Michael Pelissier

Diffraction signatures of fracture intersections

Fractured rock causes diffractions, which are often discarded as noise in ground-penetrating radar (GPR) and seismic data. Most fractures are too thin, too steep, and their displacement is too small to be imaged by reflections, and diffractions are the only detectable signal. To decipher the information about fracture geometry and distribution contained in diffractions, we compare 3D synthetic ray-Born modeling with high-density 3D GPR data and outcrop observations from the Cassis Quarry in Southern France. Our results reveal how the intersection between two fractures is the basic geologic element producing a recordable diffraction. In this new model, two intersecting fractures are represented by one finite-length line diffractor. The intersection of three fractures is a 3D cross composed of three line diffractors. Fractures extending over several meters in the outcrop display linear clusters of diffraction circles in unmigrated GPR time slices. Such large-scale fracture intersections are composed of many aligned short subwavelength line diffractors due to fracture roughness and variations of fracture opening. The shape irregularities and amplitude variations of composite diffraction signatures are a consequence of the geometry and spacing of the intersecting fractures generating them. With three simple base-type intersecting fracture models (horizontal dip, gentle dip, and steep dip), the fracture network geometry can be directly deciphered from the composite diffraction signatures visible on unmigrated time slices. The nonrandom distribution of diffractions is caused by fracture trends and patterns providing information about fracture dip, spacing, and continuity of fractured domains. With the similarity law, the diffraction phenomena observed in GPR data are very similar in character to those seen on the seismic scale with the wavelength as the scaling link. GPR data serve as a proxy to decipher seismic diffractions.

Diffraction imaging of the Eagle Ford shale

Diffraction imaging is a novel technology that uses diffractions to image very small subsurface elements. Diffraction imaging may: (1) improve prospect characterization and pre-drill assessment of the local geology; (2) improve production and recovery efficiency; (3) reduce field development cost; and (4) decrease environmental impact. Field development may be accomplished with fewer wells to optimally produce the reservoir using high-resolution images of small-scale fractures in shale or carbonate intervals. Standard approaches to obtain high-resolution information, such as coherency analysis and structure-oriented filters, derive attributes from stacked, migrated images. Diffraction imaging, in comparison, acts on the pre-stack data, and has the potential to focus super-resolution structural information. Diffraction images can be used as a complement to the structural images produced by conventional reflection imaging techniques, by emphasizing small-scale structural elements that are difficult to interpret on a conventional depth image. An efficient way to obtain diffraction images is to first separate the migration events according to the value of the specularity angle, in a similar way to offset gathers, and subsequent post-stack processing. The high-resolution potential is demonstrated by the diffraction images from the Kenedy 3D survey over the Eagle Ford shale, which show much more detail than conventional depth migration or coherence.

Semiautomated fault interpretation based on seismic attributes

Three-dimensional fault interpretation is a time-consuming and tedious task. Huge efforts have been invested in attempts to accelerate this procedure. We present a novel workflow to perform semiautomated fault illumination that uses a discontinuity attribute as input and provides labeled fault surfaces as output. The procedure is modeled after a biometric algorithm to recognize capillary vein patterns in human fingers. First, a coherence or discontinuity volume is converted to binary form indicating possible fault locations. This binary volume is then skeletonized to produce a suite of fault sticks. Finally, the fault sticks are grouped to construct fault surfaces using a classic triangulation method. The processing in the first two steps is applied time slice by time slice, thereby minimizing the influence of staircase artifacts seen in discontinuity volumes. We illustrate this technique by applying it to a seismic volume acquired over the Netherlands Sector of the North Sea Basin and find that the proposed strategy can produce highly precise fault surfaces.

