Refraction Tomography mapping of near-surface dipping layers using landstreamer data at East Canyon Dam, Utah Julian Ivanov*, Richard D. Miller, Kansas Geological Survey; Richard D. Markiewicz, U.S. Bureau of Reclamation; Jianghai Xia, Kansas Geological Survey Summary We apply the P-wave refraction-tomography method to seismic data collected with a landstreamer. Refraction-tomography inversion solutions were determined using regularization parameters that provided the most realistic near-surface solutions that best matched the dipping layer structure of nearby outcrops. A reasonably well matched solution was obtained using an unusual set of optimal regularization parameters. In comparison, the use of conven-tional regularization parameters did not provide as realistic results. Thus, we consider that even if there is only quali-tative a-priori information about a site (i.e., visual)—as in the case of the East Canyon Dam, Utah—it might be possible to minimize the refraction nonuniqueness by estimating the most appropriate regularization parameters. Introduction This refraction tomography inversion research is part of a larger applied research project (Miller et al., 2005), which attempted to evaluate the applicability of several seismic techniques for identifying, delineating, and estimating the seismic characteristics or properties of materials within and beneath East Canyon Dam. These methods include: P-wave refraction tomography (2-D turning ray), multichannel analysis of surface-wave (MASW) (Park et al., 1999; Xia et al., 1999, Miller et al., 1999), VSP (near vertical and off-set), checkshot survey (downhole), and 2-D P & S reflection. East Canyon Dam is located in north central Utah, 11 miles southeast of the town of Morgan, Utah (Figure 1). Completed in 1966, it is located in a narrow-walled canyon where the East Canyon Creek has cut through very hard, massive, well-cemented beds of late upper-Cretaceous conglomerate. This massive conglomerate is part of a sequence of layers possessing a dominant upstream dip. The analyzed seismic data set was acquired along the toe road (running parallel to East Canyon Creek, outlet of the dam) using a towed array. Parameters for these data were selected to allow a subset to be used for the MASW method and another for refraction-tomography analysis. The objec-tive of the profile along the toe road was exclusively native rock. MASW and turning ray tomography are targeting anomalies within the shallow portion of the native rock and materials. Near the ground surface the dipping layers within the conglomerate produce an irregular contact between the weathered and unweathered materials.

Figure 1: Utah Bureau of Reclamation dams.

It has been known that the inverse refraction-traveltime prob-lem (IRTP) can have many solutions (Slichter, 1932; Healy, 1963; Ackerman et al., 1986; Burger, 1992; Lay and Wallace, 1995). Sheehan and Doll (2003) showed that refraction-tomography algorithms can converge on many different, yet equally possible solutions. The general approach to resolve nonuniqueness is the inclusion of additional a-priori infor-mation (Zdanov, 2002), most often in the form of a regular-ization parameter. The most popular way of applying regularization in the inversion algorithms is the use of smoothing constraints (Constable et al., 1987; Meju, 1994). Ivanov et al. (2005) noticed that the IRTP could have a continuous range of possible solutions and showed (Ivanov et al., 2006) that regularization parameters can bias the final solution toward their predefined mathematical trend. This observation explained the wide range of solutions offered by present inversion algorithms for specific data sets. Ivanov et al. (2006) proposed the joint analysis of refractions with surface waves (JARS) method, which uses a reference com-pressional-wave velocity (Vp) model, derived from surface-wave shear-wave velocity (Vs) estimates to resolve refraction nonuniqueness. The JARS method provided more realistic results than other IRTP algorithms when applied to seismic data acquired in the Sonora Desert, Arizona, USA (Ivanov et al., 2006) and levee sites in southern Texas and southern New Mexico (Ivanov et al., 2007). However, the extent of lateral heterogeneity at this particular site did not allow the acquisition of usable surface-wave energy for the majority of the line. As a result, it was not

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Refraction-Tomography mapping of dipping layers

possible to acquire a Vs model and apply the JARS method. This situation required the search for other (than surface wave) types and ways to incorporate a-priori information for regularization parameters and thereby provide more realistic results. The steep dipping-to-the-west layers can be observed within the conglomerate on the northern side of the toe road (Figure 2). This qualitative observation was instrumental in the search for such regularization parameters that would provide solutions with a similar structure. We used 1st and 2nd order smoothing as well as model damping regularizations to various extents and weights. As well, another form of impacting the final results was used by giving different weights to the rays sampling the near surface and the deeper parts of the sections. A solution, which visually matched well the observed steep dipping layers, was obtained using an unusual set of optimal regularization parameters, namely 2nd order regularization in the horizontal direction only and model increment damping.

