ibp simultaneous inversion of multicomponent...

______________________________ 1 Bachelor, Geophysicist – DCS/SCHLUMBERGER 2 Master, Geophysicist – DCS/SCHLUMBERGER 3 PHD, Geophysicist – UN-BC/PETROBRAS 4 PHD, Geophysicist – DCS/SCHLUMBERGER 5 Master, Geophysicist – DCS/SCHLUMBERGER

IBP2756_10 SIMULTANEOUS INVERSION OF MULTICOMPONENT DATA IN

THE CAMPOS BASIN, OFFSHORE BRAZIL Josimar Silva1, Gorka Garcia Leiceaga2, Joclean Vanzeler3, Fredy Artola4

and Evelin Marquez5

Copyright 2010, Instituto Brasileiro de Petróleo, Gás e Biocombustíveis - IBP Este Trabalho Técnico foi preparado para apresentação na Rio Oil & Gas Expo and Conference 2010, realizada no período de 13 a 16 de setembro de 2010, no Rio de Janeiro. Este Trabalho Técnico foi selecionado para apresentação pelo Comitê Técnico do evento, seguindo as informações contidas na sinopse submetida pelo(s) autor(es). O conteúdo do Trabalho Técnico, como apresentado, não foi revisado pelo IBP. Os organizadores não irão traduzir ou corrigir os textos recebidos. O material conforme, apresentado, não necessariamente reflete as opiniões do Instituto Brasileiro de Petróleo, Gás e Biocombustíveis, seus Associados e Representantes. É de conhecimento e aprovação do(s) autor(es) que este Trabalho Técnico seja publicado nos Anais da Rio Oil & Gas Expo and Conference 2010. Resumo Utilizando uma linha sísmica multicomponente 2D que atravessa dois poços no campo de Albacora, Bacia de Campos, Brasil, foi avaliada a contribuição da informação da onda PS na estimativa da densidade das rochas através da inversão simultânea de dados PP e PS pré empilhados. Testes com modelagem utilizando informações de poços mostraram que pequenas variações na densidade da rocha reservatório causam maior impacto na refletividade da onda PS do que na onda PP. A inversão simultânea de dados PP e PS pré empilhados mostrou aumento na correlação com poços disponíveis na área, bem como aumento na banda de frenquência e resolução dos refletores. Estes resultados, comprovam que adicionando informação da onda PS no processo de inversão resulta em melhor estimativa da densidade das rochas. Abstract Using 2D-3C seismic data in the Albacora block, Campos Basin, Brazil, we analyzed the potential of using multicomponent data for density estimation by simultaneously inverting prestack compressional and mode converted seismic data. Initial forward modeling using the available well logs shows that small changes in density at the reservoir level affects more the PS reflectivity. The inversion engine utilizes a global optimization algorithm with a non-linear cost function to simultaneously invert a number of input stacks to an earth model. Inverting solely PP data has shown a lower correlation between the estimated density and the measured log in comparison to jointly inverting both PP and PS data. The results also show that adding PS information in the inversion process improves the density inversion bandwidth, and consequently, inversion resolution. 1. Introduction In the realm of reservoir characterization, the estimation of subsurface properties from geophysical measurements is of primary importance in order to optimize the location of drilling prospects. By evaluating amplitude variations with offset (AVO) from prestack seismic data, elastic rock property measurements may be obtained, either using solely compressional (PP) wave reflections or in conjunction with mode converted (PS) wave reflections. Ricker and Lynn (1950) first observed the potential benefits of converted wave seismology. Since, the use of PS seismic data has increased significantly as a result of new developments in the acquisition and processing technology of Ocean Bottom Cable (OBC) data. Considering PS reflection coefficients are more sensitive to density for middle and far offsets when compared to PP reflectivity, the density effect is measurable at a much sharper angle, increasing the density estimation accuracy, as the longer PP angle stacks have lower signal to noise ratio. Other advantages of using PS seismic data include the ability to better image interfaces with low P-wave reflectivity (e.g. gas chimneys) as well as provide directly rock property estimates such as Vp/Vs ratio. These benefits improve reservoir definition and reduce uncertainty in hydrocarbon prospect evaluation (Stewart, 1996; Dang et al., 2009). Other studies such as Jin, Cambois and Vuillermoz (2000) show the benefits of converted wave technology for the estimation of density.

