Tijmen Jan Moser

Stability of source mechanisms inverted from P-wave amplitude microseismic monitoring data acquired at the surface

We study the stability of source mechanisms inverted from data acquired at surface and near-surface monitoring arrays. The study is focused on P-wave data acquired on vertical components, as this is the most common type of acquisition. We apply ray modelling on three models: a fully homogeneous isotropic model, a laterally homogeneous isotropic model and a laterally homogeneous anisotropic model to simulate three commonly used models in inversion. We use geometries of real arrays, one consisting in surface receivers and one consisting in ‘buried’ geophones at the nearsurface. Stability was tested for two of the frequently observed source mechanisms:strike-slip and dip-slip and was evaluated by comparing the parameters of correct and inverted mechanisms. We assume these double-couple source mechanisms and use quantitatively the inversion allowing non-double-couple components to measure stability of the inversion. To test the robustness we inverted synthetic amplitudes computed for a laterally homogeneous isotropic model and contaminated with noise using a fully homogeneous model in the inversion. Analogously amplitudes computed in a laterally homogeneous anisotropic model were inverted in all three models. We show that a star-like surface acquisition array provides very stable inversion up to a very high level of noise in data. Furthermore, we reveal that strike-slip inversion is more stable than dip-slip inversion for the receiver geometries considered here. We show that noise and an incorrect velocity model may result in narrow bands of source mechanisms in Hudson’s plots.

Review of ray-Born forward modeling for migration and diffraction analysis

The ray-Born approximation is a very useful tool for forward modeling of scattered waves. The fact that ray-Born modeling underlies most seismic migration techniques, and therefore shares their assumptions, is a justification in itself to consider it for forward modeling. The ray-Born approximation does not make an explicit distinction between specular reflections and nonspecular diffractions. It therefore allows the modeling of diffractions from structural discontinuities such as edges and tips, as well as caustic diffractions. In the simplest implementation ray-Born seismograms are multiple-free. Ray-Born modeling can be orders of magnitude faster than finite-difference modeling, both in two-and three dimensions.

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.

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.

How Correct is a Velocity Model

We discuss fundamental properties of the kinematic inversion problem. We argue that the inverse problem is illposed and generally does not have solution in a strictly defined sense. The solution of the inverse problem based on the best fit of observed and calculated reflection travel times may result in several subsurface models with significantly different geological meaning, but which all fit the observed data equally well. Does the seismic method have the potential to resolve such problems? We present and discuss one of the possibilities related to the use of a simple locally homogeneous model.

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.

Modeling multiple elementary waves in layered media using ray field maps

Seismic ray tracing in layered media becomes complicated and demanding when modeling for multiple ray codes (reflection/transmission sequences) and/or dense acquisition geometries. However, we observe some redundancies in current algorithms: (a) the same layers are crossed repeatedly by similar ray segments, and (b) the effort of tracing through a layer is determined by variations in the incoming wavefront rather than the medium. We deal with these redundancies by separating the modeling process in two stages: (Stage 1) compute ray field maps representing all ray segments between each pair of adjacent interfaces, then (Stage 2) for each desired ray code assemble the complete ray field from ray segments by iterative lookup in the ray field maps.