# Books

Henning Hoeber et al.

ISBN: 978-1-56080-317-1

1. Edition: 2016

Soft Cover, 832 pages

## Seismic Diffraction

Society of Exploration GeophysicsISBN: 978-1-56080-317-1

1. Edition: 2016

Soft Cover, 832 pages

### Description

The use of diffraction imaging to complement the seismic reflection method is rapidly gaining momentum in the oil and gas industry. As the industry moves toward exploiting smaller and more complex conventional reservoirs and extensive new unconventional resource plays, the application of the seismic diffraction method to image sub-wavelength features such as small-scale faults, fractures and stratigraphic pinchouts is expected to increase dramatically over the next few years."Seismic Diffraction" covers seismic diffraction theory, modeling, observation, and imaging. Papers and discussion include an overview of seismic diffractions, including classic papers which introduced the potential of diffraction phenomena in seismic processing; papers on the forward modeling of seismic diffractions, with an emphasis on the theoretical principles; papers which describe techniques for diffraction mathematical modeling as well as laboratory experiments for the physical modeling of diffractions; key papers dealing with the observation of seismic diffractions, in near-surface-, reservoir-, as well as crustal studies; and key papers on diffraction imaging.

### Preface

This volume covers the fundamentals of seismic diffraction theory and addresses the practical aspects of the seismic diffraction forward and inverse problems. Seismic diffraction theory is a relatively recent addition to the theory of diffraction, which has evolved over the centuries from its roots in optics, as detailed in SEG's Classical and Modern Diffraction Theory. The inverse problem focuses on diffraction imaging. The great promise of this emerging technology, and the many excellent contributions to date, have motivated the creation of this reference volume as well as the above-mentioned companion volume.Chapter 1 includes a number of short introductory papers on the seismic diffraction problem to provide readers with an overview of the forward and inverse problems. The papers cover important concepts and include numerical and real data examples. Mathematical content is kept to a minimum.

The papers in Chapter 2 cover the theoretical fundamentals of seismic diffraction. Because the papers in this chapter focus on the mathematical physics at the core of the seismic diffraction problem, they assume the reader is familiar with the fundamentals of diffraction theory. We recommend that students of the theory take time to read the papers in Classical and Modern Diffraction Theory in conjunction with Chapter 2.

The crucial difference between classic and seismic diffraction theories is that the latter deals with step discontinuities in the propagation velocities (seismic interfaces). In such cases, the rigorous diffraction problems are analytically unsolvable, with the exception of some degenerate situations (the simplest type of the interface geometry or boundary conditions). For this reason, the development of seismic diffraction theory has primarily been associated with approximate approaches to a problem. In the conventional asymptotic ray theory approximate approaches are usually based on decomposition of the wavefield into highfrequency asymptotic series, while a clear physical meaning can be associated only with leading members of such series. In the diffraction theory the primarily necessary approximations are based on obtaining diffracted waves in the vicinity of the shadow boundaries (boundary layer approximation). This applies to the body waves emanating from interface edges. Principal waves (incident, reflected, and transmitted) are given in the asymptotic ray theory approximation (also known as the ray method) that describes the transport of energy along the corresponding rays, and have the primary shadow boundaries caused by the diffracting edges. The concepts of edge and tip diffracted waves in the classical and geometrical theories of diffraction are included in the seismic domain. Edge waves smooth the discontinuity of the principal waves on the primary shadow boundaries. Similarly, tip waves smooth the discontinuity of the edge waves on the secondary shadow boundaries caused by the tip points of the edges. The total seismic response is represented by superposition of the principal and diffracted waves.

Obtaining such kinds of representation faces a number of challenges. An individual diffracted wave may be considered as an analytical function with a given jump at the shadow boundary. Such an analytical function can be represented as a sum of uniquely defined discontinuous and continuous components. The discontinuous component smoothes the given jump and forms the boundary layer in the neighborhood of the shadow boundary, where the energy spills over from the illuminated region into the shadow region by a process of transverse diffusion. Outside the boundary layer, this component describes the transport of energy along diffracted rays. Chapter 2 focuses on the papers dedicated to the discontinuous component. The physical meaning of the continuous component can be explained in simple terms as follows. There are two power flows in a diffracted wave: one along the diffracted ray (governed by the transport equation) and one across this ray (governed by the equation of transverse diffusion). The diffusion flow incident on the interface which generates the diffracted wave under consideration would violate the boundary conditions on this interface if this flow was not taken into account in advance. To satisfy boundary conditions in such a situation, it is necessary to add in a corresponding amendment to the diffracted wave in a form of the continuous component. Because of its complexity, the treatment of this component is outside the scope of this book.