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In this paper, we present a simultaneous inversion case history of multicomponent data in the Campos Basin, offshore Brazil. The Albacora field primarily contains sandstone turbidite reservoirs which are Albian to Miocene in age. It is located offshore Rio de Janeiro state in water depths ranging from 250 to more than 2000 m, covers a surface area of 235 km2 and contains over 4.5 billion barrels of oil in place. Our study reveals an improvement in density prediction when jointly inverting PP and PS data in comparison to the conventional PP approach. The inversion process converts seismic data from interface properties to layer properties such as density and acoustic and shear impedance. The inversion engine utilizes a global optimization algorithm with a non-linear cost function to simultaneously invert a number of input stacks to an earth model. The inversion is based on a convolutional model, generating synthetic seismic data via an iterative process which seeks to reduce the error between observed and modeled seismic. The improved prediction is attributed to the PS seismic containing considerably more density information at smaller angles, given the maximum angle stack range used in the inversion process was 31-40 degrees. In most cases, 40 degrees is not a large enough angle to predict with confidence density information from just PP seismic (Khare and Rape, 2007). 2. Polarity & Reflectivity Analysis An important practice before PP PS analysis is to verify the polarity consistency between the PP and PS data. This analysis is used to correlate events in the PS section with the corresponding events in PP time. Figure 1 shows the PP and PS sections with the Marco Azul horizon interpreted in PP time and in PS time. The acoustic impedance log for the PP section is also displayed. For PS, we created pseudo shear impedance according to Thomsen (1999). Both logs were blocked for a layer thickness of 20 m. Note that the PP and PS sections show the same wiggle polarity for positive impedance contrast.

Figure 1: Blocked AI log at Well 1 (Marco Azul horizon shown in yellow). The red vertical line represents the well location. Note the increase in impedance matches the positive peak in the seismic for both PP (right) and PS (left) data. We can use one of the Zoeppritz (1919) approximations to model polarity changes on PP and PS seismic and the effect of varying rock properties. These equations fully describe, for plane waves at a welded elastic interface, the relationship between incident and reflection/transmission amplitudes. Aki and Richards (1980) approximated the Zoeppritz equations assuming small layer contrast. The approximated reflectivity for PP and PS waves is:


3

∆−−∆+−−

=

∆−

∆+∆−=

s

s

spss

spss

pps

s

ss

p

pspp

V

V

VVVpV

VVVpV

pVR

V

VVp

V

VVpR

)coscos

44()coscos

221(cos2

4cos2

1)41(

2

1

222222

222

22

ϕθρρϕθ

ϕ

θρρ

, (1)

where

1

1sin

pVp

θ= 2/)( 21 θθθ −= 2/)( 21 ϕϕϕ −=

12 ρρρ −=∆ 2/)( 21 ρρρ +=

12 pVpVpV −=∆ 2/)( 12 pVpVpV +=

12 sss VVV −=∆ 2/)( 12 sss VVV += .

The Aki & Richards equations were used to test the reflectivity sensitivity to small changes in density. Selecting the target reservoir for analysis, we found that small changes in density contrast between the cap rock and the reservoir resulted in a higher degree of variations for PS reflectivity versus PP for medium to high angles of incidence (Figure 2). These results indicate that density information can be extracted from medium angles of incidence for PS seismic versus the conventional far offsets in PP seismic. Estimating seismic-derived density from single PP inversion requires angles of incidence greater than 40 degrees, which tend to be noisier and are often not suitable for inversion. In figure 2, we varied the density at the reservoir zone for a value 8% higher and 8% lower than the in-situ conditions. The other rock properties (Vp and Vs) were kept constant. Using Equation 1, we modeled the variation of reflectivity with incidence angle for each change in density. The results show that PP reflectivity is less affected by changing the density contrast than for PS reflectivity with medium to high angles of incidence.

Figure 2: Left: Reflectivity variation with angle of incidence for small changes in density contrast between the cap rock and the reservoir rock. Right: Difference between the reflectivity using the maximum and minimum variations in density contrast. Note the variation in density contrast affects more the PS reflectivity from medium to high angles of incidence. The blue zones in the figures indicate the available angle range in the PP and PS seismic. 3. Alignment of PS data into PP time

During the preconditioning stage of any AVO inversion, it is important to ensure alignment among equivalent

events across the associated angle stacks. Unsuitable velocity models applied to normal move out corrections as part of an AVO processing sequence will contribute to the misalignment of events. Other causes include anisotropy, which may cause improperly imaged gathers where an event curls up in the farther offsets. This occurs when using an isotropic velocity field which does not account for the directional dependence of velocities in certain rock formations.

