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Papers by Michael Slawinski

Geophysical Journal International, 2017

Organic Electronics, Aug 1, 2011

Seg Technical Program Expanded Abstracts, 1999

ABSTRACT This paper considers traveltime related to oblique ray trajectories under the assumption... more ABSTRACT This paper considers traveltime related to oblique ray trajectories under the assumption of linear velocity as a function of depth. Exact travel time expressions for oblique ray paths are used for a rigorous nonlinear regression analysis of zero and offset Vertical Seismic Profile (VSP) field measurements. The statistical validity of the linear-velocity models obtained from the regression analysis, shows a good fit within an acceptable range of experimental error. Numerous earlier practical investigations, which inspired our study, have been confined to the one-dimensional realm of a wellbore and acoustic log data. By contrast, offset VSP’s provide traveltime information for many source-receiver configurations. The assumption of a simple analytic velocity function is a convenient and practical approach to traveltime estimation and for modelling the prestack surface seismic or VSP data itself. Furthermore, for large source-receiver offsets involved in imaging and AVO studies, a linear-velocity function yields a conveniently simple yet reasonable estimate of ray trajectories and angles of incidence. Even an excellent fit between a linear-velocity function and experimental data, however, does not provide a direct source of lithological information. The velocity function is related to the global rather than to the local properties.

Using orthogonal projections, we investigate distance of a given elasticity tensor to classes of ... more Using orthogonal projections, we investigate distance of a given elasticity tensor to classes of elasticity tensors exhibiting particular material symmetries. These projections depend on the orientation of the elasticity tensor, hence the distance is obtained as the minimization of corresponding expressions with respect to the action of the orthogonal group. These expressions are stated in terms of the eigenvalues of both the given tensor and the projected one. The process of minimization is facilitated by the fact that, as we prove, the traces of the corresponding Voigt and dilatation tensors are invariant under these orthogonal projections. For isotropy, cubic symmetry and transverse isotropy, we formulate algorithms to find both the orientation and the eigenvalues of the elasticity tensor that is endowed with a particular symmetry and is closest to the given elasticity tensor.

Geophysics, 2009

ABSTRACT We have proved that the innermost wavefront-slowness sheet of a Hookean solid is convex,... more ABSTRACT We have proved that the innermost wavefront-slowness sheet of a Hookean solid is convex, whether or not it is detached from the other sheets. This theorem is valid for the generally anisotropic case, and it is an extension of theorems whose proofs require the detachment of the innermost sheet. Although the Hookean solids that represent most materials encountered in seismology exhibit a detached innermost sheet, the positive definiteness of the elasticity tensor, which is its sole fundamental constraint, allows for the existence of both detached and nondetached sheets. Besides the foundational considerations, the omnipresence of computer methods requires that we investigate cases that, even if not commonly encountered, are within the realm of physical possibility, and can appear as the output of modeling. The theorem proved for a general Hookean solid, has been exemplified using a particular case of transverse isotropy. For that case, it has been shown that the innermost sheet exhibits a polarization of a quasicompressional wave. However, this need not be a general property of that sheet because the presented theorem refers to convexity of the innermost sheet, not to its polarization.

Journal of Elasticity, 2009

Canadian Acoustics, Sep 1, 1996

We consider the problem of obtaining the effective orthotropic tensor that corresponds to a given... more We consider the problem of obtaining the effective orthotropic tensor that corresponds to a given generally anisotropic one; by "effective", we mean the closest in the sense of the Euclidean or log-Euclidean distance. It is difficult to find the absolute minimum of the distance function, since the minimization process is nonlinear, exhibiting several local minima. In general, the minimization process

In this presentation, we discuss the one-to-one relation between the elasticity parameters and th... more In this presentation, we discuss the one-to-one relation between the elasticity parameters and the traveltime and polarization of a propagating signal in the context of the measurement errors. The one-to-one relationship between seismic measurements and a model postulated in the realm of the constitutive equation of an elastic continuum provides the link between the observational and theoretical aspects of seismic

Most sedimentary rocks are anisotropic. Most sedimentary basins are nonuniform. Consequently, exp... more Most sedimentary rocks are anisotropic. Most sedimentary basins are nonuniform. Consequently, exploration seismologists benefit from knowledge of these properties. This knowledge provides us with rock-physics information and also enables us to account for the effects of anisotropy and nonuniformity on seismic imaging. Anisotropy and nonuniformity are conveniently studied in the context of continuum mechanics. Aki and Richards (1980) at the beginning of their classic book, while referring to certain standard conjectures used in seismology, write “[t]hese conjectures, and many others that are generally assumed by seismologists to be true, are properties of infinitesimal motion in classical continuum mechanics for an elastic medium with a linear stress-strain relation”. This tutorial presents aspects of a scientific foundation for the study and interpretation of seismic wave phenomena in linearly elastic, anisotropic, nonuniform continua. It draws on continuum mechanics and the asympto...

$Research paper thumbnail of Angle of Incidence as a Function of Source-receiver Offset of a Dipping Refractor; An Exact Expression for VSP Apllications$

Reflection amplitudes are intimately connected to the angle of incidence. In seismology, however,... more Reflection amplitudes are intimately connected to the angle of incidence. In seismology, however, the angle of incidence is often difficult to establish. Partially, because of this difficulty it is more common to consider Amplitude Variations as a function of a lateral source-receiver Offset (AVO) rather than Amplitude Variations as a function of the Angle of incidence (AVA). Computational modelling and theoretical analysis, nevertheless, require the knowledge of angles of incidence in order to relate them directly to various forms of Zoeppritz equations (e.g., Aki and Richards, 1980). Furthermore, although a lateral source-receiver offset is eas-ily established based on field acquisition parameters, the angle of incidence requires a more involved calculation. This Short Note provides explicit and exact expressions which can be used in AVA studies using the Vertical Seismic Profile (VSP). The expressions can be conveniently used in planning an AVAiAVO survey while designing source-r...

An exact analytical expression for traveltime in a medium with a constant velocity gradient and e... more An exact analytical expression for traveltime in a medium with a constant velocity gradient and elliptical velocity dependence is used to calculate possible reflection points for a given source receiver geometry. The set of reflection points are collectively referred to as the illumination zone. Also, we give an expression that can be used to trace rays in a vertically inhomogeneous elliptically anisotropic medi-um. These expressions are applicable for both survey design and data interpretation.

Geophysics—similarly to astrophysics—relies on remote sensing. Inferring material properties of t... more Geophysics—similarly to astrophysics—relies on remote sensing. Inferring material properties of the Earth’s interior is akin to inferring the composition of a distant star. In both cases, scientists rely on matching theoretical predictions or explanations with observations. Notably, obtaining a sample of a material from the interior of our planet might not be less difficult than obtaining a sample from a distant celestial object. To infer the presence and orientations of subsurface fractures, seismologists might use directional properties of Hookean solids. In other words—using such a solid as a mathematical model— seismologists match its quantitative predictions with observations.

Journal of Elasticity, 2015

SEG Technical Program Expanded Abstracts 2000, 2000