Dennis R. Hiltunen

Two-Dimensional Inversion of Full Waveforms Using Simulated Annealing

AbstractThe paper presents a technique to invert two-dimensional (2D) full wavefields using simulated annealing and a finite-difference solution of the 2D elastic wave equation in the time-distance domain. The algorithm generates all possible wave types (body waves, surface waves, etc.) to simulate complex seismic wavefields and for comparison with observed data. Model runs with both synthetic and actual experimental data sets illustrate the capability of the inversion technique. The results from synthetic data demonstrate the potential of characterizing both low- and high-velocity layers in laterally inhomogeneous profiles, and the inversion results from actual data are consistent with the crosshole, standard penetration test N-value, and material log results. Based on the cases presented, the coupling of global optimization with full waveforms is computationally practical; the results presented herein required less than 1 day of computer time on a standard laptop computer.

A Comparison of Shear Wave Velocity Profiles from SASW, MASW, and ReMi Techniques

Three surface wave techniques, SASW, active MASW, and passive MASW, were conducted at a well-characterized test site. Crosshole shear wave velocity, SPT N-value, and geotechnical boring logs were also available for the test site. For the multi-sensor active test data, it was observed that the cylindrical beamformer transform provided the best resolution in dispersion data over a wide range of frequencies. The dispersion data obtained from all three surface wave techniques was generally in good agreement, and the inverted shear wave profiles were consistent with the crosshole, SPT N-value, and material log results.

Characterization of SASW Phase Angle and Phase Velocity Measurement Uncertainty

The spectra-analysis-of-surface-waves (SASW) method is a nondestructive test for characterization of the variation with depth of the shear wave velocity of soils. While the testing procedure is well developed, only one preliminary study has investigated measurement uncertainty associated with SASW, and the methods utilized to quantify measurement uncertainty were prohibitive to routine assessment. Knowledge of this uncertainty, and ability to include its assessment in routine testing, would allow for inclusion of SASW results in reliability based design and in assessment of the spatial variability of shear modulus. In this study, a large sample of test data was collected from two test sites. Characteristic statistics, statistical distribution, and measurement uncertainty were determined for each phase of SASW. Using the empirical statistical properties and measurement uncertainty results as validation criteria, an analytically based uncertainty assessment system was developed. Specifically, it was shown that SASW phase angle and inverse phase angle typically display a coefficient of variation (COV) of 2 %, and samples appear normally distributed. Further, SASW phase velocity data typically display a coefficient of variation (COV) of 2 %, and the COV for combined phase velocity data is typically 1.5 %. Both phase velocity and combined phase velocity samples appear normally distributed. In addition, it was found that by using a small sample of experimental data and the analytically based process developed in this study, measurement uncertainty of SASW phase angle and phase velocity could be assessed as part of routine testing.

One-Dimensional Inversion of Full Waveforms using a Genetic Algorithm

A technique is presented to invert full waveforms using a genetic algorithm. The inversion scheme is based on a finite-difference solution of the 2-D elastic wave equation in the timedistance domain. The strength of this approach is the ability to generate all possible wave types (body waves and surface waves, etc.) and thus to simulate complex seismic wavefields that are then compared with observed data to infer subsurface properties. The capability of this inversion technique is tested with both synthetic and real experimental data sets. The inversion results from synthetic data show the ability of characterizing both low- and high-velocity layers, and the inversion results from real data are generally consistent with crosshole, SPT N-value, and material log results, including the identification of a buried low-velocity layer. Based upon the cases presented, coupling of global optimization with full waveforms is computationally practical, as the results presented herein were all achieved in about two hours of computer time on a standard laptop computer.

Inversion of First-arrival Time Using Simulated Annealing

A technique is presented to invert first-arrival time using simulated annealing. The scheme is based on an extremely fast finite-difference solution of the Eikonal equation to compute the first-arrival time through the velocity models by the multistencils fast marching method. The core of the simulated annealing, the Metropolis sampler, is applied in cascade with respect to shots to significantly reduce computer time. In addition, simulated annealing provides a suite of final models clustering around the global solution and having comparable least-squared error to allow determining uncertainties associated with inversion results. The capability of this inversion technique is tested with both synthetic and real experimental data sets. The inversion results show that this technique successfully maps 2-D velocity profiles with high variation. The inverted wave velocity from the real data appears to be consistent with cone penetration test (CPT), geotechnical borings, and standard penetration test (SPT) results.

Inversion of Combined Surface and Borehole First-Arrival Time

Site characterization for the design of geotechnical structures such as deep foundations is crucial, as unanticipated site conditions still represent the most common and most significant cause of problems and disputes that occur during construction. Surface-based refraction methods have been widely used recently to assess spatial variation, but one of the biggest limitations of these methods is that they cannot well characterize reverse profiles (decreasing in velocity with depth), buried low-velocity zones, or deep bedrock. An addition of borehole data to surface data is expected to improve inversion results. In this study, the coupling of so-called downhole and refraction tomography techniques using only one borehole is presented. To both qualitatively and quantitatively appraise the capability of the data, a global inversion scheme based on simulated annealing was investigated. Many synthetic and real test data sets with or without boreholes were inverted using the developed technique to obtain both inverted profiles and associated quantitative uncertainties. A comparison of tomograms utilizing the combined borehole and surface data against tomograms developed using just the surface data suggests that significant additional resolution of inverted profiles at depth are obtained with the addition of a borehole. The uncertainty estimates provide a quantitative assessment of the reliability of the interpreted profiles. It is also found that the quantitative uncertainties associated with the inverted profiles are significantly reduced when adding a borehole. In addition, the inversion results of the combined data provide credible information for the design of deep foundations, particularly useful in implementing the new load and resistance factor design methodology that can explicitly account for spatial variability in design parameters. DOI: 10.1061/(ASCE)GT.1943-5606.0000587.