Classics of Elastic Wave Theory

In this chapter, we give a brief synopsis of each of the classic papers referred to in this collection. Where relevant, we reproduce the basic equations, recast in modern notation. Supporting works also are referred to. They are listed in the “General References” section.nnTable 1 is a quick outline of the key contributions of each paper reprinted in this book.nnRobert Hooke, “Potentia Restitutiva, or Spring” (Oxford, 1678)nnThe article by Robert Hooke, “Potentia Restitutiva, or Spring,” contains the statement of the proportional relation between stress and strain universally referred to as Hooke’s law. Although the English language has evolved somewhat since 1678, the article does not require translation. Hooke describes a variety of experiments, accompanied by illustrations, confirming the stress/strain relation over a wide range of applied loads. He emphasizes the great generality of his results.nnBased on his experimental work from 1660 onward, Hooke first published his law in 1676 in the form of an anagram in Latin,nnwhich he later revealed to be “ut tensio sic vis.” Roughly translated, this means “as the force, so is the displacement” (Love, 1911; Boyce and DiPrima, 1976).nnIn his treatise, Hooke examined the behavior of springs, so his first casting of the equations dealt with the restoring force on a spring, for a given displacement:

Azimuthal variations in scattering amplitudes induced by transverse isotropy

The study of amplitude variations of reflected and transmitted seismic waves due to anistropy has received considerable attention in recent years, but most investigations have concentrated on the effect of transverse isotropy with the symmetry axis either vertical or horizontal. The published results on the whole tend to exclude mode conversions. Amplitudes of all reflected and transmitted wave modes are addressed for P-waves incident on boundaries between isotropic and transversely isotropic media, the symmetry axis of which is oriented at 45 degrees to the interface. The results cover the full range of incidence angles and all “acquisition azimuth” in the plane of the interface. When the anistropy axis is not normal to the interface, the scattering coefficients are shown to be highly dependent on the azimuth. The pattern of azimuthal variation is especially complicated in the case of mode conversion, and scattering coefficient profiles that are 180 degrees apart are not the same. This has the implicatio...

Interpretation value of diffractions and sub-specular reflections – applications on the Zhao Dong field

We provide an overview of integrated pre-stack depth migration and diffraction imaging for the Zhao Dong field, Bohai Bay, China. This field is highly compartmentalized by complex faulting and further characterized by channel systems, fractures and volcanic features. The objective of the diffraction imaging is to better define these small-scale features. Tools to facilitate interpretation include displays with pre-stack depth migration and diffraction images overlain in different colour scales, as well as a weighted blending of them into a single volume. An important concept is that of the sub-specular reflection, which is obtained alongside the pure diffraction image by applying ultra-weak specularity tapers. Tuning properties of elementary diffractor images together with sub-specular reflectors provide a decisive uplift of diffraction imaging for the interpreter.

Seismic diffractions: How it all began

We review in historical order the key contributions to the development of the theory of diffractions. The work of Grimaldi, Huygens and Young provides the first part of this story, giving an understanding of diffraction and interference phenomena. Huygens was able to explain the laws of reflection and refraction, but lacked a deeper understanding of interference. This was provided by Young who used it to show how diffraction could arise from the interference of two waves. Fresnel, Helmholtz and Kirchhoff chose a different path and developed a full mathematical expression of Huygens’ principle, incorporating wave phase and interference. Sommerfeld and his students were able to reformulate the Huygens-Helmholtz-Kirchhoff integral as the sum of an incident geometrical-optics wave and a diffraction integral, which is interpretable as the contribution of the diffracted rays from the boundary. From our modern vantage point, this provides a rather pleasing analogy to Young’s early attempts at a theory of diffraction, using just two rays. A full ray-theoretical theory of diffraction, the Geometrical Theory of Diffraction, was given by Keller and extended by Klem-Musatov and Aizenberg to the case of seismic diffraction analysis.

Classical and Modern Diffraction Theory

Providing geophysicists with an in-depth understanding of the theoretical and applied background for the seismic diffraction method, “Classical and Modern Diffraction Theory” covers the history and foundations of the classical theory and the key elements of the modern diffraction theory. Chapters include an overview and a historical review of classical theory, a summary of the experimental results illustrating this theory, and key principles of the modern theory of diffraction; the early cornerstones of classical diffraction theory, starting from its inception in the 17th century and an extensive introduction to reprinted works of Grimaldi, Huygens, and Young; details of the classical theory of diffractions as developed in the 19th century and reprinted works of Fresnel, Green, Helmholtz, Kirchhoff, and Rayleigh; and the cornerstones of the modern theory including Keller’s geometrical theory of diffraction, boundary-layer theory, and super-resolution. Appendices on the Cornu spiral and Babinet’s principle are also included.