Traveltime Equation Research Articles

Estimation of Subsurface Flow Hydrograph of Catchments by Time-Area Hydrograph Method

Aim of the studyIn this study, a novel approach was undertaken, employing the concept of SSF isochrones in tandem with the time-area histogram (TAH) method as a fresh model for SSF estimation within catchments.Material and methodsLeveraging the subsurface travel time equation of hillslopes and GIS software, the spatial delineation of isochrones within the soil was accomplished. Furthermore, a methodology was introduced to compute the TAH of SSF. Subsequently, the subsurface hydrograph of the catchment was derived by convoluting the TAH of SSF with the infiltration hyetograph. To validate the findings, the subsurface hydrographs calculated using the geomorphologic instantaneous unit hydrograph (GIUH) model were juxtaposed with those from two catchments in northern Taiwan—Heng-Chi and San-Hsia.Results and conclusionsThe mean error in comparison with the SSF time-area model stood at 10.5%, affirming the robustness of the proposed approach.10.5%.

Detecting Reinforced Concrete Rebars Using Ground Penetrating Radars

A new algorithm is developed to automatically detect rebar locations and diameters of reinforced concrete structures using the ground penetrating radar technique. The study uses two-way travel time and biquadratic equations to formulate electromagnetic wave speed in reinforced concrete structures where hyperbolic signatures are approximated. Leveraging an established algorithm, a computer code has been developed to offer automated analysis of ground-penetrating radar data obtained from survey grids. Four reinforced concrete slabs were designed, fabricated, and tested to validate the developed evaluation approach. The proposed methodology demonstrates outstanding signal processing proficiency and reliably and effectively identifies rebar information.

Cross-related microseismic location based on improved particle swarm optimization and the double-difference location method of jointed coal rock mass

The location algorithm is the core of microseismic monitoring, and the location results directly influence the effectiveness of the subsequent source analysis. We introduced the double-difference (DD) location method in seismic location into microseismic monitoring. We built a travel time equation of the layered velocity model using the ray-tracing theory and analyzed the waveform cross-correlation of the microseismic data using a generalized cross-correlation (GCC) technique. The improved particle swarm algorithm was successfully conducted to improve the randomness of the initial location. We then adopted the DD location method to precisely locate the secondary location, and it showed better location accuracy and computational efficiency than that by a traditional location algorithm based on the simplified geological model. The theoretical simulation and practice results in deep mining show that the proposed method significantly increased the location accuracy, and the results were concentrated and consistent with the field results. Moreover, we verified the importance of the velocity model for location accuracy. This algorithm also increased the ease of identifying fracture regions, providing the necessary theoretical and technical support for the source location of the jointed coal rock mass in deep mining.

2.5D multifocusing imaging of crooked-line seismic surveys

Two-dimensional seismic surveys often are conducted along crooked-line traverses due to the inaccessibility of rugged terrains, logistical and environmental restrictions, and budget limitations. The crookedness of line traverses, irregular topography, and complex subsurface geology with steeply dipping and curved interfaces could adversely affect the signal-to-noise-ratio of the data. The crooked-line geometry violates the assumption of a straight-line survey that is a basic principle behind the 2D multifocusing (MF) method and leads to crossline spread of midpoints. In addition, the crooked-line geometry can give rise to potential pitfalls and artifacts and thus leads to difficulties in imaging and velocity-depth model estimation. We develop a novel MF algorithm for crooked-line seismic data and revise the traveltime equation accordingly to achieve better signal alignment before stacking. Specifically, we have developed a 2.5D MF reflection traveltime equation that explicitly takes into account the midpoint dispersion and cross-dip effects. The new formulation corrects for normal, inline, and crossline dip moveouts (DMOs) simultaneously, which is significantly more accurate than removing these effects sequentially. Applying normal moveout, DMO, and cross-DMO separately tends to result in significant errors, especially for large offsets. The 2.5D MF method can perform automatically with a coherence-based global optimization search on data. We investigated the accuracy of the new formulation by testing it on different synthetic models and a real seismic data set. Applying our approach to the real data led to a high-resolution seismic image with a significant quality improvement compared to the conventional method. Numerical tests indicate that the new formula can accurately focus the primary reflections at their correct location, remove anomalous dip-dependent velocities, and extract true dips from seismic data for structural interpretation. Our method efficiently projects and extracts valuable 3D structural information when applied to crooked-line seismic surveys.

