# SEISMIC INVERSION OVERVIEW

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1 DHI CONSORTIUM SEISMIC INVERSION OVERVIEW Rocky Roden September 2011

2 NOTE: Terminology for inversion varies, depending on the different contractors and service providers, emphasis on certain approaches, and the goals to be accomplished. There are numerous combinations, hybrids, and variations of these inversion methods. This overview attempts to summarize the most common terminology and inversion approaches described in the industry.

3 Seismic Inversion Outline Inversion Definition and Terms Required Data Types of Seismic Inversion Role of Inversion Realistic Expectation from Inversion Inversion and New SEC Regulations

4 What is Inversion? Inversion transforms seismic reflection data into rock and fluid properties. The objective of seismic inversion is to convert reflectivity data (interface properties) to layer properties. To determine elastic parameters, the reflectivity from AVO effects must be inverted. The most basic inversion calculates acoustic impedance (density X velocity) of layers from which predictions about lithology and porosity can be made. The more advanced inversion methods attempt to discriminate specifically between lithology, porosity, and fluid effects. Inversions can be grouped into categories: pre-stack vs. post-stack, deterministic vs. geostatistical, or relative vs. absolute. Inversion is the flip side of forward modeling.

5 Common Inversion Terms Relative Impedance Relative changes in inversion, not real values. Absolute Impedance Actual acoustic impedance, contains low frequency trend. Deterministic Inversion A single output value is determined from the input. Stochastic (Probabilistic) Inversion A range of equally probable outputs are derived from the input (under controlled number of inputs). Objective Function A quantitative measure of the misfit between the observed data and the data predicted by inversion (L1 and L2 Norm). L2 Norm Most common measure of data misfit, a least squares difference (sum of the square of the data residuals). L1 Norm Misfit measure that is the sum of the absolute data residuals. Global More than one trace is inverted at the same time within a common objective function. The number of traces inverted at once depends on the algorithm. Simulated Annealing A global optimization technique based on crystal growth in a cooling volcanic melt. Computes difference between seismic and convolutional model with applied wavelet. The model is perturbed and a new model is simulated, and the difference is again measured. Differences are compared with the smallest difference accepted and the other differences accepted with a probability (Metropolis Criterion). The process is repeated until and there is a very small residual or a threshold has been reached.

6 Forward Modeling takes well logs, combines with wavelet to produce synthetic seismic trace Inversion takes seismic trace, removes effects of estimated wavelet and creates acoustic impedance values Oilfield Review, 2008

7 Data Considerations for Inversion Pre-stack and/or post-stack time migrated seismic data Well data conditioning and editing is necessary Wavelet estimation required for all modern inversion approaches -Deterministic -Statistical Low Frequency Trend absolute acoustic impedance contains a low frequency trend that must be obtained usually from well control or stacking velocities NOTE: Without wavelet estimation and well calibration, the inversion solution is non-unique.

8 Data Considerations for Inversion Pillar, 2011

9 Data Considerations for Inversion Low Frequency Trend in Red Oilfield Review, 2008

10 Data Considerations for Inversion Missing low frequencies and their modeling from well log data cause bias in inversion, regardless of the methodology. Determining low frequency issues: Lithologies encountered at the wells thin or thicken away from the wells. In fact, some lens-like possible plays between wells are often difficult or impossible to model accurately. Lateral geological changes away from the wells have no resemblance to the geological layers at wells used fro low frequency model generation, e.g., sand injections. There are excessive lateral changes in rock and reservoir properties (e.g., porosity changes and shaling out). Ozdemir, 2009

11 Data Considerations for Inversion Rock physics approach to well log preparation for inversion: Continuous reconstruction of formation properties along the wellbore, both for reservoirs and non-reservoirs Characterization of rocks in terms of their elastic properties Establishment of causal relationships between elastic and petrophysical properties such as porosity, clay content and fluid saturation NOTE: Depends on inversion approach and stage of exploration through development cycle.

