Simultaneous multicomponent AVO inversionHüseyin Özdemir*, Shuki Ronen and Bjorn Olofsson, WesternGeco,Bill Goodway and Paul Young, PanCanadian Petroleum Limited

SummaryConverted waves have so far been used mainly in placeswhere conventional P waves fail; for example, where thetarget is obscured by gas, or where the target has a smallacoustic contrast. However, if the lithological informationcontained in the converted waves can be fully unraveled, thenthe promise of multicomponent seismic data goes muchfurther beyond these pathological cases.We propose a method of multicomponent AVO-Inversionthat will unravel more information from multicomponent datathan conventional state of the methods of separate AVO-inversion of PP and PS data. The idea is to use the AVO ofboth PP and PS data simultaneously to estimate of acousticand elastic impedance contrasts, density contrast and Laméparameters contrasts. Then invert the contrasts to estimatethe parameters themselves.

Acoustic inversionIt is well known that an acoustic plane wave incidentnormally on a discontinuity of acoustic impedance isreflected with a reflection coefficient,

RI = (I2-I1)/( I2+I1 ), (1)

where I1 and I2 are the impedances above and below theboundary, respectively. I = ρVP , and the density is ρ. If zerooffset, normal incidence reflection data are produced, andgiven suitable well logs, the impedance I can be calculatedfrom the given RI. Inversion programs produce an impedancecube I(x,y,z) from given migrated acoustic reflectivity imageRI.(x,y,z) and well logs I(xi,yi,zi).

Elastic inversionWhen a P wave is incident on a boundary at an angle θ, a Pwave with amplitude RPP(θ) and a converted shear wave withamplitude RPS(θ,ϕ) are reflected. θ is the P wave incidentangle and ϕ is the converted shear wave angle. The reflectionand conversion coefficients depend on the impedance anddensity contrasts. (J=ρVS). The amplitude versus offsetequations (Aki and Richards, 1980; Larsen et al., 1999) inmatrix form is,

Where for one angle band from each of the P and Ps wave,

Here θ is the incident angle for both P and Ps, ϕ is thereflection angle for Ps and γ is the Vs/Vp ratio.

If the density is constrained to relate to the impedance, analternative relation can be used:

Alternatively, the Lamé contrasts (λ2− λ1)/(λ2+ λ1) and (µ2− µ1)/(µ2+ µ1) can be estimated:

Ultimately, the processing sequence is: (1) Prestack depthmigration, with partial stacking; produce RPP(x,y,z, θ) andRPS(x,y,z, θ). (2) Solve for RI, RJ, and/or Rρ, Rµ, Rλ. (3) InvertRX(x,y,z) to estimate X(x,y,z), For X = I, J, ρ, λ, µ. (4) Usethe produced property cubes to characterize the rocks, theporosity, the fluid and gas, and the pressure.

Inversion algorithm and sensitivity testsThe linear equations in (2) are over-determined when there aremore than three input angle bands in total for P and Ps. Asingular value decomposition (SVD) algorithm is used to solvethe over-determined equations

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),,,(),,,(

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ϕϕθθγγϕϕθθγ

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A

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First sensitivity tests were performed with different numbers ofseismic input traces. Each input trace corresponds to a constant(incident) angle trace. These are,1. PP seismic input traces only (Rpp)2. PS seismic input traces only (Rps)3. Both Rpp and Rps input tracesNext, a random error was introduced into the three inputparameters: the incident angle, the reflection angle andthe Vs/Vp ratio. That is,4. Introduce error into incidence and reflection angle5. Introduce error into Vs/Vp ratio.

The synthetic tests showed that data from both P and Pshave to be incorporated to achieve good inversion results,especially in the case of density estimation. Three offsetsfrom each of P and Ps data are required for good densityestimates. Errors in the incidence angles (Equation 2)deteriorate the estimations where about 2 to 5 percenterror is tolerable. Another variable affecting the estimatesis the γ=Vs/Vp ratio (Equation 2) which must beapproximately less than 10 percent in error. In bothcases, the density estimates deteriorate faster comparedto the P and S estimates.

