First-arrival Times Research Articles

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. © 2012 American Society of Civil Engineers. CE Database subject headings: Radiography; Deep foundations; Simulation; Optimization; Boreholes; Site evaluation. Author keywords: Tomography; Deep foundations; Rock socket; Simulated annealing; Global optimization; Travel time.

Assessment of Tomography Models of Taiwan Using First-Arrival Times from the TAIGER Active-Source Experiment

In 2008, the TAIGER project conducted an active-source experiment in which seismic records from 10 explosions were collected at nearly 1400 locations on the island of Taiwan. In this study, we manually pick the first-arrival times from the explosion records to ensure reliable and accurate travel time observations, and use them to examine the complex P-wave structural variations in the crust beneath Taiwan.

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.

Detection of anomalous features in an earthen dam using inversion of P-wave first-arrival times and surface-wave dispersion curves

To locate anomalous features including seepage pathways through the Daeryong earth-fill dam, P and Rayleigh waves were recorded along a 250-m profile on the crest of the dam. Seismic energy was generated using a 5-kg sledgehammer and detected by 24 4.5-Hz vertical-axis geophones installed at 3-m intervals. P-wave and apparent S-wave velocities of the reservoir dam and underlying bedrock were then inverted from first-arrival traveltimes and dispersion curves of Rayleigh waves, respectively. Apparent dynamic Poisson’s ratios as high as 0.46 were obtained at the base of the dam near its north-east end, where an outlet conduit occurs, and in the clay core body near the south-west end of the profile where the dam was repeatedly grouted to abate seepage before our survey. These anomalies of higher Poisson’s ratios in the upper part of clay core were also associated with effusion of grout on the downstream slope of the dam during post-survey grouting to abate leakage. Combining P-wave traveltime tomography and inversion of Rayleigh wave velocities was very effective in detecting potential pathways for seepage and previous grouted zones in this earthen dam.

A hybrid approach for tomographic inversion of crosshole seismic first-arrival times

A sequential hybrid approach was presented here to invert crosshole seismic first-arrival times. The proposed tomographic scheme combined a simple simulated annealing algorithm with a linearized smoothness-constrained least-squares inversion. The simulated annealing was implemented to obtain a background velocity distribution used by the linearized inversion for the initial guess. The linearized component was based on the functional description of traveltimes. This indicates a nonlinear function, the eikonal equation, providing traveltimes for a given slowness model. Thus an explicit ray tracing was not required by the linearized scheme. The velocity updates were obtained by a matrix inversion based on an iterative conjugate gradient-like LSQR algorithm. Second-difference regularization was used to stabilize the solutions. The Jacobian matrix giving the partial derivatives with respect to the model parameters was constructed by a finite-difference approximation based on the perturbation of the cell slowness. The traveltimes for both the hybrid and linearized schemes were calculated by a fast finite-difference eikonal solver. The hybrid scheme was tested by using both synthetic and field data sets based on the crosshole geometry. According to the tests studies, the tomograms resulted from the hybrid approach better imaged the subsurface velocity distribution. Also the hybrid optimization was characterized by quicker convergence rate than the conventional optimization based on only the linearized inversion. The tests with the synthetic data set also showed that the hybrid approach yielded a solution having lower rms residual, smaller Euclidean distance and lower relative errors in the cell velocities.

Upper crustal P-wave velocity structure of Kii Peninsula, SW Japan by first-arrival traveltime inversion of the Kawachinagano-Kiwa refraction profile

SUMMARY We investigated the upper crustal P-wave velocity structure down to 5 km in the Kii Peninsula, SW Japan by a tomographic inversion of the first-arrival traveltimes from the seismic refraction experiment performed by the Research Group for Explosion Seismology (RGES) in 1988. The observations were carried out on a profile running in the N–S direction from Kawachinagano, Osaka Prefecture to Kiwa, Mie Prefecture. The profile extends for about 65 km across the major geological zones, which characterize the geological features of SW Japan. Six shots were fired and the generated seismic waves were recorded at 86 temporary observation sites. The inversion scheme was applied to 359 first-arrival times to delineate the velocity structure along the profile. In the tomographic scheme, velocity estimation was achieved by an iterative, linearized least-squares inversion. The Jacobian matrix was constructed via a finite-difference approximation by perturbing the slownesses of the cells instead of performing ray tracing. Traveltime calculations were carried out by using a fast finite-difference eikonal solver. Velocity updates were obtained by a matrix inversion algorithm using a conjugate gradient least-squares scheme. In addition, model covariance and model resolution matrices were obtained to assess the velocity image. Two low-velocity zones observed in the northern and southern parts of the profile are the most prominent features of the tomogram. The P-wave velocity structure is generally consistent with the surface geology, and the fault zones associated with the Median (MTL) and Gobo-Hagi (GHTL) tectonic lines across the peninsula.