12 Types of Inversion Running Sum Inversion like (Runsum) Recursive Trace integration (relative acoustic impedance) Colored Inversion Sparse Spike (CSSI) Model-Based Inversion AVO Inversion Elastic Impedance Extended Elastic Impedance Simultaneous Inversion Stochastic Inversion Geostatistical Bayesian

13 Running Sum Running Sum is the integration or adding of seismic amplitudes on a seismic trace. It is the cumulative sum of amplitude values at any time sample starting from the top to the end of the trace. Running Sum provides an approximation to acoustic impedance (velocity X density), while lacking the low frequency trend of a full inversion this can be useful over short intervals. The less noise and the broader the bandwidth (narrower the wavelet), the better will be the approximation to impedance.

14 Running Sum Normal Amplitude Running Sum Courtesy SMT

15 Recursive Trace Integration Recursive/Trace Integration (RTI) employs the discrete recursive inversion formula (below) which indicates that the acoustic impedance of a particular layer and the reflection coefficient at its base can be used to calculate the acoustic impedance of the next layer. An estimate of the acoustic impedance of the first layer is required. Normal incidence reflectivity Recursive inversion formula r = reflection coefficient Z = impedance

16 Recursive Trace Integration Seismic section from Alberta highlighting an anomalous bright spot zone. Recursive inversion of the section above Russell and Hampson, 2006

17 Colored Inversion Colored Inversion transforms migrated seismic data into a bandlimited acoustic impedance volume by shaping the mean seismic spectrum into the impedance log spectrum. This approach only gives a relative acoustic impedance which does not contain any low frequency components. This inversion method can make it simpler to interpret the variations in thickness related to various lithologic packages, properties of thin beds, and changes in acoustic impedance associated with fluid effects and rock property variations. Veeken and Da Silva, 2004

18 Colored Inversion Colored Inversion was first introduced by Lancaster and Whitcombe (2000) and involves deriving an operator that transforms the seismic amplitude spectrum to the acoustic impedance spectrum from well logs with a -90 phase change. This typically requires crossplotting the log of the well acoustic impedances versus log of amplitudes to derive a best-fit line to the data. The slope of this line is used to develop an operator to apply to the seismic data to convert to acoustic impedance. The logic employed is that the gross spectral properties from the well acoustic impedances in any given field are reasonably constant. A phase rotation may be applied to the seismic data, but this approach assumes the seismic is zero phase. Colored inversion may establish a base case to compare against more sophisticated inversion techniques Courtesy SMT

19 Colored Inversion Conventional Seismic Line Colored Inversion Colored Inversion Colored Inversion Courtesy SMT

20 Sparse Spike Inversion Sparse Spike Inversion assumes that seismic reflectivity is a series of large spikes embedded in a background of small spikes (assumes only large spikes are meaningful). This approach seeks the simplest possible reflectivity model of spikes, that when convolved with the wavelet produces a synthetic that matches the real data. Non-linear Sparse Spike Inversion (Constrained Sparse Spike Inversion-CSSI) employs an optimization loop where the wavelet is updated (non-linearly) so that the mis-match between the synthetic and real seismic is minimized.

21 Sparse Spike Inversion Saxena and Bhatnagar, 2008

22 Model-Based Inversion Model-Based Inversion typically starts with a low frequency model of the P-impedance and then the model is perturbed until a good fit is obtained between the seismic data and a synthetic trace using the recursive formula. The Generalized Linear Inversion (GLI) method perturbs an initial acoustic impedance estimate and determines the differences between the synthetic trace and the real data (simulated annealing and least square fits are often applied). Principal Component Analysis (PCA) method computes a standard response from which the input can be generated by applying specific weighting factors determined from well control (linear interpolation). The results of the convolution with the seismic wavelet are compared with the seismic traces and the velocity and density models are perturbed to reduce the discrepancy.

23 Model-Based Inversion Veeken and Da Silva, 2004

24 Model-Based Inversion Wavelet Initial Model Seismic Data Synthetic Data Misfit Function Stochastic Model Update No Optimisation by Simulated Annealing Convergent? Yes Model Based Inversion Utilizing Simulating Annealing Stop Courtesy Equipoise

25 Model-Based Inversion Seismic section from Alberta highlighting an anomalous bright spot zone. Model based inversion of the section above Russell and Hampson, 2006

26 AVO Elastic Impedance Connolly (1999) developed an angle dependent analogy to acoustic impedance to account for AVO effects. Elastic impedance is a function of P-wave velocity, S-wave velocity, density, and incidence angle. Input for elastic impedance is some form of angle stack (e.g., near, mid, and far). Wavelets are determined for each offset angle volume. This approach is accurate for small to moderate impedance changes.

