Reinaldo J. Michelena

Tomographic traveltime inversion using natural pixels

Traditionally in the problem of tomographic traveltime inversion, the model is divided into a number of rectangular cells of constant slowness. Inversion consists of finding these constant values using the measured traveltimes. The inversion process can demand a large computational effort if a high‐resolution result is desired. We show how to use a different kind of parameterization of the model based on beam propagation paths. This parameterization is obtained within the framework of reconstruction in Hilbert spaces by minimizing the error between the true model and the estimated model. The traveltimes are interpreted as the projections of the slowness along the beampaths. Although the actual beampaths are described by complicated spatial functions, we simplify the computations by approximating these functions with functions of constant width and height, i.e., “fat” rays, which collectively form a basis set of natural pixels. With a simple numerical example we demonstrate that the main advantage of this ...

Mapping distribution of fractures in a reservoir with P-S converted waves

Where reservoir rock is very impermeable (limestones, cherts, dolomite, etc.), fractures may provide all or most of its porosity and effective permeability. Studies of producing oil wells in fractured limestones have determined a single fracture of width 1 mm, under favorable reservoir conditions, can provide sufficient permeability to yield over 1500 m3 (240 bbl) of oil per day. Consequently, mapping locations of high intensity fractures and determining their orientation/lateral extent could be of great value in reservoir development, especially for locating horizontal well sites.

Singular value decomposition for cross-well tomography

I perform singular value decomposition (SVD) on the matrices that result in tomographic velocity estimation from cross‐well traveltimes in isotropic and anisotropic media. The slowness model is parameterized in four ways: One‐dimensional (1-D) isotropic, 1-D anisotropic, two‐dimensional (2-D) isotropic, and 2-D anisotropic. The singular value distribution is different for the different parameterizations. One‐dimensional isotropic models can be resolved well but the resolution of the data is poor. One‐dimensional anisotropic models can also be resolved well except for some variations in the vertical component of the slowness that are not sensitive to the data. In 2-D isotropic models, “pure” lateral variations are not sensitive to the data, and when anisotropy is introduced, the result is that the horizontal and vertical component of the slowness cannot be estimated with the same spatial resolution because the null space is mostly related to horizontal and high frequency variations in the vertical componen...

Near and far offset P-to-S elastic impedance for discriminating fizz water from commercial gas

In many practical situations when the objective is to differentiate between high and low gas concentrations, using P-to-P (PP) seismic data alone may not be enough to successfully complete the task. The abrupt reduction in P-wave velocity (VP) with the first few percent of gas controls the seismic response. Therefore, usually only the presence of gas, but not the saturation, can be detected with PP seismic. This well known physical phenomena can be modeled by Gassmanns equation, and was documented by Domenico in 1976. In contrast, density (ρ) varies more gradually and linearly with gas saturation, while S-wave velocity (VS) does not vary much. As noted by Berryman et al. (2002), the linear behavior of ρ with saturation makes seismic attributes that are closely related to density useful proxies for estimating gas saturation. Attempting to extract and to use information about rock density from AVO analysis or inversion has not been a successfully robust approach in many cases because of limitations in data...

Introduction to this special section: Practical applications of anisotropy

The use of seismic anisotropy is a topic that has evolved dramatically in the last 25 years in the oil and gas industry. Even though physicists who study waves and vibrations in solids have taught us that elastic properties of rocks should be described by a complex set of functions and parameters, many years of seismic data processing were conducted assuming that the velocities in the subsurface rocks were isotropic, and that the shear modulus was zero (that the rocks could be treated as “a liquid”). “Isotropic” means that the value measured (e.g., velocity) is the same in all directions (whether you consider angles of incidence or source-receiver azimuths) for a rock volume of interest.

Similarity analysis; a new tool to summarize seismic attributes information

Seismic attribute analysis is generally performed by correlating various attributes with reservoir properties. Even though experienced interpreters may have developed a good intuition about which attributes usually exhibit good correlation with particular reservoir properties, correlations between attributes and reservoir properties cannot be extrapolated from one reservoir to another. The analysis becomes more difficult as the number of attributes becomes larger, since the interpreter has to rely less on his/her experience and more on the actual correlations found in the data. Although some of the attributes seem to provide different information about lateral changes in the study area, they also contain redundant information that makes the analysis even more awkward.

Introduction to “Recent Advances in Shear Wave Technology for Reservoir Characterization: A New Beginning?”

Ninety-nine professionals, the majority of whom have significant experience with shear waves, gathered in October 2000 at the SEG-EAGE Summer Research Workshop in Boise, Idaho, U.S. The 63 papers presented raised many hotly debated technical issues. More general issues also emerged during the discussions: What is the application domain of a technology heralded as one that will profoundly influence the future of our profession? Why has multicomponent technology not been the commercial success we were hoping for, despite the heavy investments? What is needed to make this technology more beneficial to interpreters and decision makers? And many more.

Facies probabilities from multidimensional crossplots of seismic attributes: Application to tight gas Mamm Creek Field, Piceance Basin, Colorado

Crossplots are commonly used in the geosciences to gain qualitative insight about relationships between different variables, typically three (for two-dimensional colored crossplots). On rare occasions, the relationships among four variables are explored by using three-dimensional colored crossplots. The variable used to color the crossplot is usually related to the property of interest, sand or pay for instance. In these cases, crossplots can be used in a quantitative sense by selecting (drawing) a region in the crossplot where most of the property of interest “lives.” Drawing a polygon in a 2D crossplot to separate “good” from “bad” areas is the extension to 2D of simple cutoffs commonly applied to 1D well-log data to separate scenarios of interest. One drawback of this approach is that it works best only when there is no overlap between the region occupied by the property of interest and the region occupied by the background. Another drawback is that it is difficult to extend to three-dimensional crossp...

An introduction to this special section Reservoir modeling constrained by seismic

Reservoir modeling is recognized as the construction of a 3D numerical representation of the hydrocarbon reservoir, in depth, comprising the reservoir structure (e.g., as delimited by stratigraphic horizons and faults); internal architecture (e.g., depositional facies); petrophysical properties (e.g., porosity, permeability); and fluid distribution (e.g., water saturation). Some of the purposes of a reservoir model include quantification of hydrocarbon volumes, input to flow simulation for quantification of recoverable hydrocarbons, and well positioning.

Constraining 3D facies modeling by seismic-derived facies probabilities: Example from the tight-gas Jonah Field

Seismic reservoir characterization is usually based on the interp retation of seismic attributes that relate to the geological feature or reservoir property of interest. If we are interested in fault geometries, a variety of geometric attributes can be used to map the details of fault distributions and constrain discontinuities and flow barriers in geological and flow-simulation models. If we are interested in reservoir properties, however, the usual approach is to estimate seismic attributes that are qualitatively related to such properties. The interpretation of the attribute focuses on the identification of “good” and “bad” areas depending on how the attribute relates to the property of interest.