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Karhunen-Loeve method
Algorithm for Surface Wave Suppression on 2D Seismic Data Using the Slant Karhunen–Loeve Transform in a Time-Frequency Domain
Application of Karhunen-Loève Transform Algorithms in Hydrogeological Parameter Compression: A Comparative Study
Ground-roll extraction using the Karhunen-Loeve transform in the time-frequency domain
Efficient Propagation of Epistemic Uncertainty for Probabilistic Seismic Hazard Analyses (PSHAs) Including Partial Correlation of Magnitude–Distance Scaling
Introduction
Abstract The lowering of a recording device down a borehole for seismic investigation purposes was first reported by F.A. Fessenden (1917). This work was the basis for bore-hole seismic development in the late 1920s (Barton, 1929). Investigation of horizontal layers and first arrivals (velocity anomalies) in the area of salt domes followed in the 1930s to 1950s (McCollum and LaRue, 1931; Dix, 1939, 1945, 1946; Navarte, 1946; Gardiner, 1949; Holste, 1959). Using the check shot or velocity surveys, Levin and Lynn (1958) analyzed the recordings of later arrivals beyond the time of the first arrival (primary downgoing wave). Their work was followed by a major investigation by Gal’perin (1974). The vertical seismic profile (VSP) techniques evolved from these early seismic/borehole studies. Kennett et al. (1980) presented one of the earlier comprehensive discussions of the processing and utility of vertical seismic profile data. In this paper, higher frequency VSP data were compared with suface-seismic data for the purposes of seismic event correlation. Multiple reflection identification using the downgoing waves, surce pulse deconvolution, and prediction of reflections ahead of the bit were also examined. More recently, Hardage (1985) prepared an excellent comprehensive summary of the utility of the seismic profiling technique. This author established the basic guidelines for VSP interpretation. The benefit of the VSP in terms of understanding corresponding geologic logs and for providing additional seismic interpretational insight was reviewed by Stewart and DiSiena (1989). DiSiena et al. (1981, 1984) and Toksöz and Stewart (1984) detailed the utility of recording three-component data in the borehole. Abstract Vertical seismic profile (VSP) surveys differ from other types of borehole and surface-seismic methods in that they utilize surface sources and borehole receivers and record both upgoing and downgoing wavefields. Strong and consistent sources are available for use on or near the surface, and the borehole provides a relatively noise-free environment for VSP recording.Reverse VSP and cwsswell (CWS) surveys described by Hardage (1992) are similar to VSPs in that they record both upgoing and downgoing wavefields, but they differ with respect to source and receiver configurations. The reverse VSP utilizes downhole sources and surface receivers, and like surface-seismic recording, is affected by variable ground coupling and all the noise inherent in surface-recorded data. Downhole sources, although improving, do not yet create a good signal-to-noise ratio for the reverse VSP method in comparison to the VSP (Zimmerman and Chen, 1993). The CWS technique uses both borehole sources and receivers in adjacent wellbores. The crosswell survey can give a high resolution seismic picture of the reservoir (Khalil et al., 1993; Li, 1994; Li and Stewart, 1994) but is not yet a widespread, low-cost imaging tool.Surface-seismic surveys, with which we are most familiar, are conducted using both surface or near-surface sources and receivers and record only the upgoing wavefields. Abstract The term interpretive VSP processing is used to refer to a generalized iterative pro-cessing methodology where the interpretations of the output of a processing step and the input data are used to modify preceding steps and/or to constrain subsequent process—ing parameters. Early interpretive processing methodologies focused largely on using VSP results to guide surface-seismic processing (Stone, 1981; Hardage, 1985) and on the determination of specific processing variables such as reflector dip (Noponen, 1988). More recently, VSP and intermediate surface-seismic outputs have been interactively analysed so that the interpreter can continuously monitor the effectiveness of processing steps such as multiple attenuation. One example of such an application is described by Naess (1989) in a paper on model-based transform (MBT) processing. A second example, using marine seismic data, is presented by Hinds and Durrheim (1993). These authors used a Karhunen-Loeve (K-L) based multiple attenuation scheme (Jones, 1985; Jones and Levy, 1987) to create an output seismic section. The latter was used as input to MBT pro—cessing. In the vicinity of the well site, VSP results could be used to further constrain the MBT processing by supplying a refined definition of primary reflections. Interpretive processing of VSP data involves the continuous monitoring and interpretation of the data during processing to constrain the various processing stages. Flowchart 1 illustrates interpretive processing for median-filter-based wavefield separa—tion. Median filter wavefield separation processing involves the amplitude balancing of raw data, static shifting, median filtering to isolate the downgoing events, amplitude bal—ancing of the separated downgoing event data, Abstract On the basis of conventional surface-seismic data, an exploratory well (referred to as the VSP well) was drilled into the up-dip, raised rim of the Devonian Leduc Formation reef complex at Lanaway Field, south-central Alberta, Canada. The VSP well was expected to encounter an anomalous late-stage carbonate accretionary buildup at the Leduc level. It was anticipated that the Leduc at the VSP well location would be about 80 m higher than at adjacent rim well sites. The envisioned accretionary growth was not present; the top of the Leduc in the VSP well was consistent with other rim wells in the vicinity (Figure 3.2) and inconsistent with the seismic interpretation. Fortunately, however, the Leduc was structurally closed, and the VSP well was completed as an oil well (producing both from the Nisku and Leduc formations). To resolve the apparent discrepancy between the interpreted surface-seismic data and geology at the VSP well, a near-offset vertical