The theoretical mathematical foundations from the early 1970s of wavefield modeling associated with curvilinear interfaces are based on the Kirchhoff-type integrals and piece-wise plane approximation of the surface of integration. The latter is sufficient to account for the discontinuous components of diffraction phenomena and caustic effects caused by the interface curvature. However, such an approximation creates artifacts in the form of false edge waves caused by singularities of reflection-transmission coefficients of principal waves. Therefore, the development of the theoretical foundations for mathematical modeling includes a search for integral reflection-transmission operators free of such artifacts.

In Chapter 3, the forward problem is presented in a collection of papers which focus on numerical and physical modeling. Whereas the preceding chapter contains a number of numerical modeling studies, the topic of this chapter is the zero-offset and prestack seismic diffraction responses of simple structural and stratigraphic features. The convolutional model of seismic diffraction is another key theme. Whereas geophysicists undoubtedly have good knowledge of the convolutional model of seismic reflection, the convolutional model for seismic diffraction, and the common basis of both convolutional models in the Kirchhoff integral, is probably less well known.

Selected papers illustrating diffractions on seismic data are presented in Chapter 4, including the responses to faulting, nearsurface anomalies, seafloor features, and topography. The seismic data examples illustrate the strong diffraction response of subsurface discontinuity or heterogeneity.

Taken together, the chapters on theory (Chapter 2), forward modeling (Chapter 3), and observations (Chapter 4) are intended to build the same intuitive understanding for seismic diffraction that most exploration and production geophysicists now have for seismic reflection. The early papers presented in these chapters were written in the context of a very different seismic processing and interpretation environment wherein diffractions played a key role. Around 1970, the digital migration of 2D poststack data was still an emerging technology, and the interpretation of unmigrated data was commonplace. A fundamental understanding of the diffraction response to geologic features was essential for seismic interpretation. However, with the rapid advances in reflection imaging technology, which progressed from the 2D poststack to the 3D prestack domain, diffractions dropped out of interpretation workflows for hydrocarbon exploration and production.

Currently, the application of 3D prestack migration is routine, with over half of it now conducted in the depth domain. Thus, diffractions are not commonly used in interpretation workflows, and seismic processing specialists generally regard diffraction energy as a form of coherent noise. But, with the emerging technology of diffraction imaging to characterize small-scale faults and reservoir heterogeneities gaining momentum, the understanding of seismic diffraction from first principles is gaining relevance for seismic interpretation and processing specialists. The more recently published papers, addressing phenomena such as edge and tip rays and effective coefficients for curved interfaces, apply state-of-the-art diffraction theory to the seismic modeling forward problem, setting the stage for the diffraction inverse problem.

Chapter 5, the final section in this volume, focuses on the separation and imaging of diffractions, starting with pioneering work in the 1970s and proceeding to the current state. The separation process removes the reflection data and retains the lowerenergy diffraction data. The imaging process focuses the diffraction energy at the surface locations from which the diffractions originated. Synthetic and real data examples are included. The objective of diffraction imaging is to locate the discontinuities in the subsurface that give rise to diffraction energy. Papers in this section detail a progression of different approaches to this problem.

Several common recurrent themes exist in the literature on diffraction imaging. First, the main motivation of diffraction imaging is its impact on seismic interpretation of complex geologic structures. The introductions to most of the included papers elaborate on the benefits of diffractions to imaging small structural and stratigraphic details, such as pinch-outs, wedge-outs, reef edges, sudden changes of facies, small faults, unconformities, and small scattering objects. In spite of their small size, such structural and stratigraphic details are often crucial to understanding structural relationships and modeling fluid-flow properties in hydrocarbon reservoirs. Features that might appear to be insignificant at an exploration scale are often critical at the reservoir scale. Small faults or other subtle reservoir heterogeneities can have a dramatic effect on the fluid flow of a reservoir. The identification of flow barriers or baffles is a key objective in the use of seismic data to build models for reservoir flow simulation.

