Khiem T. Tran

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.

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.

Evaluation of Unknown Foundations Using Surface-Based Full Waveform Tomography

An application of two-dimensional (2D) time-domain full waveform tomography is presented to evaluate existing foundations using surface-based seismic wave fields. The full waveform inversion (FWI) technique is based on a finite-difference solution of 2D elastic wave equations and the Gauss–Newton inversion method. Both compression-wave (P-wave) and shear-wave (S-wave) velocities are inverted independently and simultaneously to increase the credibility of characterized profiles. The FWI technique was applied on both synthetic and real experimental data sets. Inverted results of synthetic data revealed that individual embedded foundation elements (piles) and soil between piles were distinguished. For real experimental data, seismic surface wave fields were measured next to two drilled shafts with a 1.2-m diameter and a 15-m length and then inverted by the FWI technique. The waveform analysis successfully profiled embedded shaft elements and subsurface soil stratigraphy, and shaft lengths of 15 m were also predicted.

Characterization of Abandoned Mine Voids Under Roadway with Land-Streamer Seismic Waves

The paper presents an application of two-dimensional (2-D) time-domain waveform tomography for characterization of abandoned underground mine voids under a highway. Measured surface-based seismic wave fields are inverted by a full waveform inversion technique that is founded on a finite-difference solution of 2-D elastic wave equations and the Gauss–Newton inversion method. The key advantage of this waveform approach is the ability to generate all possible wave propagation modes of seismic wave fields (body waves and Rayleigh waves) by forward modeling; the modes are then compared with measured data to infer complex subsurface properties. Both the pressure wave and shear wave velocities are inverted independently and simultaneously to increase the credibility of characterized profiles. Real experimental data sets were collected on asphalt pavement by using a land streamer, which did not require that geophones be coupled into the pavement and allowed the testing system to be moved along the road quickly. The seismic results show that the waveform analysis was able to delineate two mine voids embedded at a depth of about 15 m. The existence of the voids was confirmed by confirmation drilling.

Shear Wave Velocity via Inversion of Full Waveforms

Full waveforms are inverted using two global optimization methods, a genetic algorithm and simulated annealing. The inversion scheme is based on a finite-difference solution of the 2-D elastic wave equation in the time-distance 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 herein with synthetic data sets. The inversion results show the ability of characterizing both low- and high-velocity layers in laterally inhomogeneous profiles. Based upon the cases presented, coupling of global optimization with full waveforms is computationally practical, as the results presented herein were all achieved in a few hours of computer time on a standard laptop computer.

Evaluation of Drilled Shaft Capacity Using Embedded Sensors and Statnamic Testing

AbstractThis paper presents an application of the embedded data collector (EDC) approach using strain and acceleration measurements at the top and bottom of a pile (drilled shaft) during dynamic loading (Statnamic) for estimation of static side and tip resistance. For assessment of the skin friction, wave propagation along the pile was modeled as a one-dimensional (1D) wave equation with nonlinear static skin friction and viscous damping. The soil–pile system was divided into segments, and each segment was characterized with independent multilinear skin friction. The skin friction of each segment was determined by least-squares fitting of computed particle velocities to the measured data at the top and bottom of the pile. For assessment of the tip resistance, the pile tip was modeled as a single—degree-of-freedom nonlinear system. A nonlinear stiffness–displacement relationship was determined by balancing force and energy from inertia, damping, and stiffness against the measured tip data. The technique wa...

Shear Wave Velocity Profiles of Roadway Substructures from Multichannel Analysis of Surface Waves and Waveform Tomography

Assessment of roadway subsidence caused by embedded low-velocity anomalies is critical to the health and safety of the traveling public. Surface-based seismic techniques are often used to assess roadways because of data acquisition convenience and large depths of characterization. To mitigate the negative impact of closing a traffic lane under traditional seismic testing, a new test system that uses a land streamer is presented. The main advantages of the system are the elimination of the need to couple the geophones to the roadway, the use of only one source at the end of the geophone array, and the movement of the whole test system along the roadway quickly. For demonstration, experimental data were collected on asphalt pavement overlying a backfilled sinkhole that was experiencing further subsidence. For the study, a 24-channel land streamer and a propelled energy generator to generate seismic energy were used. The test system was pulled by a pickup truck along the roadway and the data were collected with 81 shots at every 3 m for a road segment of 277.5 m, with a total data acquisition time of about 1 h. The measured seismic data set was analyzed by the standard multichannel analysis of surface waves (MASW) and advanced two-dimensional (2-D) waveform tomography methods. Eighty-one one-dimensional shear wave velocity (VS) profiles from the MASW were combined to obtain a single 2-D profile. The waveform tomography method was able to characterize subsurface structures at a high resolution (1.5- × 1.5-m cells) along the test length to a depth of 22.5 m. Very low S-wave velocity was obtained at the repaired sinkhole location. The 2-D VS profiles from the MASW and waveform tomography methods are consistent. Both methods were able to delineate high- and low-velocity soil layers and variable bedrock.