Multifractal characterization of petrophysical data

Muller, Jiri

doi:10.1016/0378-4371(92)90539-3

Cited by 21 publications

(14 citation statements)

References 10 publications

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“…The color white, on the other hand, indicates smooth transitions, which in the Fourier domain correspond to "infrared divergerhs'. Clearly, one can see that the irregular gray-value changes support the observation that well data behave rnultifrsctally [30,32,13,16,161. Moreover, the emergence of circles 81-most everywhere is an indication of an accumulation of singularities.…”

Section: Seismic Reflectivity As the Continuous Wavelet Transformsupporting

confidence: 62%

Fast 3-D seismic modeling and prestack depth migration using generalized screen methods. Final report for period January 1, 1998 - December 31, 2000

Toksöz¹

2001

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DISCLAMERThe objective of this project has been to develop and test new methods for the modeling and migration of seismic data in complex media in 3-D, for the purpose of improved subsurface imaging. Seismic imaging of complex structures and stratigraphy in the subsurface is crucial to the petroleum industry for energy resource exploration and production, and is also an important part of the basic study of the earth's crust for understanding tectonics, deformation, and sedimentation processes. Imaging can be improved in several ways-by the development of new 3-D migration algorithms, the development of forward modeling methods for 3-D elastic media, and the development of innovative analysis methods to extract geological information from seismic images. In this project, we addressed each of the following areas. 1. We conducted a theoretical analysis of generalized screen methods with an emphasis on stability and accuracy. 2. We developed more efficient finite difference methods using variable grids and attenuation. 3. We investigated new methods of extracting stratigraphic info'rmation from images of the subsurface through attributes based on scale analysis of seismic reflection signatures. Our contribution in each of these areas is presented below. We completed a theoretical analysis of phase screen propagators to answer several critical questions: the existence of a singularity in the Green's function for the case of a zero vertical wavenumber, the stability and accuracy of such propagators, and the effects of backscattering for large contrast heterogenous media. The results of this development are given in the following manuscript by Roque Szeto. In summary, the theory is based on separating the wavefield into forescattering and backscattering parts. The resulting twoequation boundary value problem is equivalent to the Lippmann-Schwinger integral equation. This approach is robust and appropriate for earth structures with high velocity contrasts. This theory also resolves the apparent singularity problem that has persisted in generalized screen propagator formulations. With this formulation we have studied the effects of the commonly used approximations as a function of the degree of velocity contrast in the media. We find that the local Born approximation does very well for models with velocity contrasts up to about 20%. The screen propagator formulations developed by our collaborators at Los Alamos National Laboratory and the University of California at Santa Cruz are significantly more accurate than the local Born approximation. For velocity variations greater than 60% (such as might exist in sub-salt imaging applications in the Gulf of Mexico), the effects of backscattering are important and need to be included. The scalar acoustic wave equation has been widely used to study wave phenomena.For many optical and some ocean acoustical applications in which the backscattering effects can be ignored, we are justified to use the well-known paraxial/parabolic approximation. In many instances the small refractive-...

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Section: Seismic Reflectivity As the Continuous Wavelet Transformsupporting

confidence: 62%

Fast 3-D seismic modeling and prestack depth migration using generalized screen methods. Final report for period January 1, 1998 - December 31, 2000

Toksöz¹

2001

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“…Indeed, DMS have a high sampling rate (about one measurement every 2.5 mm) and a relatively high vertical resolution (1-2 cm) [Schlumberger, 1970[Schlumberger, , 1986 compared to other wire line logs (e.g., gamma, gamma density, or neutron logs) that sample information from a relatively large volume (-20-100 cm in diameter) with vertical resolution of -15 cm. Together with the borehole televiewer [Zemanek et al, 1969] and the formation microscanner [Schlumberger, 1986] focusing on two-point correlations, e.g., rescaled range (R/S) analysis (see, e.g., chapter 8 of Feder [1988] for a review of R/S analysis), variograms, and power spectra [Hewett, 1986;Muller et al, 1992]. In this paper, we investigate a texture analysis method based on multifractal scaling.…”

Section: Introductionmentioning

confidence: 99%

Electrical texture characterization of dipmeter microresistivity signals using multifractal analysis

Saucier¹,

Huseby²,

Muller³

1997

J. Geophys. Res.

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Abstract. We use multifractal analysis as a geostatistical tool for the characterization of microresistivity signals produced by dipmeter well-logging tools. A sliding window of a fixed length is placed along the signal. For each window, several electrical texture indices characterizing the irregularity of the microresistivity signal are calculated. Plotted as a function of depths, these texture indices form what we call texture logs. The methods which are developed are tested on dipmeter data and compared to other log responses and core descriptions for the well 30/9-6 in the North Sea. We show that the texture logs can be used to identify geological lithofacies for this example.

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“…Mathematically, these regions are represented by zero-or first-order transitions, which are singular in their derivatives. Multifractal analysis on well-log and seismic data [Muller et al, 1992;Herrmann, 1997Herrmann, , 1998] demonstrates that variations in the sedimentary upper crust consist of intertwined fractal sets of singularities, implying the following. First, seismic wavefields inherit the global singularity structure of the earth [Herrmann, 1998], albeit in a bandwidth-limited fashion.…”

Section: Introductionmentioning

confidence: 99%

Seismic facies characterization by monoscale analysis

Herrmann¹,

Lyons²,

Stark³

2001

Geophysical Research Letters

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Abstract.Relating sedimentary records to seismic data is a major challenge. By shifting focus to a scale-invariant sharpness characterization for the reflectors, we develop an attribute that can capture and categorize the main reflector features, without being sensitive to amplitudes. Sharpness is defined by a scale exponent, which expresses singularity order and determines the reflection signature/waveform.Local scale exponent estimates are obtained with a new monoscale method. Compared to multiscale wavelet analysis, our method has the advantage of measuring transition exponents at a single fixed scale using a simple on-off criterion. The exponents contain amplitude variation information and describe lithological onsets. We create an image of the earth's local singularity structure by applying our method to seismic traces and well-log data. The singularity map facilitates interpretation, facies characterization, and integration of well and seismic data.

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Multifractal characterization of petrophysical data

Cited by 21 publications

References 10 publications

Fast 3-D seismic modeling and prestack depth migration using generalized screen methods. Final report for period January 1, 1998 - December 31, 2000

Fast 3-D seismic modeling and prestack depth migration using generalized screen methods. Final report for period January 1, 1998 - December 31, 2000

Electrical texture characterization of dipmeter microresistivity signals using multifractal analysis

Seismic facies characterization by monoscale analysis

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