seismic profile (VSP) was recorded at the well site. The interpretation of the VSP was relatively successful in that these data con—firmed that the original interpretation of the surface-seismic data, with respect to the Nisku, Ireton, and Leduc tops, was incorrect, and also that the anomaly observed on the surface-seismic line was not a processing artifact. Our interpretation is that the surface-seismic anomaly is caused by several superposed effects, including anomalous structural relief at the pre-Cretaceous subcrop, stratigraphic anomalies (thicker sections of reefal car—bonate) within the Winterburn Group, and seismic focusing caused by draping of the Ireton Abstract On the basis of the interpretation of conventional surface-seismic data, an exploratory well (referred to as the VSP well) was drilled in the Ricinus Field, southern Alberta, Canada. Prior to drilling, the prognosis was that the VSP well had a reasonable chance of encountering gas-bearing Leduc Formation reef (the northeastern updip mar—gin of the known full reef). The known full reef had been defined by existing wells as shown in Figure 4.1. However, the VSP well encountered only off-reef shale and was ulti—mately abandoned. The final interpretation was that the VSP well had been drilled some 800 m northeast of the full reef build-up. Prior to the abandonment of the VSP well, two VSP surveys were run at the VSP well site. These data were acquired to resolve the apparent discrepancy between the inter—preted surface-seismic data and the actual geology at the VSP well site, and to evaluate the feasibility of whipstocking the VSP well to the southwest in the direction of the known full reef complex. One of the VSP surveys had a source offset of 199 m (near-offset), the other had a source offset of 1100 m (far-offset). The VSP data were definitive and allowed for a more confident and geologically consistent interpretation of the surface-seismic data, and clearly indicated that whipstocking was not an economically viable option. Abstract The deltaic sandstones of the basal Kiskatinaw Formation (Stoddart Group, upper Mississippian) were preferentially deposited within structural lows in a regime character—ized by faulting and structural subsidence. These sandstone facies can form reservoirs where they are laterally sealed against the flanks of upthrown fault blocks. Exploration for basal Kiskatinaw reservoirs generally is accompanied by the acquisition and interpreta—tion of surface-seismic data prior to drilling. These data are used to map the grabens in which these sandstones were deposited and the location of horst blocks which act as lat—eral seals. In the case study of the Fort St. John Graben area, northwest Alberta, Canada, three vertical seismic profile (VSP) surveys were conducted at the 9-24-82-11 W6M exploratory well site subsequent to drilling. These data supplemented the surface-seismic and well-log control such that:1) direct correlation was made with the surface-seismic data, ensuring that the surface-seismic control was accurately tied to the subsurface geology;2) multiples were identified on the VSP data, and their effect on the interpretation of the surface-seismic data was determined; and3) the subsurface geology, in the vicinity of the borehole, was more clearly imaged on the VSP data than on the surface-seismic control and reveals amplitude anomalies and faults which are not evident on the surface-seismic data. Abstract On the basis of conventional surface-seismic data, the 13-15-63-25 W5M exploratory well was drilled into a low-relief Leduc Formation reef (Devonian Woodbend Group) in the Simonette area, west-central Alberta, Canada. The prognosis was that the well would intersect the crest of the reef and encounter 50 to 60 m of pay. Unfortunately, it was drilled into a flank position of the reef and was abandoned. The decision to abandon the well, as opposed to whipstocking in the direction of the reef crest, was made after the acquisition and interpretive processing of both near- and far-offset (252 and 524 m, respectively) VSP data, and after the re-analysis of existing surface-seismic data. The near- and far-offset VSPs were recorded and interpreted while the drill rig remained on-site, with the immediate objectives of determining an accurate tie between the surface-seismic data and the subsurface geology, and mapping relief along the top of the reef over a distance of 150 m from the 13-15 well in the direction of the adjacent pro—ductive 16-16 well (with a view to whipstocking). These surveys proved to be cost-effec—tive in that the operator was able to determine that the crest of the reef was out of the tar—get area, and that whipstocking was not a viable alternative. The use of VSP surveys allowed the operators to avoid the costs associated with whipstocking and to feel confi—dent with their decision to abandon the well. Abstract In this Appendix, the median, K-L, f-k and t-p filtering, VSP deconvolution, and the matrix equations involved in the hodogram-based and time-variant polarizations are reviewed. These processes represent some of the fundamental processes involved in VSP data processing. One wavefield separation method utilizes a 1-D median filter combined with a band-pass filter. The band-pass filter eliminates the median filter "whiskers" (Hardage, 1985) resulting from the nonlinear operation. The theoretical basis of the median filter has been reviewed in Gallagher and Wise (1981), Nodes and Gallagher (1982), Fitch et al., (1984), Arce and McLoughlin (1984), and Arce et al., (1986). The input to the median filter is a selected window of data. The length of the window can be an even or an odd number of points (2N or 2N+1). The two ends of the time series are padded with N additional points in order to accommodate the center location of the window. The windowed data are sorted according to magnitude with the center value of the sort being termed the median value. For the odd point filter, the median value at the center of the windowed time series becomes the new value of the output series. When N is even, the mean of the two middle median values is the output of the filter. This new point of the output data is placed at the location of the center of the window of the input series. For the 1-D median filter application, a new output time series is generated as the window slides across the input series, one point at a time.