Seismic facies characterization by monoscale analysis

Abstract

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.

Full‐waveform inversion from compressively recovered model updates

“…Finally, FWI calls for some sort of regularization that imposes prior information. Because the elastic properties in the earth contain singularities (zero-, first, and fractional-order discontinuities (Herrmann, 2003;Herrmann et al, 2001;Herrmann, 2001)) that trace curved interfaces, this prior information will be in the form of one-norms on wavelet or curvelet coefficients .…”

Lithological constraints from seismic waveforms: Application to the opal‐A to opal‐CT transition

“…In this paper, we address all of these issues by presenting (i) a parametric representation for reflectors and waveforms that borrows from earlier work by the authors (see e.g. Herrmann et al, 2001;Herrmann, 2005, and the references therein), (ii) a new nonlinear estimation method for the reflector parameters, and (iii) a rock-physical model that generates transitions, consistent with the parametric model proposed by Herrmann and Bernabé (2004) to model mineralogical phase transitions at upper-mantle discontinuities.…”

“…Motivated by empirical studies on sedimentary records, Herrmann et al (2001) made the argument that reflectors can be considered as algebraic singularities, parameterized by a scaling exponent determining the transition sharpness. It was shown that this parameterization corresponds to a generalization of zero-or first-order discontinuities towards fractional-order scale-invariant transitions, indexed by a scale exponent.…”

Wavelet based multiscale analysis of geophysical downhole measurements: Application to a clayey siliclastic sequence

“…Knowing these exponents makes it possible to control the asymptotic statistical properties of the structure. Wavelet based estimators have been successfully used for estimating scaling behaviour (Li, 1998;Herrmann, 1997;Herrmann and Stark, 2001;Zaourar et al, 2006a,b). The central properties of self-affine process enable one to establish a scaling relation between wavelet coefficients at different scales from which the spectral exponent can be extracted.…”