Double event joint location method considering P-wave arrival time system errors

Microseismic (MS) source location is a core technology in MS monitoring that helps to infer the mechanical state of the rock mass and prevent dynamic disasters. However, when considering P-wave arrival time system errors (PATSEs), conventional location methods encounter the problem of high inversion dimensions and do not consider the influence of large P-wave arrival time errors. Therefore, we proposed a low-dimension double event joint location (DEJL) method that considers the PATSEs and introduces data field theory to reduce the influence of large P-wave arrival time errors. First, the P-wave travel-time equation of double events was constructed to eliminate the earthquake occurrence time and PATSEs, and the high-dimension inversion was reduced to a set of equations containing only six parameters. Then, 2000 P-wave arrival time combinations from more than six sensors were selected, and a Newton iterative based algorithm was proposed to solve the location point of each combination. Finally, the location point with the largest potential value of the data field was considered as the location result. The Institute of Mine Seismology acquisition system, placed in the Yongshaba mine in Guizhou Province, China, was selected to conduct the tests. P-wave arrival time datasets were obtained from two synthetic locations and eight blasting events. The results showed that the average location error of the blasting events using the proposed method is 32.59 m, which is lower than that of the homogeneous velocity-based location results. Thus, we determined that the proposed method offers a good MS location accuracy and broad application potential.

Generalized cross-dip moveout correction of crooked 2D seismic reflection surveys

In hard rock settings, reflection seismic surveys are often acquired on crooked roadways. Acquisition geometry-related noise resulting from these crooked profiles obscures the final image in places where there are crossline dipping reflectors. This noise can be prevented with cross-dip moveout (CDMO) corrections. The conventional practice is to apply corrections on straight processing lines; however, this aggravates reflection duplication and stretching artifacts. We have adopted an efficient method for CDMO correction that operates on any common midpoint (CMP) binning geometry. Our method suppresses reflection duplication in high-fold CMP bins. The strike and dip of the reflectors are decomposed into two horizontal orthogonal components and input into a 3D traveltime equation. Using a synthetic model, a processing workflow was developed to locally apply these generalized CDMO corrections. This workflow was then applied to a seismic profile acquired over the Larder-Lake Cadillac Deformation Zone in the Abitibi Greenstone Belt, Canada. The final processed seismic image showed an increased coherency of reflections rendering them more compatible with the known surface geology of the study area.

First-arrival traveltime inversion of seismic diving waves observed on undulant surface

SUMMARY A non-iterative first-arrival traveltime inversion method (NFTI) is proposed for building smooth velocity models using seismic diving waves observed on irregular surface. The new ray and traveltime equations of diving waves propagating in smooth media with undulant observation surface are deduced. According to the proposed ray and traveltime equations, an analytical formula for determining the location of the diving-wave turning points is then derived. Taking the influence of rough topography on first-arrival traveltimes into account, the new equations for calculating the velocities at turning points are established. Based on these equations, a method is proposed to construct subsurface velocity models from the observation surface downward to the bottom using the first-arrival traveltimes in common offset gathers. Tests on smooth velocity models with rugged topography verify the validity of the established equations, and the superiority of the proposed NFTI. The limitation of the proposed method is shown by an abruptly-varying velocity model example. Finally, the NFTI is applied to solve the static correction problem of the field seismic data acquired in a mountain area in the western China. The results confirm the effectivity of the proposed NFTI.

