about motion surface Phase waves velocity and V R their V R use for near Vsurface characterization; S1 V R = l f? V S2 > V S1 Wavelength l V S3 > V S2 Velocity profile Z Z Short wavelength High frequency Long wavelength Low frequency Frequency f Dispersion Curve Experimental INVERSE PROBLEM

Seismology Since the early 60 to map the earth crust. Applications Exploration geophysics Only in the last decade for various targets. Geotechnical engineering Since the early 80 to estimate V S profiles. [Yilmaz et al., 2006] [Shapiro and Ritzwoller, 2002] [Brown, Boore and Stokoe, 2002] [Park et al., 2005]

The surface wave method ACQUISITION RAW DATA k f DISPERSION PROCESSING V S INVERSION z VELOCITY MODEL

The surface wave method 1.9 2 2.1 time [s] 2.2 2.3 ACQUISITION 2D FFT 2.4 2.5 5 10 15 20 25 30 35 40 45 50 offset [m] RAW DATA k f DISPERSION PROCESSING 2p f V( f) = k V S INVERSION z VELOCITY MODEL

The surface wave method Shear Wave Velocity (m/s) 100 200 300 400 500 600 700800 5 RAW DATA ACQUISITION Depth (m) 10 15 20 25 z k V S f DISPERSION VELOCITY MODEL PROCESSING INVERSION phase velocity, m/s 30 35 700 600 experimental 500 400 300 200 100 0 10 20 30 40 50 60 70 frequency, Hz

Summary of SW methods: potentials Surface waves are easy to gather and to recognize; Robust; Available in any seismic gather no matter which is the purpose of acquisition (seismic reflection, P-wave refraction); Allow S-wave velocity to be estimated.

Summary of SW methods: limitations Strong non linearity of the invers problem à the result is non unique (no matter if we use global or local search strategies) and the sensitivity to model parameters decreases with depth limiting the investigation depth ; 1D; VP is not estimated.

Laterally heterogeneous media The seismogram is windowed in the spatial domain with several asymmetric Gaussian windows whose maxima span the survey line

Laterally heterogeneous media The seismogram is windowed in the spatial domain with several asymmetric Gaussian windows whose maxima span the survey line [Bergamo, P., D. Boiero, L. V. Socco, 2012, Retrieving 2D structures from surface wave data by means of a space-varying spatial windowing: Geophysics, 77, 4, EN39-EN51, doi: 10.1190/GEO2012-0031.1.]

Laterally heterogeneous media

Spatially Constrained Inversion Full model built up of a number of 1D shear wave velocity models, model parameters are shear wave velocities and depths; Lateral constraints couple the different 1D-models. The constraints consist of the spatially dependent covariance between the model parameters... and can be considered as a priori information on the geological variation in the area; LCI allows for smooth transitions in model parameters along the profile; All data are inverted simultaneously as one system. [AUKEN and CHRISTIANSEN, 2004]; [SOCCO, D. BOIERO, S. FOTI, R. WISÉN, 2009, Laterally constrained inversion of ground roll from seismic reflection records, Geophysics, 74, 6, G35-G45]

Field case: shallow bedrock mapping Land-streamer 48 ch 1.25m 55 ch 2.50m Vibroseis Sweep: 7-80 Hz Length: 15 s

Field case: shallow bedrock mapping

Field case: shallow bedrock mapping [Boiero, D., L.V. Socco, S. Stocco, R. Wisén, 2013, Bedrock mapping in shallow environments using surface-wave analysis: The Leading Edge, June, 664-672.]

Summary: SW method in laterally varying media Several strategies can be implemented to mitigate the limitations of surface wave method; 2D sites can be investigated and the results are in agreement with body wave methods; The inversion process remains a critical aspect of the workflow (deterministic methods are non unique, stochastic methods are computationally heavy). still we estimate only VS and assume VP L

What am I going to show? We move from interval velocity to time-average velocity We identify a relationship between wavelength and investigation depth and we use it to get VS without inverting; This relationship is sensitive to Poisson s ratio and we can hence use it to estimate directly VP;

The concept of time-average velocity Time-average velocity is used in many applications ranging from seismic hazard (VS,30) to static corrections (provides directly the one-way time). V Sz, = å n n å h i h V i Si h 1, V S1 h i, V Si z h n, V Sn

The wavelength-depth relationship W/D We search a relationship between the time-average velocity at a given depth z (V S,z ) and the surface wave velocity at a given wavelength.