27 AVO Elastic Impedance Connolly relates the Aki-Richards (Shuey) linear Zoeppritz approximation: to an elastic impedance relationship: Combining the two expressions gives elastic impedance: Variations of this approach include using the Shuey two-term approximation (good to ), assume Vp/Vs=2 or Vs calculation, and Extended Elastic Impedance (Whitcombe et al., 2002)

28 AVO Elastic Impedance Veeken and Da Silva, 2004

29 AVO Elastic Impedance Elastic impedance displays for different offset angles Veeken and Da Silva, 2004

30 AVO Extended Elastic Impedance Whitcombe et al (2002) describes an approach that extends beyond a typical incident angle range of 0 to 30 for seismic data to -90 to +90. The sin²ɵ term in the Shuey 2-term Zoeppritz linear approximation limits the range at which reflectivities can be defined. If this approximation is re-written as R = A + Btanx then scaled by cosx then a scaled reflectivity equation can be written: R = A cosx + B sinx. Extended Elastic Impedance logs can be generated from P-wave, S- wave, and density logs for each angle x. Once x is known then equivalent seismic sections can be generated.

31 AVO Extended Elastic Impedance EEI logs at different angles: Compressional modulus = +12 Lame s parameter = =20 Shear impedance = -50 Vp/Vs = +45 Acoustic impedance = 0 Francis and Hicks, 2006

32 AVO Extended Elastic Impedance Connolly, 2010

33 AVO Extended Elastic Impedance Connolly, 2010

34 AVO Extended Elastic Impedance Francis and Hicks, 2006

35 AVO Simultaneous Inversion Simultaneous inversion is a prestack inversion method that uses multiple offset or angle stacks. This method solves for S impedance, P impedance, and density, which are key for descriminating lithology, porosity, and fluid effects. For each input partial stack a wavelet is estimated. All models, partial stacks, and wavelets are input into a single inversion algorithm and solved simultaneously compensating for offset dependent phase, bandwidth, tuning and NMO stretch effects.

36 AVO Simultaneous Inversion NMO Gather (Full Offset) Wavelets Macro-models Simultaneous Inversion Constrained Model-driven Global (SA) P-wave Impedance Model S-wave Impedance Model Simultaneous Inversion Workflow Courtesy Equipoise

37 AVO Simultaneous Inversion Russell and Hampson, 2006 Simultaneous P-Impedance Inversion

38 AVO Simultaneous Inversion Simultaneous P-Impedance Inversion Vp/Vs ratio from dividing P and S-impedance sections from simultaneous inversion Russell and Hampson, 2006

39 Predicting Other Rock Properties from Pre-Stack Inversion Pre-stack Inversion Vp/Vs Poisson s Ratio Acoustic (Ip) Impedance Shear (Is) Impedance Elastic Impedance EI Lamé Parameter Lamé Parameter Lithology Fluid Content Porosity Pore Pressure Lamé Parameter Courtesy Equipoise

40 Pre-Stack Inversion allows discriminating lithologies and fluids Bunch and Dromgoole, 1995 Pillar, 2011

41 AVO Elastic Impedance Reservoir attributes from Elastic Impedance Inversion Veeken and Da Silva, 2004

42 Elastic Impedance Simultaneous Inversion Rasmussen et al., 2004

43 Elastic Impedance-Simultaneous Inversion Poisson s Ratio From Elastic Impedance Inversion From Simultaneous Inversion Saxena and Bhatnagar, 2008

44 Stochastic Inversion - Geostatistical Geostatistical or probabilistic inversion uses quantification of uncertainties attached to the inversion input data. Probability density functions (PDF) are defined and an earth model is simulated, which is perturbed to minimize the discrepancy between the modeled and measured seismic data (simulated annealing) producing multiple realizations. The PDF determination comes from well logs, spatial properties (variograms) and lithological distributions. It is critical that the interpreter quantify the uncertainties in a realistic way, especially in the absence or minimal well control in specific areas.