Predicting Travel Times of Bus Transit in Washington, D.C. Using Artificial Neural Networks

This study aimed to develop travel time prediction models for transit buses to assist decision-makers improve service quality and patronage. Six-months’ worth of Automatic Vehicle Location and Automatic Passenger Counting data for six Washington Metropolitan Area Transit Authority bus routes operating in Washington, DC was used for this study. Artificial Neural Network (ANN) models were developed for predicting travel times of buses for different peak periods. The analysis included variables such as length of route between stops, average dwell time and number of intersections between bus stops amongst others. Quasi-Newton algorithm was used to train the data to obtain the ideal number of perceptron layers that generated the least amount of error for all peak models. Comparison of the Normalized Squared Errors generated during the training process was done to evaluate the models. Travel time equations for buses were obtained for different peaks using ANN. The results indicate that the prediction models can effectively predict bus travel times on selected routes during different peaks of the day with minimal percentage errors. These prediction models can be adapted by transit agencies to provide patrons with more accurate travel time information at bus stops or online. Doi: 10.28991/cej-2020-03091615 Full Text: PDF

Rational approximation of P-wave kinematics — Part 1: Transversely isotropic media

In seismic data processing and several wave propagation modeling algorithms, the phase velocity, group velocity, and traveltime equations are essential. To have these equations in explicit form, or to reduce algebraic complexity, approximation methods are used. For the approximation of P-wave kinematics in acoustic transversely isotropic media, we have developed a new flexible 2D functional equation in a continued fraction form. Using different orders of the continued fraction, we obtain different approximations for (1) phase velocity as a function of phase direction, (2) group velocity as a function of group direction, and (3) traveltime as a function of offset. Then, we use them in the approximation of the group direction as a function of phase direction, and phase direction as a function of group direction. The proposed approximations have a rational form, which is considered algebraically simple and computationally efficient. The used continued fraction form rapidly converges to exact kinematics. By introducing the optimal ray into our approximations and using it for parameter definition, the convergence becomes faster, so the accuracy of the existing most accurate approximations is available by the third order, and new most accurate approximations are obtained by the fourth order of the proposed general form. The error of the most accurate version of the proposed approximations is below 0.001% for moderate anisotropic models with an anellipticity parameter up to 0.3. This high accuracy is considered to be attractive in practical implementations that use the kinematic equations and their derivatives.

Traveltime computation and OBN seismic record simulation for rugged seafloor in VTI medium

ABSTRACT To improve the computational accuracy of seismic traveltime for complex structures in inhomogeneous media, a mesh generation method that is adaptive to a rugged seafloor or interface is presented. A hybrid mesh discrete velocity model consisting of conventional rectangular mesh and irregular quadrilateral mesh is also proposed. The local traveltime equations for the hybrid mesh are derived from the linear traveltime interpolation (LTI) method and are shown to be stable. The relationship between the group velocity and group angle is converted into that between group velocity and interpolated point coordinates, extending the LTI ray tracing algorithm to multiwave simulation in vertical transversely isotropic (VTI) medium by multi-stage partitioning. Computations of the first arrival, reflection, multiple reflection, multiple transmission conversion, and multiple reflection conversion seismic waves in the VTI medium with rugged seafloor and complex structural interfaces are realised. The results show that the proposed method can adapt to the rugged seafloor and velocity interfaces of complex structures, resulting in higher computational accuracy of the traveltime and ray paths for ocean bottom node (OBN) seismic wave simulation. The accuracy of the proposed method is verified by comparison with the finite-difference method. This method will be useful for modelling of seismic waves, wavefield identification, and study of seismic wave propagation in OBN seismic observations.