The seismic response from all such details is characterized by diffractions. It is fair to say that traditional exploration and production workflows are almost entirely based on the seismic reflection method and that diffraction imaging represents an emerging complementary seismic diffraction method. On the one hand, reflection seismology is recognized as an appropriate tool for processing and imaging the main reflectors in the subsurface, as long as they are laterally smooth and have a pronounced reflective response. On the other hand, discontinuities in smooth reflectors and small scattering objects give rise to diffractions. Thus, they fall outside the scope of reflection seismology and justify the technology of diffraction imaging. Similar to the concept of reflectivity, a concept of diffractivity can be developed. In addition to the reflection image, the diffraction image allows a more detailed and conclusive interpretation.

Diffraction imaging technology is designed to complement reflection imaging. Kinematically, the diffraction image allows small discontinuities to be located and the geometric aspects of structural reflectivity interpretation to be completed. The dynamic interpretation of diffractivity deals with the relation of diffraction amplitude and polarity with structural properties, and it has great potential. Diffractions have been associated with seismic bright spots and flat spots. In a 4D/time-lapse context, diffractions can help monitor the edges of a vertically moving oil − gas deposit. In the context of reservoir flow barriers, there is a great potential for diffraction imaging to complement time-lapse seismic techniques by identifying small faults and baffles in the reservoir.

A topic closely related to the interpretability of a seismic image is resolution. Seismic resolution quantifies the amount of detail that can be retrieved from an image. The classic resolution limit is given by the Rayleigh criterion. This semi-heuristic rule states that the images of two point diffractors can be distinguished if they are further apart than half the seismic wavelength. The Rayleigh criterion puts an upper limit on the resolution of conventional images obtained from the full seismic wave recording, depending on its frequency content.

However, under ideal circumstances, super-resolution, the recovery of image details of subwavelength scale, is achievable. Several papers argue that diffractions are the key to superresolution. Intuitively, this is understandable because diffractions originate from subwavelength-scale features, and the possibility of imaging them depends on isolating diffractions from the full wavefield. In practice, many factors compromise superresolution — most importantly, the signal-to-noise ratio of the data. Nevertheless, the literature on diffraction imaging has numerous examples in which subwavelength-scale information indiscernible on the full-wave image could be recovered from the diffraction image. In many other fields of science, the effort to move past the Rayleigh resolution limit is a leading-edge topic.

The resolution achievable by diffraction imaging is sometimes set against resolution obtained by so-called image-based resolution enhancement techniques. Examples of such techniques are coherency cube analysis (Marfurt et al., 1998), migration deconvolution (Hu et al., 2001), instantaneous attribute extraction (Liu and Marfurt, 2007), and various structure-oriented filters. The point of view taken in diffraction papers is that the high-resolution information from diffractions is essentially lost in conventional processing and imaging. Edge-detection algorithms may show details that have been blurred by the finite-bandwidth nature of the seismic signal. These details, however, are not necessarily related to the physics of wave propagation and inversion or to the underlying structural geology. For instance, an image obtained by an inaccurate migration velocity can contain migration artifacts that are picked up by the edge-detection algorithm and could be mistaken as real edges. Analysis and imaging of diffractions offers a way to unmask such false edges and provides a basis for more reliable interpretation.

The fact that the application of diffraction imaging faces a number of practical challenges is another theme of Chapter 5. The relative strength of the reflection energy and the need to separate the diffraction and reflection energy represent the principal difficulties. The behavior of reflection and diffraction energy in various data domains is an important consideration for the separability of the diffracted and reflected wavefields.

A brief Epilogue to the volume discusses possible future developments and applications of diffraction imaging technology, and highlights some of the key directions for the forward and inverse problems.

We envision rapid advances in applied seismic diffraction theory. Given recent dramatic advances in imaging algorithms and computing power, we are confident that the application of full 3D diffraction imaging will progress rapidly in the industry. Seismic diffraction technology has a compelling potential to impact the entire spectrum of exploration and production workflows, including seismic processing, interpretation, and reservoir modeling, and this potential applies to conventional as well as unconventional resources.