This issue of the RECORDER features contributions from four senior graduate students working with the research group CREWES in the Department of Geoscience at the University of Calgary. These researchers present short summaries of their recent progress towards a better understanding of how seismic waves interact with geological structures, and the creation of new or refined technology for analyzing seismic data. These papers can be read in either one of two possible ways – individually, or as parts of a whole. Individually, each research project provides insights into a particular way, at some point during the data processing flow, we can better or more precisely extract information from seismic data, and then exemplifies algorithms for doing so. But, no doubt because each project has been devised on the backdrop of some common general themes – themes that we as a group have identified as being critical for meaningful seismic research and technology development – they strike me as telling quite a coherent story. My aim in this short overview will be to emphasize this whole cloth view, and to talk a little bit about the main themes as I see them.
The four papers cover a range of topics: (i) wave-based methods for correction of multicomponent statics problems; (ii) data-driven means for separating primaries from multiples in complex and imperfectly characterized geological settings; (iii) the radiation patterns and inversion sensitivities for viscoelastic waves interacting with point scatterers and horizontal reflectors; and (iv) solving for multiple elastic and anisotropic parameters in accelerated multi-parameter full waveform inversion.
Four main themes drive these research projects.
1. Waveform consistency
An increasing number of the processing and inversion steps we carry out, or would at least like to retain the possibility of carrying out, involve treating seismic data as waveforms. That is, as measurements of fields having significant extent in space and time, satisfying a partial differential equation, and having a complex and rich variability that carries large amounts of information about the medium in which it propagates. An obvious example would be full waveform inversion, which derives its potential for high resolution velocity model building, and determination of multiple parameters, from just that starting point: the insistence that the data are measurements of waves. But there are subtler examples also. For instance, in order to carry out seismic amplitude analysis such that it constrains rock properties of real relevance to the reservoir (and to the geologist and engineer), clear AVA/AVAz signal across wide azimuths and near or even beyond critical angles are needed. These amplitudes are understandable outside of a full waveform framework, in terms of a process of reflection at a boundary, and so they don’t explicitly involve analysis of full waveforms. But, in order to reliably estimate these amplitudes as they appear at the instant of reflection, all of the intervening wave processes affecting the data must be understood and accounted for, and doing so requires that we treat data as waveforms. A major theme in our development of any seismic processing technology is to either make sure the step is waveform consistent – meaning it does not carry out any significant manipulation of the data that leaves it unintelligible in terms of a wave equation, or, failing that, to make sure that the manner in which the approach deviates from waveform consistency is very well understood.
2. Accounting for differences between event types.
One of the inconveniences of the “purist” full waveform view in item (1.) above is that it makes interpretations of seismic data in terms of individual events (primaries, multiples, etc.) less meaningful. Events just aren’t part of the language of full and exact wave theory. In order to quantitatively discuss an arrival as an individual thing, fully isolated from other parts of the waveform measurement, one is forced to make an approximation of one stripe or another: single-scattering, stationary-phase, etc. This is contrary to the full waveform "philosophy", in which we try as hard as we can to think of the wave as a single, unified entity. Nevertheless, no matter how committed to a waveform view we wind up becoming in the future, it will never be useless to consider events individually. For one thing, they allow us to quickly, qualitatively and intuitively analyze the data we are working with. But, equally importantly, any seismic methodology that relies on iteratively reducing residuals, i.e., differences between observed and modeled data, and this includes most waveform based technologies, will probably have to come to grips with the differences between types of events. Approximate though the idea is, categorization of seismic data variations into events tends to coarsely divide a seismic record up, based on (a) what part of the geology the seismic wave has interacted with, and (b) what its amplitude is on the backdrop of the wide dynamic range seismic signals occupy. It seems highly likely that in applying any full waveform approach, these two auxiliary pieces of information will be critical to deciding whether a certain update and reduction in residuals is of value or not. A large reduction in residuals associated with an event on the high end of the seismic dynamic range (e.g., a directly propagating arrival) may not be as “valuable” as a small reduction associated with a primary reflection, which was a smaller-amplitude event in the first place, and, in the second place, has tended to interact with more interesting parts of the geology.
3. Multicomponent as a mission critical idea
Multicomponent seismic technology has attracted varied levels of interest and buy-in in the years since it was first considered seriously. But, for us to take meaningful next steps in quantitative interpretation and inversion in aid of seismic monitoring of reservoirs (where we account for the complex relationship between seismic motions and rock properties), involving the full elastic wave field will be necessary. This means that maintaining waveform consistency, item (1.) above, should probably instead be read as maintaining elastic waveform consistency, with 3- or 9-component signals being processed such that the output is understandable as P, SV and SH components of solutions of an elastic equation.