The wavelength-depth relationship W/D We search a relationship between the weighted average velocity at a given depth z (V S,z ) and the surface wave velocity at a given wavelength. Linear regression

The meaning of the W/D relationship [Karray, M., and G. Lefebvre, 2008, Significance and Evaluation of Poisson s ratio, Canadian Geotechnical Journal, 45, 624-635] [Pelekis, P.C., and G.A. Athanasopoulos, 2011, An overview of surface wave methods and a reliability study of a simplified inversion technique, Soil Dynamics and Earthquake Engineering,31, 1654 1668]

The W/D sensitivity to Poisson If this is true, also our W/D relationship should be sensitive to Poisson s ratio. Let s see what happens with a constant Poisson with depth (0.33). Depth or Wavelength [m] 0 0 500 1.000 1.500 2.000 2.500 3.000 VS 10 20 30 40 VP SW DC Estimated VSz true VSz Estimated VPz True VPz 50 60 70 80 90 V [m/s] Wavelength [m] 160 140 120 100 80 60 0.1 0.45 40 20 0 0 20 40 60 80 Depth [m]

The W/D sensitivity to Poisson The sensitivity to Poisson s has a strong physical meaning and is related to the pattern of vertical displacement with depth. Depth [m] 0 10 20 30 40 50 60 0.1 0.15 0.2 0.25 0.3 0.35 0.4 70 0 0.5 1 1.5 2 2.5 3 normalized vertical displacement [-] wavelength [m] 80 70 60 50 40 30 20 10 Poisson 0.1 0.2 0.3 10 20 30 40 50 50 depth [m] 1 0.9 0.9 0.6 0.8 0.8 0.7 0.7 0.5 0.6 0.6 0.4 0.5 0.5 0.4 0.3 0.4 0.3 0.3 0.2 0.2 0.2 0.1 0.1 0.1

The W/D sensitivity to Poisson Hence we can use this sensitivity to estimate the Poisson ratio for the different depth and use it to transform the VSz model into a VPz model. Depth or Wavelength [m] 0 0 500 1.000 1.500 2.000 2.500 3.000 VS 10 20 30 40 VP SW DC Estimated VSz true VSz Estimated VPz True VPz 50 60 70 80 90 V [m/s] Wavelength [m] Wavelength [m] 160 90 140 85 120 100 80 80 75 60 40 70 20 65 0 0 20 60 40 65 60 70 80 Depth [m]

The W/D sensitivity to Poisson Hence we can use this sensitivity to estimate the Poisson ratio for the different depth and use it to transform the VSz model into a VPz model. Depth or Wavelength [m] V [m/s] 0 0 500 1.000 1.500 2.000 2.500 3.000 VS 10 20 30 40 VP SW DC Estimated VSz true VSz Estimated VPz True VPz 50 60 70 80 90 Wavelength [m] Wavelength [m] 160 90 140 85 120 100 80 80 75 60 40 70 20 65 0 0 20 60 40 65 60 70 80 Depth [m] [m]

I have shown that A relationship exists between VSz at various depth and SW phase velocity at various wavelengths (W/D); The W/D relationship is sensitive to Poisson s ratio; If the Poisson s ratio is constant with depth this sensitivity is enough to estimate the correct Poisson s ratio and transform the VSz into VPz. but what happens if Poisson ratio varies with depth?

The apparent Poisson ratio Here we use the same VS model of the previous example but with variable Poisson with depth (0.33 for the first 4 layers and 0.2 for the deeper ones). Depth or Wavelength [m] 0 0 500 1000 1500 2000 VS 10 VP true VPz 20 SW DC true VSz 30 40 50 60 70 V [m/s] ævpz ö ç - 2 1 VSz n z = è ø 2 2 ævpz ö ç - 1 èvsz ø 2 Depth [m] 0 0.1 0.2 0.3 0.4 0.5 0 10 20 30 40 50 60 70 Poisson [-]

The apparent Poisson ratio Here we use the same VS model of the previous example but with variable Poisson with depth (0.33 for the first 4 layers and 0.2 for the deeper ones). Depth or Wavelength [m] 0 0 500 1000 1500 2000 VS 10 VP true VPz 20 SW DC true VSz 30 40 50 60 V [m/s] Wavelength [m] 160 140 120 100 80 60 40 20 0.1 0.45 70 0 0 20 40 60 80 Depth [m]

The apparent Poisson ratio Here we use the same VS model of the previous example but with variable Poisson with depth (0.33 for the first 4 layers and 0.2 for the deeper ones). Depth or Wavelength [m] 0 0 500 1000 1500 2000 VS 10 VP true VPz 20 SW DC true VSz 30 40 50 60 70 V [m/s] Wavelength [m] Wavelength [m] 160 30 140 25 120 20 100 15 80 10 60 5 40 0 20-5 0 0 2 20 4 6 40 8 Depth Depth [m] [m] 60 10 12 80 14

The apparent Poisson ratio Here we use the same VS model of the previous example but with variable Poisson with depth (0.33 for the first 4 layers and 0.2 for the deeper ones). Depth or Wavelength [m] 0 0 500 1000 1500 2000 VS 10 VP true VPz 20 SW DC true VSz 30 40 50 60 70 V [m/s] Wavelength [m] 110 105 100 95 90 85 80 75 70 65 60 50 60 70 80 Depth [m]

