A scale attribute for texture in well- and seismic data
Journal
2000 SEG Annual Meeting
Date Issued
2000-01-01
Author(s)
Herrmann, Felix
Abstract
For many years people have been struggling to integrate w ell and seismic data. As main reasons for this struggle one may list the inherent bandwidth limitation of seismic data; the problem of seismic amplitudes and finally the apparent inabilit y to delineate and characterize those transitions in w ells that can be linked to and held responsible for the major reflection events and their signatures. As a means of approaching these problems an alternative approach is presen ted and partly tested in this paper. The method is based on the introduction of a new attribute which, at a fixed scale, characterizes the location and sharpness of the transitions in the well and the location and signature of the corresponding reflection events. As such the method entails an approach where the variations in the magnitude of the well properties and reflection amplitudes are characterized by their order of magnitudes. These orders of magnitude are represented by scale exponents, whic h express the localtexture (sharpness) of the interfaces and the nature of the reflection signature. It appears that these exponents are robust and localized and truly independent of the actual point values in the log and seismic data. This independence makes these exponents righ tful candidates for a new trace attribute, complemeiting existing attributes such as instan taneous phase and frequency. Because sharpness characterizes the local texture the attribute promises to serve as a key quantity for the integration of well and seismic data on the level of texture, with the additional benefit of being able to generate pseudo wells and seismic data. The proposed method to obtain the scale exponents w as first introduced in Herrmann and Stark (1999; 2000; 2000). There it w as shown that, as opposed to multiple scale wavelet methods, it is possible to estimate fractal scale exponents at a fixe d scale b y the monoscale β-transform. Similar attempts (Dessing, 1997) have been made, using the instantaneous phase, which is difficult to compute from well and/or seismic data. As shown below the application of the monoscale method to m ulti-trace post-stac k migrated data my be regarded as highly successful in the sense that the attribute assigns only one value to a reflector, in a manner that is lateral consistent and insensitiv eto amplitude variations along the interface. This lateral consistency makes the scale attribute useful for revealing the (singularity) structure of the subsurface. Besides the strict locality additional advan tages are physical interpretation; scale-in variance; insensitivit yto the seismic w aveletand reconstruction capabilit y. The locality opposessineared attributes sue h as instantaneous frequency/phase while the scale-in variance refers to the scale-invarian t manner in whih the sharpness of the reflectors is characterized. This sharpness characterization has the advantage that it also applies to the seismic w avelet and is additativ under convolution. This latter propert yfacilitates both the interpretation and seismic wavelet deconokition on the level of the attribute. Finally, the reconstruction capability allows for the generation of pseudo wells and reflectivity, based on the location and sharpness characterization of the attribute. The setup of this paper is as follows. Generalized layer transitions of varying sharpness are introduced first, followed by a brief outline of the fixed scale analysis method. Subsequently, attention is paid to the directionalit yof fractional order transitions and the construction of pseudo w ells and seismic data from the scale attributes. Finally, the method will be put to the test on the Mobil A V O dataset and some reflection traces from the Gulf of Mexico. The well of the first data set is "blocked", post stack migrated data is analyzed and reconstructed.
Type
conference paper