For AVO analysis using PP and PS datasets, the alignment not only has to be performed within the angle stacks in each dataset, but also between the datasets themselves. As converted shear waves possess longer travel times than compressional waves, corresponding reflectors among PP and PS seismic data are recorded at different times. A common approximation of Vp/Vs ratio equal to two serves as an initial estimate for seismic interpreters to identify PS time events using PP time events as a reference (see TWT for both PP and PS sections at in Figure 4.) However, Vp/Vs


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ratio values may vary depending on lithology and particular conditions of the rocks in the subsurface, which will lead to variable TWT shift between datasets.

Figure 3: Calculated time shift after the cross-correlation between PS angle stack and PP angle stack

The alignment technique for PS to PP data used in this study is implemented using a statistical approach where one of two datasets is modified by a constrained mathematical transformation such that the cross-correlation between the two datasets is maximized.

This technique comprises several steps including a rigorous QC of the aligned datasets to ensure they are fit for purpose. In summary, it envisages the use of reliable interpreted common horizons for PP and PS data and a selected constant Vp/Vs ratio, in order to compute trace by trace the necessary time shift to convert from PS time to PP time. In this case, a constant Vp/Vs equal to 2.0 was applied. Figure 3 shows the optimized computed time shift from the cross-correlation between the PS angle stacks and the PP fullstack seismic. 4. Joint PP PS Inversion Workflow

The key steps in the joint PP PS inversion workflow include well to seismic calibration, wavelet extraction, prior model building and finally, the inversion. From this point forward, the mentioned PS seismic data has been converted to PP time (discussed in previous section).

4.1. Input Data Analysis Initially, five angle stacks for a single 2D line were available for both PP and PS datasets. After carefully

analyzing the data, the ultra near and ultra far stacks in the PS seismic were considered beyond repair and therefore dropped from the joint inversion. This meant that three angle stacks, near, mid and far, with angle configurations of 10-20, 21-30 and 31-40 degrees respectively, would have to be used in the analysis.

Figure 4 illustrates the fullstack seismic data for both PP and PS; the vertical well trajectories are also illustrated (Well 1 and Well 2). The log suite for each well contained the velocity and density logs which are required for AVO inversion. In addition, PP and PS seismic horizons were available, which are necessary for a more accurate alignment as well as the conversion of PS data into PP time.

4.2. Log to Seismic Calibration The calibration of well data into the time domain is performed using the available checkshot or VSP

information, which serves as the initial calibration before making any bulk shifts or adding visual ties. For deviated wells, logs are calibrated to seismic data extracted from the 3D data volume along the well trajectory. The primary objective is to create a reflectivity series for PP and for PS data with the same sample rate as the seismic data for use in the process of wavelet extraction. Since the quality of the estimated wavelets highly depends on the correlation between seismic and well log data, the calibration must be optimized by compensating for necessary alignment shifts. These imperfections in the initial calibration may be due to various reasons including:

• Well logs measurements are made at much higher frequencies than the seismic, consequently the well velocities may be up to 10% higher than seismic velocities


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• Seismic migration does not perfectly place the reflectors in their correct position as the migration velocities are flawed

• Residual NMO correction is imperfect, particularly for deep and dipping reflectors

The shifts are determined by analyzing the synthetic trace generated from convolving the reflectivity series with a zero phase wavelet, and the seismic trace at the well location. This is done for both PP and PS data since both datasets require wavelets. It should be noted that the calibration is a process which changes the relationship between depth and TWT; the changes are not physically applied to the logs. This being true, one way to QC the adjustment is to compare the true velocity log with the edited log as if the changes were actually applied. This QC allows us to stay within the proper bounds, preventing too much stretching and squeezing.

Figure 4: PP seismic section (left) and PS seismic section in PS time (right). The interpreted horizon corresponds to the Marco Azul of the Campos Basin. 4.3. Wavelet Estimation

The wavelet is the convolutional operator between the seismic data and the reflectivity of the subsurface. Using the log data and seismic trace at the well location, wavelet extractions were attempted at the available wells for PP and PS seismic datasets. Variations in frequency, phase and amplitude between the different seismic input stacks is captured by the wavelets, so there is no need for scaling, phase rotation or frequency balancing of the seismic data. The most significant wavelet parameters which have the highest impact on wavelet quality include the log calibration into the time domain, the method of extraction (amplitude and phase assumptions), the analysis window, and to some degree, the size of the wavelets.