Applications

The Vp/Vs ratio versus gamma ray (GR) cross-plot inFigure 1 is from an offshore vertical well from the studyarea. The reservoir sands are identified with low GR andVp/Vs values near the lower left corner of the plot.Although the reservoir sands are about 1.5 to 2 m thick atthis well, and not resolved seismically, they can bemapped using the Vp/Vs ratio when they are thickenough to be identified on the inverted sections. TheVp/Vs ratio can be obtained by converting the P and Sreflectivity contrasts from the joint inversion to absoluteimpedance and then dividing, i.e. Vp/Vs = Ip/Is.

The P and Ps joint inversion has been applied to the seabottom recording of 2D and 3D data from a North SeaUK field around the above well. Displays of P and PsCMP gathers from 2D lines and bin gathers from the 3Ddata indicated that the useable data is limited to offsetsabout 2150 m and the incident angles to about 30-35degrees at the potential reservoir horizon. The jointinversion results from the 2D line shown in Figure 2 arepresented here. Figure 2 shows the P stack and Ps stackdata with the Ps section snapped to P times. These stackdata were obtained by stacking data from 0 to 35 degreeincident angles.

After decomposition of the P and Ps data into commonincidence angle traces from 0 to 10, 10 to 20 and 20 to 30degrees, stacks of the angle gathers were migrated usinga phase shift algorithm. Next all angle gathers were zerophased and well matched at a key well where check-shotcalibrated well data was available. Wavelet estimationsfrom near offset and mid offset stacks indicated about -20 ms bulk shift and -100 degrees phase shift to tie the P

seismic data to a zero phased synthetic created from thecalibrated well data. Also, phase shift of –100 degrees isapplied to the Ps data.

The zero-phased angle bands jointly inverted to P, Ps anddensity contrasts; then to absolute impedance anddensity. Figure 3 shows the latter impedance and thedensity sections. The corresponding log data are insertedat the well position. The acoustic impedance estimationsshow reasonably good correlation to the well data whilethe density estimation is poor. Tests showed that thedensity estimates are very sensitive to the choice ofVp/Vs ratio. However, for reliable assessments, blindwell testing with shear wave sonic data is required. Asparse spike inversion has been used for the absoluteestimates. The background impedance and densitymodels have been created using the well data and pickedhorizons. The contributions from the background modelshave been limited to below 8 Hz.

Figure 4 shows the Vp/Vs ratio obtained by dividing theinverted P wave absolute acoustic impedance by theinverted S wave absolute impedance in Figure 3. As seenfrom the Vp/Vs curve at the well position, the Vp/Vsrecovery at the well is not good especially around themarker horizons Balder and Chalk. This is expectedprimarily because the snapping of Ps data to P times isnot accurate. However, when the relative changes areexamined, the buildups at CDPs 1358 to 1450 around1800 ms with Vp/Vs ≈1.7 may indicate reservoir sands.

Alternately other Lamé petrophysical factors can becomputed from Vp/Vs and density for further reservoirdelineation (Goodway et al., 1999).

Conclusions

The multicomponent seismic data with P and Psconverted wave data can be jointly inverted for P, S anddensity or other elastic contrasts. This is feasible whenthe reservoir reflections can be reliably picked and Psdata is snapped to P times. The wavelet differences inboth data sets should be minimized by zero phasing. Thechoice of Vs/Vp ratio affects density estimates more thanP and S estimates.

References

Aki, K. and Richards, P. G., 1980, Quantitative Seismology:theory and methods: W. H. Freeman.

Goodway, W., Chen, T. and Downton, J., 1999: Rockparameterization and AVO fluid detection using Lamépetrophysical factors: 61st Ann. Conf. And Tech. Exhib.,Eur. Geosci. Eng., Expanded Abstracts,

Larsen, J., Margrave, G. and Lu, H., 1999, AVO analysisby simultaneous P-P and P-S weighted stacking appliedto 3-C--3-D seismic data: 69th Ann. Internat. Metg. Soc.Expl. Geophys., Expanded Abstracts, 721-724.

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Figure 1. Vp/Vs ratio versus GR at the key well. The values around Vp/Vs ≈1.5 and GR≈45-50 API are from the thin (1.5 to 2.0 m) thinreservoir sandstone and are well separated from the main cluster.

Figure 2. Stack of P (top), Ps (middle) and Ps snapped to P times (bottom). P acoustic impedance is inserted at the projected welllocation. Two-way times are in ms. Red is positive and blue is negative amplitude.

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Figure 3. P acoustic impedance (top) S impedance (middle) and density (bottom) sections.

Figure 4. Vp/Vs section obtained from Ip/Is in Figure 3.

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