Seismic amplitude variation with offset holds information on density and two elastic parameters: compressional and shear velocities (or impedances). We simultaneously invert multiple offset stacks to transform P-wave offset seismic reflection data to these parameters. Prior to the inversion, wavelets are estimated separately for each offset stack. This enables the inversion to compensate for offset-dependent phase, bandwidth and tuning and nmo stretch effects. The impedance volumes can be interpreted separately or combined to estimate other geophysical parameters which might optimally discriminate between facies. In this regard, we have found the Lame' parameters, Lambda and Mu particularly useful. From well log analysis we expect that reservoir sands have lower Lambda (incompressibility) and higher Mu (rigidity).
Several approaches exist to use trends in 3D seismic data, in the form of seismic attributes, to interpolate sparsely sampled well-log measurements between well locations. Kriging and neural networks are two such approaches. We have applied a method that finds a relation between seismic attributes ͑such as two-way times, interval velocities, reflector rough-ness͒ and rock properties ͑in this case, acoustic impedance͒ from information at well locations. The relation is designed for optimum prediction of acoustic impedances away from well sites, and this is accomplished through a combination of cross validation and the Tikhonov-regularized least-squares method. The method is fast, works well even for highly underdetermined problems, and has general applicability. We apply it to two case studies in which we estimate 3D cubes of low-frequency impedance, which is essential for producing good porosity models. We show that the method is superior to traditional least squares: Numerous blind tests show that estimated low-frequency impedance away from well locations can be determined with an accuracy very close to estimations obtained at well locations.
Acoustic impedance is a rock property that, under specific conditions, can be derived from seismic data and can provide important insights into reservoir parameters-such as porosity, lithology, fluid content, etc. Direct measurements of acoustic impedance are available from sonic and density well logs. Seismic inversion, a process of converting seismic data into relative impedance, provides estimates of relative acoustic impedance away from the well locations. Because absolute acoustic impedance can be related to other rock properties, the inverted relative seismic impedance could be used to predict these properties away from the wells if the missing low frequencies could be reliably calculated and compensated for. In chalk, seismic inversion finds its most significant application in porosity prediction. Compared to the well acoustic impedance, inverted relative acoustic impedance has a limited bandwidth, which is restricted on low and high ends of the frequency spectrum. Band-limited impedance (in this article referred to as relative impedance) is a useful seismic attribute for a better qualitative understanding of reservoir properties, and it often can be used for quantitative estimation of other reservoir properties, especially in clastic reservoirs. Since chalk consists of homogeneous lithofacies with clean matrix character with its porosity as the main variable, it is a perfect medium for qualitative prediction of this specific attribute. However, quantitative reservoir characterization in chalk is severely limited by the lack of low-frequency information because the bulk of the strong correlation between impedance and porosity is carried by the low-frequency trend. The missing low-frequency part of the inverted impedance data can be modeled by lateral interpolation of impedance logs between well locations. Conventionally, this interpolation has been driven by distance between the wells, which often leads to artifacts and generation of nongeologic solutions. Distance-based, well-log interpolation can be significantly improved by using seismic velocities to guide the well-log interpolation. Although the use of velocities is a major improvement, it is limited by seismic resolution and accuracy that generally deteriorates with depth. Velocity data only partially provide the missing information in the lowest frequency range. In the present study, event-based validated multivariate interpolation was successfully applied to recover lowfrequency acoustic impedance using well data, velocity data, and seismic attributes. The examples given in this article originate from the Danish sector in the North Sea. Using seismic estimates of interval velocities, layer depths, formation thicknesses, and reflection amplitudes, it was possible to significantly improve the accuracy of the predicted low-frequency response and therefore the porosity estimates as compared to conventional methods. Impedance information in the frequency interval between 0 and somewhat higher than 8 Hz was estimated, achieving an improvement especially ...
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