Comparison of Conduit Volumes Obtained from Direct Measurements and Artificial Tracer Tests

An isolated phreatic loop in a natural cave was used to test the reliability of artificial-tracer tests for estimating the volume of a flooded karst conduit. The volume of a phreatic tube was measured by filling a drained phreatic loop with a constant inflow over a known time period. The volume of the phreatic loop is 190 6 20 m 3 , and it was compared to independent calculations of conduit volumes based on values based on tracer breakthrough curves. The best results were for mean transit time, where tracer-test calculations yielded volumes very similar to the volume obtained by direct filling of the loop. On the other hand, using the first-arrival time or peak time in the volume calculation resulted in considerable underestimation of the phreatic tube's volume, and these methods should be avoided except when breakthrough curves are affected by molecular diffusion. This demonstrates that volume estimation by tracer tests may be quite precise for common natural conduits, but results are strongly affected by the breakthrough-curve parameter chosen by the experimenter.

Upper mantle seismic velocity anomaly beneath southern Taiwan as revealed by teleseismic relative arrival times

Probing the lateral heterogeneity of the upper mantle seismic velocity structure beneath southern and central Taiwan is critical to understanding the local tectonics and orogeny. A linear broadband array that transects southern Taiwan, together with carefully selected teleseismic sources with the right azimuth provides useful constraints. They are capable of differentiating the lateral heterogeneity along the profile with systematic coverage of ray paths. We implement a scheme based on the genetic algorithm to simultaneously determine the relative delayed times of the teleseismic first arrivals of array data. The resulting patterns of the delayed times systematically vary as a function of the incident angle. Ray tracing attributes the observed variations to a high velocity anomaly dipping east in the mantle beneath the southeast of Taiwan. Combining the ray tracing analysis and a pseudo-spectral method to solve the 2-D wave propagations, we determine the extent of the anomaly that best fits the observations via the forward grid search. The east-dipping fast anomaly in the upper mantle beneath the southeast of Taiwan agrees with the results from several previous studies and indicates that the nature of the local ongoing arc–continent collision is likely characterized by the thin-skinned style.

A New Vector Waveform Inversion Algorithm for Simultaneous Updating of Conductivity and Permittivity Parameters From Combination Crosshole/Borehole-to-Surface GPR Data

We have developed a new full-waveform groundpenetrating radar (GPR) multicomponent inversion scheme for imaging the shallow subsurface using arbitrary recording configurations. It yields significantly higher resolution images than conventional tomographic techniques based on first-arrival times and pulse amplitudes. The inversion is formulated as a nonlinear least squares problem in which the misfit between observed and modeled data is minimized. The full-waveform modeling is implemented by means of a finite-difference time-domain solution of Maxwell's equations. We derive here an iterative gradient method in which the steepest descent direction, used to update iteratively the permittivity and conductivity distributions in an optimal way, is found by cross-correlating the forward vector wavefield and the backward-propagated vectorial residual wavefield. The formulation of the solution is given in a very general, albeit compact and elegant, fashion. Each iteration step of our inversion scheme requires several calculations of propagating wavefields. Novel features of the scheme compared to previous full-waveform GPR inversions are as follows: 1) The permittivity and conductivity distributions are updated simultaneously (rather than consecutively) at each iterative step using improved gradient and step length formulations; 2) the scheme is able to exploit the full vector wavefield; and 3) various data sets/survey types (e.g., crosshole and borehole-to-surface) can be individually or jointly inverted. Several synthetic examples involving both homogeneous and layered stochastic background models with embedded anomalous inclusions demonstrate the superiority of the new scheme over previous approaches.

