Seismic impedance is widely used in our industry because it allows an integrated approach to geological interpretation. The transformation of seismic amplitudes to impedance data can be essentially seen as the change from an interface property to a layer property. This stratal interval property (impedance) simplifies the lithologic and stratigraphic identification and can be directly converted into lithologic or reservoir properties such as porosity, fluid fill and net pay. It also allows for direct interpretation of three-dimensional geobodies.
As seismic data are bandlimited (typically exhibiting a bandwidth of 10-70 hertz), the direct transformation of seismic amplitudes into impedance yields a relative impedance. The missing low frequencies (1-10 hertz) are usually derived from well logs or stacking velocities and used as a priori information during the inversion process. The quality of the low-frequency impedance model used in the inversion has a pronounced effect on the final impedance result and thus needs to be constructed carefully. More details on seismic impedance inversion can be picked up from our earlier published articles of Geophysical Corner (May and June 2015 issues).
Seismic impedance inversion can be carried out on both poststack and prestack seismic data. In a seismic gather, the near-offset amplitudes relate to changes in impedance of the subsurface rocks, and thus depict the correct time of the reflection events. The far-offset amplitudes relate to not only the changes in P-wave velocity and density, but the S-wave velocity as well. The inversion of far-offset amplitudes in a gather yields the elastic impedance (as was described in the October 2012 Geophysical Corner) and can be used for lithology and fluid discrimination.
Since the inversion process transforms seismic amplitudes directly into impedance values, special attention needs to be paid to their preservation, which ensures that the observed amplitude variations are related to geological effects. Besides this, preconditioning of seismic data is usually carried out by adopting processes such as muting, bandpass filtering, random noise removal and trim statics (see January and November 2016, and January, October and November 2019 installments of Geophysical Corner). But sometimes these processes are not enough. In such cases we can adopt some poststack processing steps for preconditioning noisy prestack seismic data (see the July 2019 Geophysical Corner).
Four Ways of Using LFM
As mentioned above, the low-frequency model to be used in the inversion is constructed such that the different subsurface interval impedance values are constrained by the horizons interpreted on the seismic data. When the LFM is extracted from a single well and is used in the impedance inversion, the impedance section may or may not match the impedance logs at the other well locations falling on the 3-D seismic volume.
A second way to generate the LFM is to make use of a few wells for inclusion in the impedance inversion. Such a technique linearly interpolates the impedance data between the wells using weights calculated on the basis of inverse distance, and similarly extrapolates away from the well control. When quality checks are performed on the generated LFMs using this technique, they often are found to exhibit artifacts in the form of artificial tongues with anomalous impedance values, appearing more like bull’s eyes.
A third workflow for building a low-frequency model for impedance inversion uses both the well log data as well as seismic data. Suitable attributes derived from seismic data, as well as the data from different wells, are used to estimate a linear regression relationship. This relationship is then used to predict the low-frequency component for use in impedance inversion. In this analysis, the target log is modeled as a linear combination of several input attributes at each sample point. This modeling yields a series of linear equations, which are solved for obtaining a linear weighted sum of the input seismic attributes in such a way that the error between the predicted and the target log is minimized in a least squares sense. (For more details of this method please see the September 2015 Geophysical Corner). This workflow for generating a low-frequency impedance model is superior to the existing methods of low-frequency impedance generation.
Yet another way to build a LFM which avoids the downside of the inverse-distance approach and artifacts, such as bull’s eye features, is with the use of a kriging approach. In this method, instead of estimating the values at the unknown sample points through inverse-distance weighting, they are estimated with the use of variograms. We will describe the application of this method in a future installment of Geophysical Corner.
An Additional Approach
In this article, we describe the application of yet another way to build an accurate LFM using the first-pass impedance inversion and then running the inversion process a second time. This approach brings in more spatial continuity from the inverted impedance data generated in the first pass of inversion. The workflow for this approach is shown in figure 1.
The different steps in this workflow are:
- A LFM is generated using the multiattribute regression analysis method described above and constrained with the available horizons.
- Prestack simultaneous impedance inversion is run with this LFM.
- Both the P- and S-impedance attributes so generated are low-pass filtered and referred to as the updated LFMs.
- The updated LFMs from step 3 are used to run a second pass of Prestack simultaneous impedance inversion.
- The impedance attributes so generated are then visualized for quality control.
Application
The Volve oilfield is situated approximately 200 kilometers west of Stavanger in 80 meters of water and located in block 15/9 in the southern Norwegian North Sea on the continental shelf. The discovery well found oil in the Middle Jurassic Hugin sandstone formation. The Base of Cretaceous Unconformity represents the separation of the syn-rift depositional sequence from the post-rift depositional sequence and covers large areas in the North Sea. It is easily identified on surface seismic data and well logs and is an important marker. The dashed black marker represents the base of the Hugin sandstone reservoir, which forms a combined structural and stratigraphic trap, with depths varying from 2,750 to 3,120 meters. These sandstones are not preserved over the entire survey. It is of interest to determine the distribution of the Hugin sandstone reservoir within the available 3-D seismic survey available over the area.
Figure 2 shows a comparison of the vertical sections drawn out of the P-impedance LFM (henceforth referred to as model-1) generated with the use of multiattribute regression analysis method and using the available well log data as well as the single well low frequency volumes for P and S impedance, relative acoustic impedance volume, seismic velocity volume (figure 2a), and the use of the proposed method wherein the low-pass filtered P-impedance first pass of simultaneous impedance inversion (henceforth referred to as model-2). Notice the lateral variations in the different intervals segmented by the marked horizons brought about by the first pass of simultaneous inversion.
Figure 3 shows the stratal slice comparison at the ‘Hugin-formation top’ marker and drawn from the S-impedance volumes generated by using the two different LFMs (models 1 and 2). The white block arrows indicate the changes brought about in S-impedance with the use of model-2, with respect to the equivalent S-impedance generated with the use of model-1.
An equivalent comparison for VP/VS attribute is shown in figure 4. Again, notice the change in VP/VS values brought about in the highlighted areas as well as at the locations marked with white block arrows.
Conclusions
In the interest of better reservoir definition, the impedance attribute is expected to be derived accurately from the available seismic data. For this the low-frequency model generated for use in the simultaneous inversion should be carefully processed. We have shown the advantage of using the LFMs derived from the first pass of simultaneous inversion attributes (P- and S- impedance) by low-pass filtering and adopting them in the second pass of simultaneous inversion. The evaluation of the results has shown improvements by way of better definition of features as seen on stratal displays. While only qualitative comparison evaluations have been shown here, such evaluations open the door for quantitative interpretation by bringing in adequate data.
Acknowledgements
We wish to thank Equinor and partners for access to the Volve 3-D seismic data used in this exercise.