23855 Rock Physics Constraints on Seismic Inversion

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1 23855 Rock Physics Constraints on Seismic Inversion M. Sams* (Ikon Science Ltd) & D. Saussus (Ikon Science) SUMMARY Seismic data are bandlimited, offset limited and noisy. Consequently interpretation of seismic amplitudes is prone to large uncertainties. Seismic inversion is an interpretation technique that requires rock physics constraints at all frequencies to produce realistic models of reservoir properties. Therefore the role of rock physics extends beyond the normal role of preparing wells and establishing a template for interpreting inversion results to being fully integrated within the inversion process.

2 Introduction It is widely recognised that rock physics plays a crucial role in seismic reservoir characterisation. Rock physics represents the link between the reservoir properties of interest and the seismic reflectivities through the elastic properties of the rocks. Therefore rock physics is required to interpret the elastic properties coming from a seismic inversion, say. In addition, rock physics is essential for preparing the well log data for the wide variety of uses leading up to an inversion. Rock physics is used to condition, correct and synthesise elastic logs and to carry out scenario modelling such as fluid, porosity and lithology substitution. This is required for generating accurate logs for wavelet estimation, setting expectations about the AVO behaviour in the seismic, carrying out feasibility studies and providing a framework for the interpretation of the elastic properties coming from an inversion. The use of rock physics within the inversion process itself is less well known. Seismic data are bandlimited, have limited offsets and are noisy. As a result, there is a huge range of elastic property distributions that can honour the seismic amplitudes within acceptable limits. Not all of the solutions are by any means geologically or geophysically meaningful. Constraints need to be applied to ensure that the results at least make sense. Some of these constraints can address some of the geological aspects such as lateral and vertical continuity or the solution sparseness, but rock physics constraints are required to ensure that the results are also consistent with our expectations of the rock properties. The following sections describe how rock physics can be used below, within and above the seismic bandwidth during seismic inversion. It is noted in the context of this paper that we refer to rock physics as any relationship between different elastic properties, between elastic properties and depth or environmental conditions, as well as between elastic properties and reservoir properties. It is also assumed that inversion refers to simultaneous inversion of partial pre-stack seismic data to generate estimates of at least acoustic impedance and shear impedance. Low Frequencies Seismic data contain no information within a frequency range from zero Hertz up to some level determined mainly by acquisition and processing. If absolute values of elastic properties are required a low frequency model must be provided. This low frequency model comprises values for all elastic properties for which inversion is carried out. The most common approach to constructing low frequency models is the interpolation of well data within a structural and stratigraphic framework. However, the often biased distribution of wells and the mathematical interpolation algorithms cannot guarantee that a low frequency model thus derived is geologically reasonable or has values that represent any real rock, let alone provides the optimal input for inversion. More complex processes to construct low frequency models are available. These techniques use rock physics in their construction. One such technique is an iterative process. A simple set of depth trends is used to form the first pass low frequency model. These trends may be derived from depth trend analysis of well data. For example, in a sand-shale sequence the trend of the elastic properties of shales with depth might be chosen. Inversion is run with these trends and the distribution of sand interpreted based on these first pass inversion results. The simple low frequency model can then be updated by using the sand depth trends where sand is predicted. In an optimal case, the final low frequency model is at least consistent with the final lithology prediction. This process can be adapted to deal with several lithologies and fluids. Another approach was presented by Sams and Focht (2012). In that case the porosity within a channel sand reservoir was initiated through well interpolation. Using several assumptions including the location of gas-oil and oil-water contacts, a rock physics model was used to convert the porosity to elastic properties. This process provided a detailed model of the channel. This model was filtered back to provide low frequencies for inversion. Then the inversion result was compared with the detailed model. Differences were used to update the porosity model and the process iterated until convergence. In both of these examples the reflectivity within the seismic bandwidth are being used to extrapolate to the low frequency domain. Rock physics is being used to constrain those extrapolations. It should also be noted that if seismic velocity data are used to help construct the low frequency model, rock physics relationships are required to convert the compressional velocity to density and shear velocity. This is not a straightforward process.

