Spectral Inversion: Lessons from Modeling and Boonesville Case Study Oleg Portniaguine*, Fusion Petroleum Technologies, Inc. and John Castagna, University of Houston Summary Spectral inversion produces sparse reflectivity estimates which, under ideal conditions, resolve thin layers below the tuning thickness. Synthetic examples show that under conditions of high signal-to-noise ratio and perfect knowledge of the wavelet the method resolves thicknesses far below tuning. While the performance deteriorates as the noise level increases, the method always produces a stable solution, which remains useful for interpretation in that the wavelet is effectively removed from the data without magnifying noise appreciably. On Boonesville data we demonstrate that, besides resolving thin layers, our reflectivity attribute has other useful properties. For example, it deconvolves complex seismic interference patterns into interpretable stratigraphic patterns with remarkable detail, thus making it a very useful new addition to the family of seismic attributes. Introduction Seismic inversion is a non-unique process. Common methods of inverting a stacked seismic trace include trace integration (or recursive trace inversion) producing a band limited impedance estimate which can be incorporated with low frequency information to recover impedance, generalized linear inversion (which requires a starting model close to the solution), and sparse-spike inversion (which applies somewhat arbitrary mathematical assumptions to arrive at a unique reflectivity). Recently, spectral inversion (Castagna, 2004; Partyka, 2005) has become popular. Spectral inversion can be viewed as a form of sparse-spike inversion in that it outputs a sparse reflectivity series. However, it differs in being driven by geological rather than mathematical assumptions. The inversion, rather than being driven to achieve maximum sparseness, keys on aspects of the local frequency spectrum obtained using spectral decomposition of various types (Partyka et al., 1999; Castagna et al., 2003). Reasonable geological assumptions are then made to interpret the thin layering (below tuning) that produces such spectral characteristics. The thin bed inversion is a trace-by-trace operation which takes in a single stacked seismic trace and produces high- resolution reflectivity model trace as an output. As demonstrated in this paper, the apparent resolution of thin bed inversion is far superior to that of the input seismic, Figure 1. Upper panel: data for the idealized wedge model. Three lower panels: reflectivity inversion with noise levels of 0.01%, 0.1% and 1% from top to bottom, respectively. Wedge resolution is ideal under low noise conditions.
Transcript
Spectral Inversion: Lessons from Modeling and Boonesville Case Study Oleg Portniaguine*, Fusion Petroleum Technologies, Inc. and John Castagna, University of Houston Summary
Spectral inversion produces sparse reflectivity estimates which, under ideal conditions, resolve thin layers below the tuning thickness. Synthetic examples show that under conditions of high signal-to-noise ratio and perfect knowledge of the wavelet the method resolves thicknesses far below tuning. While the performance deteriorates as the noise level increases, the method always produces a stable solution, which remains useful for interpretation in that the wavelet is effectively removed from the data without magnifying noise appreciably. On Boonesville data we demonstrate that, besides resolving thin layers, our reflectivity attribute has other useful properties. For example, it deconvolves complex seismic interference patterns into interpretable stratigraphic patterns with remarkable detail, thus making it a very useful new addition to the family of seismic attributes. Introduction
Seismic inversion is a non-unique process. Common methods of inverting a stacked seismic trace include trace integration (or recursive trace inversion) producing a band limited impedance estimate which can be incorporated with low frequency information to recover impedance, generalized linear inversion (which requires a starting model close to the solution), and sparse-spike inversion (which applies somewhat arbitrary mathematical assumptions to arrive at a unique reflectivity). Recently, spectral inversion (Castagna, 2004; Partyka, 2005) has become popular. Spectral inversion can be viewed as a form of sparse-spike inversion in that it outputs a sparse reflectivity series. However, it differs in being driven by geological rather than mathematical assumptions. The inversion, rather than being driven to achieve maximum sparseness, keys on aspects of the local frequency spectrum obtained using spectral decomposition of various types (Partyka et al., 1999; Castagna et al., 2003). Reasonable geological assumptions are then made to interpret the thin layering (below tuning) that produces such spectral characteristics. The thin bed inversion is a trace-by-trace operation which takes in a single stacked seismic trace and produces high-resolution reflectivity model trace as an output. As demonstrated in this paper, the apparent resolution of thin bed inversion is far superior to that of the input seismic,
Figure 1. Upper panel: data for the idealized wedge model. Three lower panels: reflectivity inversion with noise levels of 0.01%, 0.1% and 1% from top to bottom, respectively. Wedge resolution is ideal under low noise conditions.