The apparent Poisson ratio Here we use the same VS model of the previous example but with variable Poisson with depth (0.33 for the first 4 layers and 0.2 for the deeper ones). Depth or or Wavelength [m] [m] V [m/s] 0 500 1000 1500 2000 0 VS VS 10 VP VP true VPz true VPz data4 SW DC 20 estimated true VPz VSz Estimated VSz 30 30 true VSz 40 40 50 50 60 60 70 70 Depth [m] 0 0.1 0.2 0.3 0.4 0.5 0 apparent Poisson 10 estimated Poisson 20 30 40 50 60 70 Poisson [-]

Retrieving the interval velocity If we can estimate the time-average velocity at any depth we can apply a Dix-like equation and retrieve the interval velocity at all depths à we have the V S and the VP profile. V Si = z zi V i - z z - V i-1 i-1 Si, Si, -1

I have shown that Using the W/D and the apparent Poisson s ratio we can estimate VSz and VPz profile; By applying a Dix-like relationship we can transform the time-average velocities into interval velocities;. but To estimate W/D we need the VSz model, so we are in a kind of loop and we need to find a strategy to make all this useful in practical applications.

Real world applications To make the outlined concepts (W/D and apparent n) of practical use we operates according to the following workflow: 1. Estimate W/D for one reference model along a line 2. Apply it to all the DCs along the line à VSz 3. Retrieve apparent n and transform VSz à VPz 4. Apply dix-like relation à VS and VP

Real world example

VS and VP benchmark DHT VS VS model from LCI of dispersion curves along the line- DHT VP VP model from travel time tomography [Socco, L.V., D. Boiero, C. Comina, S. Foti, R. Wisén, 2008, Seismic Characterization of an Alpine Site: Near Surface Geophysics, 6, 255-267]

The reference model To define the reference model we select one of the broadband DC obtained by merging active and passive data and we invert it with a MC inversion (Poisson free to vary). Wavelength [m] 0 200 400 600 800 0 10 20 30 40 Phase Velocity [m/s] Depth or Wavelength [m] 0 200 400 600 800 1000 1200 0 VS MC inversion 10 VSz SW DC 20 30 40 50 V [m/s] 50 60 60 70

The W/D relationship and apparent Poisson s ratio The W/D is computed for the reference model and, using the reference VS model the W/D for different Poisson s ratio values is computed and compared with the experimental one to find the apparent Poisson s ratio. 140 120 Poisson [-] 0 0.1 0.2 0.3 0.4 0.5 0 100 10 Wavelength [m] 80 60 40 Depth [m] 20 30 40 20 0 0 10 20 30 40 50 60 Depth [m] 50 60

Results: VSz The comparison between VSz from LCI results and the VSz estimated with W/D data transform has difference mostly below 10%. [Socco L.V., C. Comina, F. Khosro Anjom, 2017, Time-average velocity estimation through surface-wave analysis: Part 1 S-wave velocity: GEOPHYSICS, 82, 3, U49 U59]

Results: VPz The comparison between VPz from P-wave tomography and VPz estimated with apparent Poisson s ratio applied to the VSz results has difference mostly below 10%. [Socco L.V., C. Comina, 2017, Timeaverage velocity estimation through surface-wave analysis: Part 2 P- wave velocity: GEOPHYSICS, 82, 3, U61 U73]

Results: interval VS LCI From VSz The comparison between VS from LCI results and VS estimated by applying Dix-like relation to VSz data has difference mostly below 15% in the upper part of the model, but rech error of 100% in deeper part where data are coarser. Normalized difference

Results: interval VP P-wave tomography From VPz Normalized difference The comparison between VP from P-wave tomography and VP estimated by applying Dix-like relation to VPz data has difference mostly below 20% in the upper part of the model, but reach errors of 100% in deeper part where data are coarser.

Borehole benchmark About 700 m far from reference model The comparison between VS and VP local model from down-hole test, inversions (LCI and P-wave tomo) and our approximate estimation shows very good agreement for VS, and reasonable agreement for VP with lower difference from DHT at shallow depth and greater difference for deeper layers.

I have shown that We can apply the W/D relationship and the apparent Poisson s ratio concepts in a practical workflow and obtain a VS and VP model along a seismic line knowing only one reference VS model.. but The interval velocity has high uncertainties for noisy data. There is a strong assumption: weak lateral variations of VS and negligible lateral variations of Poisson s ratio.

Conclusion The SW dispersion curve is extremely sensitive to time-average velocities and a relationship (W/D) exists between V S,z at various depth and SW phase velocity at various wavelengths. This relationship can be used to estimate V S,z and, consequently a smooth approximated V S profiles for a set of similar models. The W/D is sensitive to Poisson s ratio, hence the direct estimation of V P,z and V P becomes possible. The VP and VS models obtained with this workflow have proven to be suitable as initial models for FWI being within cycle skipping at high frequency.

Aknowledgements European Union DG12 for SISMOVALP Project - La Salle data. Total E&P for supporting Farbod Khosro PhD grant. Italian Ministry of Research for supporting Daniela Teodor PhD grant. All the PhDs and Post-docs who contributed developing our processing and inversion codes (Claudio Strobbia, Daniele Boiero, Margherita Maraschini, Claudio Piatti, Paolo Bergamo, Flora Garofalo). Thank you for your attention