Figure 5: Extracted wavelets for PP (left) and PS (right) seismic datasets.

The estimation method used in our analysis is a least squares approach which minimizes the sum of squared differences (the misfit) between the seismic trace and a synthetic trace. In addition, the computation was stabilized by parameterizing the phase spectrum as a constant. Figure 5 illustrates both the PP and PS wavelet suites extracted for the near, mid and far angle stacks. The significant differences in amplitude when comparing the compressional and mode converted datasets were to be expected. On the other hand, the phase properties were of concern since the PS data showed nearly zero phase versus a 30-120 degree phase for the PP data.

4.4. Generation of prior model A prior or low-frequency model (LFM)

multicomponent data, models for acoustic impedance, extrapolating the low frequency information from thegeometry. The LFM may be constrained by seismic velocities as well as dips estimated from the fullstack PP seismic volume.

In our study, the velocity informaextrapolation of the well logs. Dips estimated from the seismic data are converted to a layer sequence field (LSF). The LSF therefore assists in gua valuable tool in complex geologic environments.

−=S x

where d(t,x,y) denotes the seismic signal; depth measured in TWT; x identifies the horizontal distance in the indistance in the cross-line direction (Rasmussen, 1999)for real signals, both the numerator and denominator are lowline direction is estimated using a similar procedurereliable starting point in the iterative inversion process, giving more confidence

4.5. Joint PP PS Inversion

The simultaneous inversion is the final stepimpedance and density. The inputs to the inversion kernel are the corresponding wavelets along with the three prior

Figure 6: Simultaneous inversion of multicomponent inputs and outputs

The simultaneous inversion process is implemented by extending the individual terms of that:

• Penalty for the differences between the seismic data and the synthetic seismstacks

• Penalties for deviation of the estimated layer properties from the lowover all layer properties

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(LFM) is created for each output domain in the seismic inversionmodels for acoustic impedance, shear impedance and density in PP time are derived

low frequency information from the calibrated logs into a 3D cube, identical to the seismic data strained by seismic velocities as well as dips estimated from the fullstack PP seismic

In our study, the velocity information was not available. Instead, the seismic dip was used to help guide the extrapolation of the well logs. Dips estimated from the seismic data are converted to layer-based information

therefore assists in guiding the extrapolation process between horizons, which is a valuable tool in complex geologic environments. The seismic dip in the inline direction is estimated as

22

∂∂

+

∂∂

∂∂

∂∂

+∂∂

∂∂

−

t

d

t

d

x

d

t

d

x

d

t

d

h

hh

,

) denotes the seismic signal; dh(t,x,y) shows the Hilbert transform of the seismic signal; identifies the horizontal distance in the in-line direction; and y designates the horizontal

(Rasmussen, 1999). Equation 1 is exact for a sine signal. To stabilize the estimation for real signals, both the numerator and denominator are low-pass filtered before the division. The dip

imated using a similar procedure. The end product using the layer sequence field starting point in the iterative inversion process, giving more confidence in subsurface geology

simultaneous inversion is the final step in the workflow, with output volumes of acoustic impedance, and density. The inputs to the inversion kernel are the six angle stacks (three PP, three PS)

ong with the three prior models (Figure 6).

eous inversion of multicomponent inputs and outputs.

is implemented by extending the individual terms of a nonlinear cost function, such

enalty for the differences between the seismic data and the synthetic seismic is accumulate

enalties for deviation of the estimated layer properties from the low-frequency prior models are accumul


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the seismic inversion process. For in PP time are derived by

, identical to the seismic data strained by seismic velocities as well as dips estimated from the fullstack PP seismic

used to help guide the information known as

extrapolation process between horizons, which is The seismic dip in the inline direction is estimated as

(2)

shows the Hilbert transform of the seismic signal; t indicates the designates the horizontal

. Equation 1 is exact for a sine signal. To stabilize the estimation pass filtered before the division. The dip Sy in the cross-

uct using the layer sequence field yields a more subsurface geology prediction.

, with output volumes of acoustic impedance, shear (three PP, three PS) with their

a nonlinear cost function, such

ic is accumulated over all partial

frequency prior models are accumulated


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• Penalties for horizontal and vertical changes in the estimated layer properties (e.g., acoustic impedance, VP/VS, and density) are accumulated over all layer properties.