Automatic estimation of traveltime parameters in VTI media using similarity-weighted clustering

Compared with hyperbolic velocity estimation methods, nonhyperbolic methods (such as shifted hyperbola) are better choices for large offsets or vertical transverse isotropy (VTI) media. Since local seismic event slope contains subsurface information, they can be used to estimate zero-offset two-way traveltime and normal moveout velocity. The traditional velocity estimation methods require a great deal of manual work and are also prone to human error. In order to estimate the traveltime parameters for VTI media automatically, in this paper, we propose to use predictive painting and similarity-weighted clustering to obtain traveltime parameters. The predictive painting is used to estimate zero-offset two-way traveltime, and the shifted-hyperbola traveltime equation is used to obtain velocity and anisotropy attributes. We first map local slopes to zero-offset two-way traveltime and moveout-parameters domain and then use similarity-weighted k-means clustering to find the maximum likelihood anisotropy parameters of the main subsurface structures. In order to demonstrate that, we apply the similarity-weighted clustering method to synthetic and field data examples and the results are of higher accuracy when compared to the ones obtained using multiparameter semblance-based method. From estimation error section, it can be seen that the estimation error of multiparameter semblance-based method is about 3–5 times that of the proposed method.

Automated static and moveout corrections of high‐resolution seismic data from the Baltic Sea

ABSTRACTHigh‐frequency multichannel seismic systems provide detailed images of the shallow marine subsurface. In order to exploit the redundancy inherent in such data optimally, traveltime corrections need to account for normal moveout and static effects due to vertical source and receiver variations. Misalignment of reflections in common‐midpoint gathers will significantly lower the frequency content in the final stack, making this correction particularly important for very high‐frequency seismic data. Traditionally, normal moveout correction involves labour‐intensive picking of stacking velocities, while static corrections can be, by some techniques, performed automatically. In this paper, we present a high‐frequency seismic case study from the Baltic Sea, using seismic image matching as a novel, fully automated technique to perform joint moveout and static corrections. Our multichannel test profiles were acquired offshore Rügen island for wind farm development. Owing to the regular passage of up to 1.5 m high ocean waves during data acquisition, these boomer profiles suffer from strong static effects. We perform joint normal moveout and static corrections by defining the nearest common offset section as a fixed reference frame and minimizing its difference in traveltime with respect to all available common offset sections. Time shifts are computed independent of a pre‐defined traveltime curve, using the normalized cross‐correlation as a measure of data similarity while penalizing irregular displacements by a regularization term. Time shifts are converted to stacking velocities based on the traditional hyperbolic traveltime equation. Our results are compared with those derived by conventional manual velocity analysis and subsequent trim static corrections. We find that image matching produces stacks of similar quality and stacking velocity models of similar to slightly better quality compared with the conventionally derived ones, revealing the potential of this technique to automatize and significantly speed up this first part of the seismic processing chain.

Effect of hillslope topography on soil erosion and sediment yield using USLE model

Catchment hillslopes in nature have a complex geometry. Complex hillslopes have different plans (convergent, parallel and divergent) and different curvature (straight, concave and convex). In this study, the erosion rates of the nine complex hillslopes were investigated using the universal soil loss (USLE) method. The topography factor (LS function) in the USLE was developed as a function of plan shape and profile curvature. The hillslopes studied were divided into sets of complex pixels and the erosion over the pixels was calculated. Total erosion was regarded as the sum of erosion of all pixels. Furthermore, to calculate the sediment delivery ratio of each pixel, a new travel time equation for complex hillslopes was employed. Results showed that the mean erosion of convex hillslopes was 1.43 times that of concave and 1.19 times that of straight slopes. The effect of curvature shape on erosion was much greater than plan shape effect. The highest erosion belonged to convex divergent slopes, and the least erosion was related to concave divergent slopes. The laboratory results intended for validation of the numerical model also show that in hillslopes with fixed plan, the erosion rate in the convex hillslopes exceeds that of concave and straight hillslopes. Also, in the hillslopes with fixed curvature profile, the erosion rate in the convergent hillslopes is more than in the divergent and parallel ones.