Effects of uncertainty of lithofacies, conductivity and porosity distributions on stochastic interpretations of a field scale tracer test

We investigate the importance of selecting two different methodologies for the determination of hydraulic conductivity from available grain-size distributions on the stochastic modeling of the depth-averaged breakthrough curve observed during a forced-gradient tracer test experiment. The latter was performed in the Lauswiesen alluvial aquifer, located near the city of Tubingen, Germany, by injecting NaBr into a well at a distance of about 50 m from a pumping well. We also examine the joint effect of the choice of the transport model adopted to describe solute transport at the site and the way the spatial distribution of porosity is assessed. In the absence of direct measurements of porosity, we consider: (a) the model used by Riva et al. (J Contam Hydrol 88:92–118, 2006; J Contam Hydrol 101:1–13, 2008), which relates the natural logarithms of effective porosity and conductivity through an empirical, experimentally-based, linear relationship derived for a nearby experimental site; and (b) a model based on a commonly used relationship linking the total porosity to the coefficient of uniformity of grain size distributions. Transport is described in terms of a purely advective process and/or by including mass exchange processes between mobile and immobile regions. Modeling of flow and transport is performed within a Monte Carlo framework, upon conceptualizing the aquifer as a random composite medium. Our results indicate that the model adopted to describe the correlation between conductivity and porosity and the way grain-sieve information are incorporated to depict the heterogeneous distribution of hydraulic conductivity can have relevant effects in the interpretation of the data at the site. All the conceptual models employed to describe the structural heterogeneity of the system and transport features can reasonably reproduce the global characteristics of the experimental depth-averaged breakthrough curve. Specific details, such as the peak concentration and the time of first arrival, can be better reproduced by a double porosity transport model when a correlation between conductivity and porosity based on grain size information at the site is considered. The best prediction of the late-time behavior of the measured breakthrough curves, in terms of the observed heavy tailing, is offered by directly linking porosity distribution to the spatial variability of particle size information.

Distribution and invasion genetics of the quagga mussel (Dreissena rostriformis bugensis) in German rivers

The quagga mussel Dreissena rostriformis bugensis, native to the Dnieper and the northern Black Sea, has become a major invasive species in both the Volga River and the North American Great Lakes since the early 1990s. Findings in the Netherlands (2006) and Germany (2007) mark the start of its establishment in Western Europe. We investigated the current distribution, time of first arrival and population structure of D. rostriformis bugensis from the rivers Rhine, Main and in the Main-Danube canal in Germany. Two putative sources of the German populations were analysed by genetically comparing these populations to older invasive populations from North America and the southeast Danube. Dreissena rostriformis bugensis was abundant in the Main and in three Rhine harbours, but rare in the actual Rhine river and absent south of the Main-Danube canal. Mussels found in the Rhine harbours were significantly smaller than in the Main. Population genetic analyses found no sign of founder effects and minimal differentiation between German, North American and southeast Danube populations. The genetic data suggest that these invasive populations derive from a common and rapidly expanding source. Based on the non-continuous distribution and shell size differences of Rhine harbour and Main populations, our results indicate that expansion in Germany involved at least two independent settling events, one of which happened before 2005, and most likely was caused by jump dispersal.

An analysis of the first-arrival times picked on the DSS and wide-angle seismic section recorded in Italy since 1968

We performed an analysis of refraction data recorded in Italy since 1968 in the frame of the numerous deep seismic sounding and wide-angle reflection/refraction projects. The aims of this study are to construct a parametric database including the recording geometric information relative to each profile, the phase pickings and the results of some kinematic analyses performed on the data, and to define a reference 1D velocity model for the Italian territory from all the available refraction data. As concerns the first goal, for each seismic section we picked the P-wave first-arrival-times, evaluated the uncertainties of the arrival-times pickings and determined from each travel time-offset curve the 1D velocity model. The study was performed on 419 seismic sections. Picking was carried out manually by an algorithm which includes the computation of three picking functions and the picking- error estimation. For each of the travel time-offset curves a 1D velocity model has been calculated. Actually, the 1D velocity-depth functions were estimated in three different ways which assume: a constant velocitygradient model, a varying velocity-gradient model and a layered model. As regards the second objective of this work, a mean 1D velocity model for the Italian crust was defined and compared with those used for earthquake hypocentre locations and seismic tomographic studies by different institutions operating in the Italian area, to assess the significance of the model obtained. This model can be used in future works as input for a next joint tomographic inversion of active and passive seismic data.