45 Stochastic Inversion - Geostatistical The workflow for performing a geostatistical inversion showing the input data and the outputted model realizations. McCrank et al., 2009

46 Stochastic Inversion - Geostatistical The acoustic impedance inversion results with the mean acoustic impedance results of the multiple realizations in the upper left. McCrank et al., 2009

47 Stochastic Inversion - Bayesian Seismic inversion that uses Baye s rule allows the information from all available measurements to be integrated into a consistent image of the reservoir and constrain these solutions based on a priori knowledge about the subsurface parameters. Prior knowledge about the model parameters usually is combined with a likelihood function, which depends on the misfit between the model response and the observed seismic data

48 Stochastic Inversion - Bayesian Pillar, 2011

49 Stochastic Inversion - Bayesian Pillar, 2011

50 Categories of Seismic Inversion Running Sum Well Control Post Stack Pre Stack Relative Imp. Absolute Imp. Deterministic Probabilistic Recursive Trace Integration Colored Inversion Sparse Spike (CSSI) Model Based Inversion Elastic Impedance Simultaneous Inversion Geostatistical Inversion Bayesian Inversion

51 Applicable Inversions for Exploration through Development Running Sum Exploration Exploitation Development Recursive Trace Integration Colored Inversion Sparse Spike (CSSI) Model Based Inversion Elastic Impedance Simultaneous Inversion Geostatistical Inversion Bayesian Inversion

52 A Few Additional Types of Inversion Simultaneous geostatistical partial stack inversion Spectral inversion Pre-stack waveform inversion Multi-component inversion Multi-azimuth inversion Inversion incorporating EM and FTG data 3D Full Waveform Inversion

53 Seismic Inversion Checklist (modified from Ikon website) 1. Check log data and edit accordingly. 2. Perform rock physics analysis to determine if inversion is useful. 3. Check seismic data for proper processing and conditioning, S/N, accurate partial stacks, etc. 4. Well ties and low frequency background model: -Do you get credible wavelets? -Are wavelets consistent across wells? -Is a broadband inversion required? 5. Be sure and employ appropriate inversion algorithm. 6. QC is paramount: -Check all wells and match of wavelets. -From impedances forward model to synthetic seismic; compare with actual seismic. -Does it make geological sense? -Is low frequency trend applied correctly? 7. Use impedance results intelligently they are not the end goal!

54 SEC Regulations and Inversion Pillar, 2011

55 SEC Regulations and Inversion Oil and gas companies may use any "reliable technology" to establish reserves volumes in addition to those established by production and flow test data. Oil and gas companies may classify proved undeveloped reserves ("PUDs") any distance from known proved reserves (rather than only in immediately offsetting units) based on a reasonable certainty standard. Use of reliable technology: A registrant is required to disclose, in general terms, the technologies used in ascertaining the reasonable certainty of the PUD locations producing hydrocarbons. Any technology stated must be field tested to demonstrate consistency and repeatability. In reviewing disclosures of the technologies used, some very simple statements that a combination of these technologies was used were noted: analogy, 2-D and 3-D seismic data, volumetric and material balance analysis, decline curves, petrophysics, and log analysis. A company does not need to disclose proprietary technologies or the mix of proprietary methods.

56 Conclusions 1) Seismic Inversion is not a unique process. 2) Seismic and well log information should be optimally conditioned for reliable inversion results. 3) There is a trade-off between work involved/cost/time and quality of the final inversion. 4) A rock physics study can help determine what the end product from inversion should be and whether this is attainable with the existing data. 5) Even when advanced inversion algorithms are chosen, a simpler deterministic inversion perhaps should be run for feasibility and as a yardstick of what can be resolved. 6) Most seismic inversion workflows are not linear and require reasonable inputs and usually numerous iterations. 7) Will the SEC accept inversion results for booking reserves?

57 Indeed, given that we can now directly invert to the acoustic properties using simultaneous inversion, some workers hold the view that conventional two-term AVO techniques are now passé. This is naïve given that deriving an accurate estimate of Poisson ratio from seismic is actually quite difficult, requiring a stringent set of data conditions. In many cases, bias of one form or another is introduced into the result, for example when merging the low frequency component. The interpreter needs to understand both conventional AVO approaches as well as the latest trends in inversion. Rob Simm What makes the wiggle waggle: a perspective on rock physics, First Break, June 2011

58 DHI CONSORTIUM Thank You

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