Data Acquisition The seismograph used for all components was a Geometrics StrataView w/NZC StrataVisor controller. A total of 240 channels were available. MASW and turning ray tomography data were acquired using a towed spread of geophones. A total of 30 Geospace 4.5 Hz geophones connected to steel shoes on a fire hose were dragged behind a skid-steer style loader with a rubberband assisted weight drop (RAWD) (Figure 3). Receiver spacing was 4 ft and source station spac-ing was 8 ft. Continuous surveys were acquired by dragging the geophone spread behind the source from source point to source point. Results P-wave first-arrivals were picked from data acquired along the toe line. The first-arrivals appear irregular from trace to trace. First-arrival patterns appear wavy and change rapidly within a few shots from one another (Figure 4).

Figure 2. View to the west of the toe road from the dam crest(east). Dipping layers (to the west) can be defined by changes inmaterial “weatherability.”

We used 1st and 2nd order smoothing with different weights to obtain a series of IRTP solutions. Selecting regularization parameter weights is considered subjective (Claerbout, 1992, p. 82), regardless of the algorithm used (Hansen, 1998; Xia et. al., 2005). No matter its forms, API quantifies expecta-tions (about the solution) that are not based on actual data (Menke, 1989, p. 48). Consequently, the selection of the weight and type of the smoothing constraints was influenced by the qualitative overall smoothness and expectations of the final Vp solution. Another criteria for selecting weights was the absence of unstable and sporadic (randomly appearing) values. Initially, we acquired similar to solutions similar to those offered by existing commercial software. An IRTP solution

Figure 3. Towed spread and RAWD. Collecting data along the toe roadmoving from east to west.

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Refraction-Tomography mapping of dipping layers

Figure 4. First-arrival picks from P-wave seismic shot records recorded at levee crest in southern Texas. was selected using second-degree smoothing regularization (Depprat-Jannaud and Lailly, 1993), often preferred over other types of regularization (Zhang and Toksoz, 1998) (Figure 5a). Another solution was acquired using first-degree smoothing regularization with the same weight as in the first case (Figure 5b). Both solutions provided reasonable overall Vp models but did not manage to provide significant details. To test if different initial models could lead to different solutions, we searched for solutions using different initial models while keeping the rest of the inversion parameters identical. All inversion results converged to the same solu-tions, suggesting that the regularization parameters were the major factor influencing the final results for this data set. Consequently, the initial model was considered an irrelevant in finding the most appropriate solution. In an effort to provide a more accurate image of the near surface, we looked for different approaches for regularization by testing different weights for 1st and 2nd order smoothing in the horizontal direction only, combined with model damp-ing. The IRTP solution that seemed to fit the observed dipping layer structure well (Figure 5c) was obtained using the same weight for damping and half the weight for 2nd order smoothing in comparison to the weight used for the standard smoothing solutions (Figure 5a and 5b) The chosen turning-ray tomography solution (Figure 5c) suggests a low-velocity thin veneer of weathered conglom-

erate overlays a very high-speed conglomerate. Dipping and associated subcrop of unweathered conglomerate are evident on tomography data as shingling of high-velocity slabs with an apparent dip consistent with surface mapping. We also tried to provide better focusing of the IRTP solution by giving different (greater or smaller) weights to the rays that sample the shallow portion of the section relative to those sampling the deepest parts. The corresponding weights changed linearly or non-linearly with receiver offset. There were indications that emphasizing longer ray paths could further support the steep-dipping layered structure but at the expense of instability and greater randomness of some parts of the finals solution (Figure 5d). The numerous IRTP data results using different initial models, raypath length emphasis, regularization types, and weights are not presented for shortness. The selected solu-tions with unusual regularization (Figure 5c and 5d) appear more plausible from geologic perspective. Conclusions Emphasizing longer ray paths at the expense of instability and more irregular ray coverage is reasonable for this particular site. It makes sense that rays would tend to propagate through the high-velocity parts of the section and sample less or pass around the low-velocity areas in view of the velocity contracts of the shingled steep dipping layers. In view of such reasoning, this poorer ray coverage solution was included in the final results for consideration. It is evident from the results that a traditional regularization approach did not provide accurate imaging of the subsurface that is consistent with the observed outcrops. Comparisons of the experimental regularization in the application of the IRTP with conventional regularization demonstrate that the suggested approach of partial regularization is advancement in the application of the inverse refraction-traveltime problem algorithms. Acknowledgments The authors would like to thank the U.S. Bureau of Reclamation for providing on-site assistance and access. We also thank Jamie Lambrecht, David Thiel, Chad Gratton, and Andrew Newell, the field crew from KGS. We also appreciate Mary Brohammer for her assistance in manuscript preparation. Disclaimer The opinions expressed herein are those of the authors and not necessarily those of the U.S. Bureau of Reclamation or the Kansas Geological Survey.