An Implementation of Parallel Fast Marching Using the Message Passing Interface

This document introduces a program based on the algorithm described by Maria Cristina Tugurlan. The program uses file readers, image filters, and file writers from the Insight Toolkit ITK www.itk.org. It produces as output an image whose values are the times of first arrival of a wavefront that spreads from seed points with a speed at every point equal to the input image intensity. It performs the computation in parallel on distributed memory computers using the Message Passing Interface MPI. Each MPI process reads a small piece of the input image into memory. It computes fast marching on its piece. It sends and receives the values from fast marching at piece boundaries. It recalculates fast marching a number of times set from the command line using the new boundary values each time. Each MPI process writes only a small piece of the output file.A substantial difference is seen when the output of MPI fast marching is compared to the output of serial fast marching. This difference may be acceptable for some uses. The program should be able to handle input images that are too large to fit in the memory of a single computer.

Traveltime tomographic inversion with simultaneous static corrections — Well worth the effort

We have developed a first-arrival traveltime inversion scheme that jointly solves for seismic velocities and source and receiver static-time terms. The static-time terms are included to compensate for varying time delays introduced by the near-surface low-velocity layer that is too thin to be resolved by tomography. Results on a real data set consisting of picked first-arrival times from a seismic-reflection 2D/3D experiment in a crystalline environment show that the tomography static-time terms are very similar in values and distribution to refraction-static corrections computed using standard refraction-statics software. When applied to 3D seismic-reflection data, tomography static-time terms produce similar or more coherent seismic-reflection images compared to the images using corrections from standard refraction-static software. Furthermore, the method provides a much more detailed model of the near-surface bedrock velocity than standard software when the static-time terms are included in the inversion. Low-velocity zones in this model correlate with other geologic and geophysical data, suggesting that our method results in a reliable model. In addition to generally being required in seismic-reflection imaging, static corrections are also necessary in traveltime tomography to obtain high-fidelity velocity images of the subsurface.

Seismic first-arrival tomography with functional description of traveltimes

A two-dimensional smoothness-constrained least-squares inversion scheme was applied to seismic first-arrival time data. The inversion scheme was based on the functional description of traveltimes; thus, it did not require a step of ray tracing, and traveltimes were obtained by a finite-difference eikonal solver. The Laplacian difference of cell slownesses was used for the smoothness constraint. Model velocities were obtained by matrix inversion including the QR decomposition and iterative LSQR method. The Jacobian matrix of the partial derivatives was constructed by a finite-difference approximation based on the perturbation of the cell slowness. Since the construction of the Jacobian matrix was the most time-consuming step of the inversion scheme, Broyden's update was used for this matrix, and it was replaced by its numerical approximation obtained from Broyden's method after the third iteration and for all subsequent iterations to expedite the inversion process. This significantly improved the computational performance of the scheme by reducing the computer time for the calculation of the Jacobian matrix. The algorithm was tested by using a number of synthetic and field data sets. The test studies included both surface seismic refraction and crosshole seismic data acquisition configurations. Also image appraisal analyses were performed for the solutions obtained from both surface and crosshole field data sets by calculating model covariance and model resolution matrices. The presented algorithm yielded satisfactory results during the test studies. The stability and fast convergence rate were the main characteristics of the algorithm.

Assisted traveltime picking of crosshole GPR data

We introduce two new traveltime picking schemes developed specifically for crosshole ground-penetrating radar (GPR) applications. The main objective is to automate, at least partially, the traveltime picking procedure and to provide first-arrival times that are closer in quality to those of manual picking approaches. The first scheme is an adaptation of a method based on cross-correlation of radar traces collated in gathers according to their associated transmitter-receiver angle. A detector is added to isolate the first cycle of the radar wave and to suppress secon-dary arrivals that might be mistaken for first arrivals. To improve the accuracy of the arrival times obtained from the crosscorrelation lags, a time-rescaling scheme is implemented to resize the radar wavelets to a common time-window length. The second method is based on the Akaike information criterion(AIC) and continuous wavelet transform (CWT). It is not tied to the restrictive criterion of waveform similarity that underlies crosscorrelation approaches, which is not guaranteed for traces sorted in common ray-angle gathers. It has the advantage of being automated fully. Performances of the new algorithms are tested with synthetic and real data. In all tests, the approach that adds first-cycle isolation to the original crosscorrelation scheme improves the results. In contrast, the time-rescaling approach brings limited benefits, except when strong dispersion is present in the data. In addition, the performance of crosscorrelation picking schemes degrades for data sets with disparate waveforms despite the high signal-to-noise ratio of the data. In general, the AIC-CWT approach is more versatile and performs well on all data sets. Only with data showing low signal-to-noise ratios is the AIC-CWT superseded by the modified crosscorrelation picker.