Spectral Inversion
which makes it ideal for detailed delineation ancharacterization of thin reservoirs.
d
thin bed inversion is milar to that of spiky spectral decomposition
2004), superior resolution to at predicted by the Widess (1973) model is obtained from
odel
orst case scenario for achieving below tuning solution using spectral thin-bed inversion occurs when
model results, depicted in igure 1. The top panel shows synthetic 30 Hz data for the
ver, rops below 1%. Therefore, the solution exhibited in the
ity) is only possible under ideal onditions (very low noise level). The other major factor
y the xamples depicted in the Figure 2.
The methodology of our spectralsi(Portniaguine and Castagna, 2004) and the minimum support method (Portniaguine and Zhdanov, 2002). In the literature, there are other spiky inversion methods (e.g., Debeye and Van Riel, 1990) as well as thin bed identification methods based on spectral decomposition (Marfurt and Kirlin, 2001; Castagna et al, 2003). Spectral thin bed inversion is a means of quantitatively and objectively interpreting spectral decomposition results. In contrast to spectral decomposition, which produces multiple frequency cubes which tend to overwhelm the interpreter with volumes of data, the result of the spectral thin bed inversion method are compact and generally more intuitive than the spectral decomposition results. The inverted reflectivity can then be integrated to produce a band limited impedance estimate that is unbiased by existing well information. Thus, it is superior to conventional GLI methods that are, by their very nature, biased against lateral heterogeneities that are so important in reservoir characterization. As discussed by Castagna (ththe contribution of the even part of the seismic waveform to the inversion. As the even part may be relatively weak, especially in the case of bright spots, it is apparent that noise, rather than dominant frequency, will control the fundamental limit of resolution. Experience has also shown that knowledge of the wavelet, in addition to the wavelet characteristics (especially bandwidth), will determine the quality of the inversion result. Thus, it is instructive to study this effect on noisy synthetic data. Influence of noise and knowledge of wavelet on a wedge m The wrethe even part of the signal is small, such as occurs when there are two large reflection coefficients that are nearly equal and of opposite sign. Consider the series of wedge Fwedge model, with 1% random noise added. The next three panels show the spectral thin bed inversion results with noise levels of 0.01%, 0.1% and 1% (bottom panel). We can see that for the smallest noise level the resolution of the wedge below tuning is nearly perfect, and, understandably, the resolution deteriorates as the noise level increases.
Commenting on the influence of the noise factor we should mention that noise level in real seismic data rarely, if edlowermost panel in Figure 1 is the closest to reality. While resolution of the thin part of the wedge is imperfect, nevertheless the inversion is robust to noise and simply does not attempt to go further below tuning than the noise will allow it to do robustly. As shown in Figure 1, ideal resolution of such a thin wedge (equal and opposite reflectivcwhich limits practical applicability of this idealized wedge model is assumed perfect knowledge of the wavelet. Spectral thin bed inversion method is highly sensitive to the shape of the estimated wavelet, as illustrated be
Figure 2. Inversion with imperfect wavelet, estimated from the data. Upper panel: correct phase of the wavelet. Lower panel: phase is 20 degrees off.