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Refraction-Tomography mapping of dipping layers

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Figure 5. East Canyon Dam refraction-tomography 2D images from P-wave seismic data acquired at the base of the dam. a) P-wave refraction-tomography solution using conventional 2nd order smoothing regularization, b) P-wave refraction-tomography solution using conventional 1st order smoothing regularization, c) P-wave refraction-tomography solution using non-conventional regularization: 2nd order smoothing in the horizontal direction only and model increment damping, and d) P-wave refraction-tomography solution using non-conventional regularization: 2nd order smoothing in the horizontal direction only and model increment damping giving 16 times greater weight to the ray arriving at the farthest offset. Blank areas within the images indicate lack of ray coverage and are intentionally left in.

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EDITED REFERENCES Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 2008 SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web. REFERENCES Ackerman, H. D., L. W. Pankratz, and D. Dansereau, 1986, Resolution of ambiguities of seismic refraction traveltime curves:

Geophysics, 51, 223–235. Burger, H. R., 1992, Exploration geophysics of the shallow subsurface: Prentice Hall. Claerbout, J. F., 1992, Earth-sounding analysis: Processing versus inversion: Blackwell Science Publications. Constable, S. C., R. L. Parker, and C. G. Constable, 1987, Occam’s inversion: A practical algorithm for generating smooth

models from electromagnetic sounding data: Geophysics, 52, 289–300. Delprat-Jannaud, F., and P. Lailly, 1993, Ill-posed and well-posed formulations of the reflection traveltime tomography problem:

Journal of Geophysical Research, 98, 6589–6605. Hansen, C., 1998, Rank-deficient and discrete ill-posed problems: Numerical aspects of linear inversion: Technical University of

Denmark, Lyngby. Healy, J. H., 1963, Crustal structure along the coast of California from seismic-refraction measurements: Journal of Geophysical

Research, 68, 5777–5787. Ivanov, J., R. D. Miller, and J. Xia, 2007, Applications of the JARS method to study levee sites in southern Texas and southern

New Mexico: 77th Annual International Meeting, SEG, Expanded Abstracts, 1725–1729. Ivanov, J., R. D. Miller, J. Xia, and, D. Steeples, 2005, The inverse problem of refraction traveltimes, part II: Quantifying

refraction nonuniqueness using a three-layer model: Pure and Applied Geophysics, 162, 461–477. Ivanov, J., R. D. Miller, J. Xia, D. Steeples, and C. B. Park, 2006, Joint analysis of refractions with surface waves: An inverse

refraction-traveltime solution: Geophysics, 71, R131–R138. Lay, T., and T. Wallace, 1995, Modern global seismology: Academic Press. Meju, M. A., 1994, Biased estimation: a simple framework for inversion and uncertainty analysis with prior information:

Geophysical Journal International, 119, 521–528. Menke, W., 1989, Geophysical data analysis: Discrete inverse theory: Academic Press. Miller, R. D., J. Ivanov, R. D Markiewicz, and D. O’Connell, 2005, Estimating vibration response of East Canyon Dam, Utah,

from P-, S-, and surface-wave measurements: Proceedings of the Symposium on the Application of Geophysics to Engineering and Environmental Problems.

Miller, R. D., J. Xia, C. B. Park, and J. M. Ivanov, 1999, Multichannel analysis of surface waves to map bedrock: The Leading Edge, 18, 1392–1396.

Park, C. B., R. D. Miller, and J. Xia, 1999, Multichannel analysis of surface waves: Geophysics, 64, 800–808. Sheehan, J., and W. Doll, 2003, Evaluation of refraction tomography codes for near-surface applications: 73rd Annual

International Meeting, SEG, Expanded Abstracts, 1235–1238. Slichter, L. B., 1932, The theory of interpretation of seismic traveltime curves in horizontal structures: Physics, 3, 273–295. Xia, J., C. Chen, G. Tian, R. D. Miller, and J. Ivanov, 2005, Resolution of high-frequency Rayleigh-wave data: Journal of

Environmental and Engineering Geophysics, 10, 99–110. Xia, J., R. D. Miller, C. B. Park, J. A. Hunter, and J. B. Harris, 1999, Evaluation of the MASW technique in unconsolidated

sediments: 69th Annual International Meeting, SEG, Expanded Abstracts, 437–440. Zhang, J., and M. N. Toksoz, 1998, Nonlinear refraction traveltime tomography: Geophysics, 63, 1726–1737. Zhdanov, M. S., 2002, Geophysical inverse theory and regularization problems: Elsevier.

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