The Individual Travel Cost Method with Consumer-Specific Values of Travel Time Savings

The treatment of the opportunity cost of travel time in travel cost models has been an area of research interest for many decades. Our analysis develops a methodology to combine the travel distance and travel time data with respondent-specific estimates of the value of travel time savings (VTTS). The individual VTTS are elicited with the use of discrete choice stated preference methods. The travel time valuation procedure is integrated into the travel cost valuation exercise to create a two-equation structural model of site valuation. Since the travel time equation of the structural model incorporates individual preference heterogeneity, the full structure model provides a travel cost site demand model based upon individualized values of time. The methodology is illustrated in a study of recreational birdwatching, more specifically, visits to a ‘stork village’ in Poland. We show that the usual practice of basing respondents’ VTTS on 1/3 of their wage rate is largely unfounded and propose alternatives—including a separate component of the travel cost survey aimed at valuation of respondents’ VTTS or, as a second best, asking if they wish if their journey was shorter and for those who do—use full hourly wage as an indicator of their VTTS.

Prediction of the subsurface flow of hillslopes using a subsurface time-area model

Prediction of subsurface flow (SF) in hillslopes is more complicated than prediction of surface flow; hence, a simple and practical SF model would interest hydrogeologists. For the first time, the time-area method is employed to estimate the SF of hillslopes. The locations of the isochrone curves for complex hillslopes were determined using SF travel-time equations. Some equations were developed to delineate the isochrones and the subsurface time area (STA). The analytic equations suggested by the characteristics method of solving a hillslope-storage kinematic wave were used for validation of the STA method results in complex hillslopes. The average values of the coefficient of efficiency (CE), correlation coefficient (R), error of peak flow (EPF) and root-mean-square error (RMSE) of the STA method for the nine defined hillslopes are, respectively, 0.96, 0.96, 1.35, and 0.076. To further verify the results, a laboratory rainfall simulator with sandy loam soil was employed, which was conditioned under artificial rainfall intensities of 31.7, 4.6 and 63.46 mm/hr, and slopes of 3°, 6° and 9°. The STA model results were compared with those of a laboratory model of subsurface flow. The average values of CE, R, EPF and RMSE of the STA method for the nine events are, respectively, 0.81, 0.85, 0.98, and 0.017, which are regarded as good values. For the final evaluation of the STA model, the subsurface flow rates obtained from the Richards’ equation using HYDRUS were also used. The proposed STA model has good agreement with the results of the laboratory and HYDRUS models.

Reducing Residual Moveout for Long Offset Data in VTI Media Using Padé Approximation

Modification of the hyperbolic travel time equation into non-hyperbolic travel time equation is important to increase the reduction residual moveout for long offset data. Some researchers have modified hyperbolic travel time equation into a non-hyperbolic travel time equation to obtain a more accurate value NMO velocity and parameter an-ellipticity or etha on the large offset to depth ratio (ODR) so that the residual moveout value is smaller mainly in large offset to depth ratio. The aims of research is to increase the reduction value of error residue at long offset data using Padé approximation then compare with several approximations. The method used in this study is to conduct forward modeling of the subsurface coating structure. The results of the three-dimensional analysis show that the Padé approximation has the best accuracy compared to the other travel time equations for ODR value up to 4 with an-ellipticity parameter is varying from 0 to 0.5. Testing of synthetic data for single layer on vertical transverse isotropy (VTI) medium obtained the maximum residual error value produced by the Padé approximation is 0.25% in ODR=4. Therefore, Padé approximation is better than other methods for reducing residual moveout.

Enhancement of diffractions in prestack domain by means of a finite-offset double-square-root traveltime

Exploration of redundancy contained in the seismic data set assures enhancement of images that are based on stacking results. This enhancement is the goal of developing multiparametric traveltime equations that are able to approximate reflection and diffraction events in general source-receiver configurations. The main challenge of using these equations is to estimate a large number of parameters in a computationally feasible, reliable, and fast way. To obtain a better fit for diffraction traveltime events than the ones in the literature, we have derived a finite-offset (FO) double-square-root (DSR) diffraction traveltime equation (which depends on 10 parameters in three dimensions and four parameters in two dimensions). Moreover, to reduce the number of parameters, we have developed another version called simplified FO-DSR diffraction traveltime equation (which depends on five parameters in three dimensions and two parameters in two dimensions), which delivers a similar performance. We have developed operators that make use of the simplified FO-DSR traveltime equation to construct the so-called diffraction-only data set volumes (or, more simply, D-volumes) assuring enhancement in the diffraction extraction process. The D-volume construction has two steps: first, a stacking procedure to separate the diffraction events from the input data set and second, a spreading procedure to enhance the quality of these diffractions. As proof of concept, our approach has been tested on 2D/3D synthetic and 2D field data sets with successful results.