As the inversion estimates the physical properties, the reflection coefficients for each partial stack are calculated and convolved with the appropriate wavelet for comparing the synthetic with the measured seismic data. The far stack will strongly contribute for estimating shear impedance (or Vp/Vs velocity ratio) in the frequency band where the far stack resolves the information. The weaker but higher-resolution contribution from the near and mid stacks is used without contradicting the lower-frequency information in the far stack. For all partial stacks, the application of a separate wavelet ensures that the synthetic seismic for each partial stack has frequency content and phase comparable to that of the measured seismic data.

5. Results Figure 7 shows a comparison of the joint inversion of PP and PS data and PP data only. Both results are

compared to the up-scaled density curve for Well 1. Note the improved density prediction when adding PS information in the inversion process. In addition, the reservoir top is better defined by the joint inversion of PP and PS data. The maximum angle stack range used in the inversion process was 31-40 degrees, which in most cases may not be a large enough angle range to predict with confidence, the density information from just PP seismic. From our modeling study, we determined that at this angle range, the PS seismic contains considerably more density information, which explains the enhanced resolution when jointly inverting both datasets.

Figure 7: Well 1 density inversion results for joint PP PS (left) and PP simultaneous (right).

In Figure 8, we may observe the inverted density for the entire 2D line, which shows that by adding PS information, the inversion process increases considerably the frequency content (Figure 9) and the lateral continuity of reflectors when compared to the PP inversion. This is due to the density information coming from an angle range which exhibits higher frequency content, versus coming from the ultra far offsets as in conventional PP inversion.

Figure 8: Section showing the density inversion results. Left: simultaneous inversion of PP and PS data. Right: simultaneous inversion of PP data only.

We have now shown that adding PS information improves significantly the estimation of density from seismic amplitudes. When combined with PP analysis, the PS waves can reduce interpretation errors and lead to better reservoir characterization. Also, the increase in frequency content may improve resolution and reduce uncertainty in estimating fluid contacts and volumetrics.

Density – PP PS Inversion – Well 1 Density – PP Inversion – Well 1


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Figure 9: Spectrum plots for PP PS simultaneous inversion and single PP inversion results for density. 6. Conclusions and Recommendations

Our results show that adding PS information in the inversion process increases the resolution of events and

reduces uncertainty in reservoir analysis. We obtained a better correlation of estimated density with the measured well data for the PP PS inversion in comparison to the conventional PP simultaneous inversion. Another significant observation is the considerable increase in frequency content from PP PS joint inversion, which is due to the density information coming from smaller angles which contain higher frequency content as well as signal to noise ratio. To further improve the results, we recommend the reprocessing of PS seismic to correct for the observed static problems in order to improve the shear wave velocity analysis. 7. Acknowledgements

We would like to thank Petrobras UN-BC for the permission to publish this paper.

8. References AKI, K. and RICHARDS, P.G, Quantitative Seismology - Theory and Methods, Volume 1: W. H. Freeman and Company, 1980.

DANG, Y., LOU, B., MIAO, X., WANG, P., SHEN, L., and ZHANG, S., Delineating oil sand reservoirs by high resolution PP/PS processing and joint inversion in Junggar Basin, Northwest China., SEG Expanded Abstracts, Houston, 2009.

KHARE, J., and RAPE, T., Density inversion using joint PP/PS data: sensitivity to the angle range, SEG Expanded Abstracts, San Antonio, 2007.

JIN, S., CAMBOIS, G., and VUILLERMOZ, C., 2000, Shear-wave velocity and density estimation from PS-wave AVO analysis: Application to an OBS dataset from the North Sea, Geophysics. 65, 1446-1454.

RASMUSSEN, K.B., 1999, Use of dip in seismic inversion, 61st Meeting Eur. Assoc. Expl. Geophys., 4-49.

RICKER, N., and LYNN, R. D., 1950, Composite reflections: Geophysics, v.15, 30-50. 1950

STEWART, R. R., FERGUSON, R. J., MILLER, S., GALLAND, E., and MARGRAVE, G., The Blackfoot seismic experiments: Broad-band, 3C - 3D, and 3-D VSP surveys: CSEG Recorder, 6, 7 – 10, 1996. THOMSEN, LEON, Converted-wave reflection seismology over inhomogeneous, anisotropic media. Geophysics, Vol. 64, No. 3, P 678-690, 1999.

ZOEPPRITZ, K. Erdbebenwellen VIII B, On the reflection and penetration of seismic waves through unstable layers. Goettinger Nachr., 66-84, 1919.

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