Applications of engineering seismology for site characterization

We determined the seismic model of the soil column within a residential project site in Istanbul, Turkey. Specifically, we conducted a refraction seismic survey at 20 locations using a receiver spread with 484.5-Hz vertical geophones at 2-m intervals. We applied nonlinear tomography to first-arrival times to estimate the P-wave velocity-depth profiles and performed Rayleigh-wave inversion to estimate the S-wave velocity-depth profiles down to a depth of 30 m at each of the locations. We then combined the seismic velocities with the geotechnical borehole information regarding the lithology of the soil column and determined the site-specific geotechnical earthquake engineering parameters for the site. Specifically, we computed the maximum soil amplification ratio, maximum surface-bedrock acceleration ratio, depth interval of significant acceleration, maximum soil-rock response ratio, and design spectrum periods TA-TB. We conducted reflection seismic surveys along five line traverses with lengths between 150 and 300 m and delineated landslide failure surfaces within the site. We recorded shot gathers at 2-m intervals along each of the seismic line traverses using a receiver spread with 4 840-Hz vertical geophones at 2-m intervals. We applied nonlinear tomography to first-arrival times to estimate a P-wave velocity-depth model and analyzed the reflected waves to obtain a seismic image of the deep near-surface along each of the line traverses.

Uncertainty analysis in statics corrections obtained by tomographic inversion: Application in a mountainous zone in Catatumbo (Colombia)

Seismic tomography techniques are frequently used to obtain velocity models of the weathering layer, which are then used to calculate static corrections times. The main idea in tomography is to use the misfit between synthetic and observed first-arrival (refraction) times to correct an initial velocity model. Due to the nature of the seismic method where, in general, sources and receivers are placed on only one edge of the medium, the Earth surface, it can be shown that inverting for velocities using the observed times does not give a unique solution. Instead, a family of solutions is obtained that explains the same data set. To give a meaning to a nonunique solution, uncertainty analysis techniques are necessary. They can give information about the family of solutions such as which zones have a larger error, which zones are better resolved, is there a dispersion measurement (such as variance) associated with the solution model family, and is there a more probable solution model. To give clues to the answ...

First-Passage and Extreme-Value Statistics of a Particle Subject to a Constant Force Plus a Random Force

We consider a particle which moves on the x axis and is subject to a constant force, such as gravity, plus a random force in the form of Gaussian white noise. We analyze the statistics of first arrival at point $x_1$ of a particle which starts at $x_0$ with velocity $v_0$. The probability that the particle has not yet arrived at $x_1$ after a time $t$, the mean time of first arrival, and the velocity distribution at first arrival are all considered. We also study the statistics of the first return of the particle to its starting point. Finally, we point out that the extreme-value statistics of the particle and the first-passage statistics are closely related, and we derive the distribution of the maximum displacement $m={\rm max}_t[x(t)]$.

Turning-ray tomography using a low-spatial-frequency model parameterization

A linear least-squares inversion is applied to the turning-ray first-arrival times of a shallow-marine seismic reflection data set to estimate the slowly varying (laterally and vertically) components of the near-surface velocity field. The velocity model is represented with a low-spatial-frequency parameterization (2D cubic B-splines) designed specifically for the predicted components of the data. This model parameterization effectively decouples the slowly varying background from the higher spatial-frequency component of the velocity field produced by shallow, low-velocity, gas-charged sands and allows the solution to be obtained in a single iteration. The observed first-arrival times (background and shallow anomaly-induced perturbations) and the slowly varying first-arrival times related to the background velocity are inverted separately. Similar velocity-model estimates result, demonstrating the decoupling imposed by the B-spline model parameterization. The background velocity and the low-velocity anomalies are best treated as separate inverse problems using very different model parameterizations. Ray tracing a synthetic model containing local low-velocity anomalies embedded in a smooth background does not accurately predict the anomaly-induced first-arrival time perturbations seen in the field data. Acoustic finite-difference waveform modeling shows that reflections and diffractions from the anomalies interfere with the diving-wave first arrivals. First-arrival times picked from the full-waveform synthetics more accurately predict the field data first-arrival times.