3 Mid Frequencies Even if a very accurate low frequency model has been constructed, there will still be significant uncertainties in the inversion of the reflectivities within the seismic bandwidth. These uncertainties are related to noise, the limited angle range subtended by the seismic data and other factors. The impact of a limited angle range can easily be understood by considering the result of inverting a zero angle stack only. In such a case the results are independent of the shear impedance, which can take any value. As the angle range increases, so the uncertainties of fitting a reflectivity model to the data will decrease. However, the presence of noise in the seismic, uncertainties in the wavelets, the assumption of a convolutional model, the uncertainty in the reflectivity model, amongst others, will mean that a range of solutions is still possible that fit the seismic to an acceptable level. Inversion algorithms work by optimizing an objective function. This function contains at least some measure of the misfit to the seismic, but will also contain other elements that attempt to reduce the impact of the uncertainties and noise. They may include a sparsity term or a term to limit the deviation from an initial model or a constraint to control lateral variations. The objective function will nearly always contain a rock physics term that controls the interrelationship between acoustic impedance, shear impedance and density. In most cases this rock physics constraint is the only reason that the density result from inversion looks reasonable as it is normally poorly constrained by the reflectivities. Figure 1 The results of a simultaneous inversion at a well. The relative elastic properties from inversion in red are compared with the bandlimited log data in black. Also shown are the seismic traces at four angles, the inversion synthetics and residuals. The inversion that produced the results in the upper plot only differs from the lower plot inversion through the strength of the rock physics constraint applied.

4 High Frequencies Seismic data are also bandlimited at the high frequency end due to acquisition, processing and propagation effects. This imposes limits on thin bed resolution. Many attempts are made to increase resolution for exploration and appraisal or to model detail for static and dynamic models. The sparsity constraints mentioned previously have the potential to introduce higher frequencies than present in the seismic. For example, a spike has infinite bandwidth. Therefore a sparse spike inversion, say, has the potential to increase the bandwidth of the inversion result beyond the seismic bandwidth both at the low and high frequency ends. Such an inversion uses the information within the seismic bandwidth to extrapolate to higher frequencies. No matter what constraints are applied within the seismic bandwidth there is no guarantee that in the high frequency range the spikiness or sparsity will produce detail that is consistent with known rock physics relationships. Geostatistical inversion produces results with high detail usually significantly beyond the seismic bandwidth. Simple geostatistical inversions sample from probability density functions that are built from well data and rock physics modelled data and therefore produce high frequencies that are consistent with known rock physics relationships. The high frequencies are introduced through the imposition of vertical variation defined by a variogram. Saussus and Sams (2013) suggest that including facies in the geostatistical inversion is a preferred method for building high detail models. The inclusion of facies in the inversion scheme allows for the explicit use of rock physics models in the solution. A model proposal can be made in terms of facies and reservoir properties in the depth domain, for example. This model can be converted to elastic properties through an explicit facies dependent rock physics model and converted to time for generation of synthetics and comparison with the seismic data. Other facies based inversions (e.g. Gunning and Kemper, 2013) use facies dependent rock physics based depth trends and elastic property correlations for rock physics compliance. The high frequencies in these facies based inversions are introduced through the spikiness at the boundaries between facies, which are in turn driven by the bandlimited seismic and imposed spatial smoothness constraints. The low frequencies are determined by the spikiness, the facies based depth trends and prior facies probabilities. Even when strong rock physics constraints are applied, there are still multiple solutions that honour all the input data to an acceptable level. Geostatistical inversions allow for the quantification of this uncertainty through the realisation of many solutions. Conclusions Due to the limited information present in seismic data and the presence of noise, the solution space for inversion of seismic reflectivities to elastic properties is extremely large. There are a number of constraints that can be applied during inversion to help to reduce this space such as sparsity or continuity assumptions. These might be thought of as geologically motivated. That is the results are guided to match an expectation based on geological concepts. Even when these are applied the solution space can still be very large and there is no guarantee that the inversion will make sense. Rock physics constraints can be applied in various ways within the complete inversion process to ensure that the final results at least make sense geophysically and to ensure that the final interpretation in terms of reservoir properties is valid. Even with rock physics input the solution space is still fairly broad, yet there is a strong tendency for a single solution to be generated without any indication of the uncertainties. It is often assumed that such output represents the most likely result based on the data and information available, although this is rarely tested. This strongly suggests that inversion is an interpretative process, not a commodity that can be generated through the blind minimisation of some objective function. Although good quality inversions require good quality data, workflows, quality control procedures and inversion engines, the understanding of the geology is equally as important and the use of rock physics is crucial.

5 References Sams, M. S. and Focht, T., [2012] Porosity estimation from deterministic inversion, EAGE Annual Meeting, Paper X015. Saussus, D. and Sams, M. S., [2012] Facies as the key to using seismic inversion for modelling reservoir properties, First Break, 30(7), Kemper, M. and Gunning, J. [2014] Joint Impedance and Facies Inversion Seismic inversion redefined, First Break, 32(9),