el, depicts results using a avelet with the wrong phase (20 degrees off the true
The wavelet for Figure 2, upper panel, was estimated from the data. Figure 2, lower panwphase). Figure 2 shows that while the resolution of the inversion suffers from poor knowledge of the wavelet (i.e. the thin part of the wedge is badly resolved), nevertheless
Spectral Inversion
the inversion is robust to the wavelet imperfections. This is supported by the fact that the result consistently shows two strong reflectors with minor artifacts around them. Reflectivity inversion of Boonesville data
e demonstrate practical advantages of the specW tral thin e Boonesville ributed by the
and stacked Boonesville dataset. The middle anel of the same figure shows the thin bed reflectivity
(especially mediately above and below the strong marker reflector at
from the iddle panel. While the impedance section has lower
riginal data displayed as a time slice at 875 ms. The
ed inversion produces conditions,
can be resolved. In the
bed reflectivity inversion method on thdataset (public domain 3-D data are distBureau of Economic geology of Texas; Hardage et al., 1996). Figure 3, upper panel, depicts one line (inline 150) of the migratedpattribute for this line. Since this is an inversion result, the convolution of reflectivity with the wavelet produces very close match to the original data (not shown). Studying the middle panel from the Figure 3 we notice remarkable resolution of the thin layersim880 ms) which is not visible in the input data (the upper panel in Figure 3). Notice that the features are continuous laterally in both inline and cross line directions. Figure 3, lower panel shows the resulting band-limited impedance which corresponds to reflectivitymapparent vertical resolution than the reflectivity, it is especially useful for stratigraphic differentiation of the strata themselves rather than the stratal boundaries. The impedance is especially useful when displayed as a lateral slice (time slice). Figure 4, upper panel showsomiddle panel shows the reflectivity attribute, the same time slice. While the picture in the Figure 4 middle panel shows very fine details of the stratal boundaries, arguably it is hard to infer geology from such a slice. That is why the conversion to impedance is advantageous. The lower panel shows the inversion results converted into impedance (same time slice). Using this picture the interpreter can easily feel the underlying geology. Conclusions and Discussion
e have shown that spectral thin-bWsparse reflectivity estimates. Under ideal thicknesses far below tuningpresence of appreciable noise the resolution deteriorates as the noise level increases. The method always produces a stable solution, which remains useful for interpretation in that the wavelet is effectively removed from the data without magnifying noise appreciably.
Figure 3. Original data from Boonesville field, inline 150 (upper panel). Results of broadband reflectivity inversion (middle panel), and its conversion to band-limited
impedance (lower panel).
Spectral Inversion
On Boonesville data we demonstrate that, besides resolving thin layers, our reflectivity attribute has other useful properties. For example, it deconvolves complex seismic
terference patterns into interpretable stratigraphic patterns
the spectral flectivity attribute has many practical advantages and
eology, The niversity of Texas at Austin, GRI-96/0182
A., Gridley, J.M., and Lopez, J., 1999, terpretational Applications of Spectral Decomposition in
, 353-360
ortniaguine, O. and Zhdanov, M.S., 2002, 3-D magnetic
cknowledgements
inwith remarkable detail, thus making it a very useful new addition to the family of seismic attributes. In conclusion, we would like to stress that in spite of practical limitations due to presence of noise and imperfections in the wavelet estimationreproduces finely resolved seismic sections. References
Castagna, J.P. 2004, Spectral Decomposition and High esolution Reflectivity Inverison, pR
Oklahoma Ci Castagna, J.P., S. Sun and R.W. Siegfried, 2003, Instantaneous spectral analysis: Detection of low-frequency shadows associated with hydrocarbons2 Debeye, H.W.J. and Van Riel, P., 1990, Lp-norm deconvolution: Geophys. Prosp., 38, 381-404. HR.Y., Edson, R.D., and D.L. Carr 1996, Boonesville 3-D Seismic Data Set, Bureau of Economic GU Marfurt, K. J., and R. L. Kirlin, 2001, Narrow-band spectral analysis and thin-bed tuning: Geophysics, v. 66, p. 1274-1283. Partyka, G., 2005, SEG Distinguished Lecture. Partyka, G.InReservoir Characterization, Leading Edge, 18(3) Portniaguine, O., and J.P. Castagna, 2004, Inverse spectral decomposition, 74th SEG meeting, SI 1.2, 1786-1789. Pinversion with data compression and image focusing, Geophysics, v. 67, 1532-1541. Widess, M. B., 1973, How thin is a thin bed? Geophysics 38, 1176-1180. A
Financial support for this work was provided by Fusion etroleum Technologies, Inc. P
Figure 4. Original data from Boonesville field, time slice at 875 ms (upper panel). Results of reflectivity inversion, the same time slice (middle panel) and its conversion to impedance (bottom panel).