Ground Proving Three Seismic Refraction Tomography Programs

During a recent ground-proving exercise at the shared University of North Florida and University of Florida karstic limestone geophysical and ground-proving test site in central Florida, the limestone bedrock surface was mapped along several survey lines with both intrusive and geophysical techniques. Analyses of the site investigation data revealed a highly erratic limestone bedrock surface, which is common in karst terrane. Analysis of seismic refraction data demonstrated that three commercially available refraction tomography software systems can reveal the undulating bedrock surface. However, the tomography data revealed marked differences in the compression wave velocities at the top of the bedrock surface at various locations along one of the survey lines. Compression wave velocities were highest within slots or valleys and lowest at the tops of blocks or pinnacles. This variability is attributed to the geologic history of the limestone, which includes how the limestone was formed and how the limestone weathered. Ground proving via cone penetration tests and geotechnical borings appears to corroborate this finding and demonstrates the importance of measuring multiple material parameters during site characterization activities in complex terranes.

Effects of Moisture and Time on Stiffness of Unbound Aggregate Base Coarse Materials

Resilient modulus and Youngs modulus are parameters increasingly used to characterize the behavior of pavement materials, both in the laboratory and in the field. The small-strain modulus response of unbound aggregate base coarse materials to various moisture environments was documented. Modulus is not constant, even when held at constant moisture, and significant changes in modulus occur with drying and wetting of the material. The response to drying and wetting cycles appears to be repeatable and suggests that the underlying mechanism that controls the response is reversible. This behavior can have a significant effect on the use of modulus for pavement design and quality acceptance.

Rebar Detection with Cover Meter and Ultrasonic Pulse Echo Combined with Automated Scanning System

A sufficient concrete cover is essential to ensure the durability of reinforced concrete structures. Nondestructive testing methods that can measure the concrete cover are therefore promising tools. As a part of a research project funded by the Florida Department of Transportation, the capabilities and limitations of cover meter measurements in relation to this testing problem were investigated. Researchers designed a reinforced concrete test block on which properties such as rebar depth, size, and spacing and number of reinforcement layers were varied; the effects these variations had on the measurements were studied. The use of an automated testing frame consisting of two scanners that examined the test block from both sides ensured high positioning accuracy and constant quality in data acquisition and made possible the collection of the data along an extremely dense grid. In addition to the cover meter measurements, which referred only to the cover of the layer closest to the surface, ultrasonic pulse echo measurements were conducted, and a synthetic aperture focusing technique was applied to the data to make the rebars become apparent in refined B-scan images.

Detailing of a Systematic Protocol for Surface Wave Inversion

Surface wave methods provide an in situ shear wave velocity profile for a soil system. The most difficult component of the various methods is typically the inversion process. The study presented herein demonstrates a new protocol to guide or constrain the inversion process to provide a quality, realistic shear wave velocity profile. In this study, a database of experimental dispersion data was created, from which five general trends of dispersion data were chosen. The simplified models were used to demonstrate details of the new protocol. Based upon the analyses performed, the inversion protocol is shown to successfully invert a wide range of dispersion data. For the cases presented, the observed fit between experimental and predicted dispersion curves is excellent, and the shear wave velocity profile appears reasonable, believable, and in sufficient detail. Further, the trend in shear wave velocities determined via the protocol is quite consistent with material classification and standard penetration test results available. Using shear wave velocity uncertainty estimated via an error prediction procedure as a criterion, a conclusive stopping criterion for the inversion was noted: follow the protocol until no further layers as small as 0.3048 m (1 ft) can be added to the profile. INVERSION PROTOCOL ABSTRACT: Surface wave methods provide an in situ shear wave velocity profile for a soil system. The most difficult component of the various methods is typically the inversion process. The study presented herein demonstrates a new protocol to guide or constrain the inversion process to provide a quality, realistic shear wave velocity profile. In this study, a database of experimental dispersion data was created, from which five general trends of dispersion data were chosen. The simplified models were used to demonstrate details of the new protocol. Based upon the analyses performed, the inversion protocol is shown to successfully invert a wide range of dispersion data. For the cases presented, the observed fit between experimental and predicted dispersion curves is excellent, and the shear wave velocity profile appears reasonable, believable, and in sufficient detail. Further, the trend in shear wave velocities determined via the protocol is quite consistent with material classification and standard penetration test results available. Using shear wave velocity uncertainty estimated via an error prediction procedure as a criterion, a conclusive stopping criterion for the inversion was noted: follow the protocol until no further layers as small as 0.3048 m (1 ft) can be added to the profile.