4. A unified development of AVO and full waveform inversion
There have been enough successes in wave-based seismic inversion, and also in rock property determination from AVO (AVA, AVAz, etc.), to suppose there is more yet we can do. That is, more reliably use a wider range of reflection amplitudes to constrain rock properties of direct interest to the engineer and the geologist - fluids, stresses, viscosities, etc.; more completely use full waveform inversion to characterize multiple parameters in the reservoir at high resolution, etc. Should we be promising the moon with full waveform methods? It’s too early for that. But, the potential is worth the risk of some significant research and development investment, and I believe the risk can be mitigated with the right approach. An important way to mitigate the risk of research in any new or poorly understood technology is to understand and leverage its relationship to conventional methodology. It turns out that there is an unambiguous link between the ideas and concepts of AVO and AVO inversion, and those of multi-parameter full waveform inversion. In fact, it is correct to consider AVO inversion to be a special case of FWI as applied to pre-critical reflection data. Now this sounds like a piece of technical trivia, but it has important consequences. It means that, given what we currently understand about how AVO analysis and inversion works, we also understand, to leading order, about how FWI will work in a multi-parameter, reflection-mode setting. Consequently, decades of AVO wisdom developed in the community about what can and cannot be done with real seismic data: which parameters are difficult and which are easier to determine, what is required from acquisition and migration as pre-processing, and what geological or other prior information is needed or desirable to stabilize analysis, etc., will be transferable to properly formulated multi-parameter FWI. The pipeline may work in the other direction, too: new ideas and new capability deriving from FWI research may transfer with a minimum of fuss to existing AVO/inversion workflows. We can view progress made in FWI as progress in AVO inversion, and vice versa.
In the first of the four papers in this issue of the RECORDER, Raul Cova and co-authors (What Should Multicomponent Near-Surface Corrections Look Like in a World of Waveforms?) develop and exemplify a wave-theoretic solution to the converted wave statics problem. Themes (1.) and (3.) appear very clearly in Raul’s work. The statics problem, when solved in a surface-consistent manner, invokes assumptions that elastic waves, especially S-waves, often seriously violate. So, not only may we not be entirely satisfied with surface-consistent statics as applied to multicomponent data, we may furthermore, by carrying this out, have treated it in such a way that its interpretation as a meaningful observation of a wave is damaged. The ray-path consistent approach discussed by Raul goes a long way towards improving the near-surface corrections, and importantly, to maintaining the wave character of the output. So with Raul and co-authors' work, we have the introduction of a practical tool, but we also move closer to a state where our pre-processed multicomponent data can be operated on with full wave methods.
In the second paper, Jian Sun (Interbed Multiple Prediction on Land: Which Technology, and Which Domain?) considers a variant of the internal multiple prediction algorithm that was derived from the inverse scattering series in the 1990s. The practical aim is to understand how the domain of application of the basic concept of the prediction might affect the precision of the result; critical for land application of this powerful but challenging methodology. Beyond that, themes (1.) and (2.) above are evident. The inverse scattering prediction is a wave-equation based procedure, and it separates portions of the field we consider to be multiples from portions we associate with primaries without removing our ability to consider their sum to be waveform consistent1 . This allows us to proceed (as is standard) to subtract the internal multiples from the primaries, a critical step, as Sun discusses, prior to many imaging methods and the quantitative interpretation of amplitudes. But, it also provides us with the ability to discuss multiples and primaries individually, while still considering the impact of both on, say, the residuals of FWI. This may turn out to be critical in understanding how residuals decrease, or should decrease, in a full waveform inversion procedure.
In the third paper, Shahpoor Moradi (Reflections from Contrasts in Isotropic Attenuative Media AVO and Beyond) summarizes work that exemplifies themes (1.), (3.) and (4.). He analyzes the results of P- and S-waves impinging on viscoelastic interfaces in the Earth, describes the consequences this has for viscoelastic extensions of AVO methods, and discusses the connections of this work with the more general problem of scattering from viscoelastic inclusions. The importance of viscoelastic sensitivities to multi-parameter FWI is discussed, as is their close relationship to the AVO equations. Moradi has, in other words, set up very general foundations for: (a) understanding how viscosity (and other mechanisms for attenuating seismic waves) impacts AVO; (b) full multicomponent viscoelastic FWI; and their connectivity.
In the final paper, Wenyong Pan (A Summary of Several Challenges Facing Multi-Parameter Elastic Full Waveform Inversion) assemble and analyze a multi-parameter FWI procedure, geared towards the reconstruction, from elastic data, of anisotropic parameters in a reservoir. Here a range of issues are discussed and exemplified, including themes (1.) and (4.), i.e., the manner in which a full waveform methodology extracts information from seismic data in order to simultaneously estimate a large number of elastic properties, and the role of the scattering / radiation patterns in the sensitivities in increasing/ decreasing the problem of parameter cross-talk.
My hope is that this set of papers will provide an interesting crosssection of the research projects ongoing in exploration and monitoring seismology at the University of Calgary in the CREWES research group. It is far from an exhaustive summary of CREWES research: the full set of seismic problems ranging from instrumentation and acquisition, field and lab, through to processing and inversion methods, through further to theory and modeling, are being considered. This is deliberate, because the most ambitious possible uses of 3D seismic technology will only be realized if this entire chain of issues in the seismic problem are developed in contact with one another. But I think these four young research scientists, in discussing the outcomes of the projects they are taking the lead on, have provided a good, clear view of the kind of science our whole group is pursuing.
1 Doesn’t this contradict the earlier statement, that events cannot be discussed as separate entities without losing the full wave equation character of a method? Not really. It does amount to defining internal multiples in a particular way, in terms of elements of the inverse scattering series, as well as the geometry of the surface on which measurements are made. But within that definition the output (predicted multiples and remaining primaries added together) remains a bona fide wave field measurement.
About the Author(s)
Kris Innanen is an Associate Professor in the Department of Geoscience at the University of Calgary, and Director of the CREWES Project.