S‐wave kinematics in acoustic transversely isotropic media with a vertical symmetry axis

ABSTRACTAcoustic transversely isotropic models are widely used in seismic exploration for P‐wave processing and analysis. In isotropic acoustic media only P‐wave can propagate, while in an acoustic transversely isotropic medium both P and S waves propagate. In this paper, we focus on kinematic properties of S‐wave in acoustic transversely isotropic media. We define new parameters better suited for S‐wave kinematics analysis. We also establish the travel time and relative geometrical spreading equations and analyse their properties. To illustrate the behaviour of the S‐wave in multi‐layered acoustic transversely isotropic media, we define the Dix‐type equations that are different from the ones widely used for the P‐wave propagation.

Analysis of flow-sediment rating curve hysteresis based on flow and sediment travel time estimations

A flow-sediment rating curve is used to describe the relation between flow discharge and suspended-sediment concentration for a specific location. Five types of flow-sediment rating curves - single-valued line, clockwise loop, counterclockwise loop, single-valued line plus loop, and figure eight - were found to rely on the flow and available sediment arriving at the measuring site. In this study, equations for flow and sediment travel time were derived according to soil, rainfall, and watershed geomorphologic characteristics. The hysteresis of the rating curve was related to the travel times by a series of numerical tests. Field data collected from the Goodwin Creek Experimental Watershed, Mississippi, United States were used to verify the proposed rating curve hysteresis analysis. The results indicate that when the flow travel time is more extended than the sediment travel time, the rating curve shows a clockwise loop. A counterclockwise loop in the rating curve shows that the flow travel time is less extended than the sediment travel time. If the flow travel time exceeds the sediment travel time in specific runoff states and is less than the sediment travel time in other runoff states, then a single line plus a loop rating curve or a figure-eight rating curve is observed. The criterion for the model parameters to obtain equalization of the flow and sediment travel times was derived, which can identify the type of flow-sediment rating curve in a specific watershed.

A multi‐azimuth seismic refraction study for a horizontal transverse isotropic medium: physical modelling results

ABSTRACTTo investigate the characteristics of the anisotropic stratum, a multi‐azimuth seismic refraction technique is proposed in this study since the travel time anomaly of the refraction wave induced by this anisotropic stratum will be large for a far offset receiver. To simplify the problem, a two‐layer (isotropy–horizontal transverse isotropy) model is considered. A new travel time equation of the refracted P‐wave propagation in this two‐layer model is derived, which is the function of the phase and group velocities of the horizontal transverse isotropic stratum. In addition, the measured refraction wave velocity in the physical model experiment is the group velocity. The isotropic intercept time equation of a refraction wave can be directly used to estimate the thickness of the top (isotropic) layer of the two‐layer model because the contrast between the phase and group velocities of the horizontal transverse isotropic medium is seldom greater than 10% in the Earth. If the contrast between the phase and group velocities of an anisotropic medium is small, the approximated travel time equation of a refraction wave is obtained. This equation is only dependent on the group velocity of the horizontal transverse isotropic stratum. The elastic constants A11, A13, and A33 and the Thomsen anisotropic parameter ε of the horizontal transverse isotropic stratum can be estimated using this multi‐azimuth seismic refraction technique. Furthermore, under a condition of weak anisotropy, the Thomsen anisotropic parameter δ of the horizontal transverse isotropic stratum can be estimated by this technique as well.