Travel-time Curves Research Articles

Near-surface attenuation estimation using wave-propagation modeling

The effect of the near surface on seismic land data can be so severe that static corrections are insufficient. Full-waveform inversion followed by redatuming may be an alternative, but inversion will work only if the starting model is sufficiently close to the true model. As a first step toward determining a viscoelastic near-surface model, we assume that existing methods can provide a horizontally layered velocity and density model. Because near-surface attenuation is strongest, we propose a method to estimate the P-wave attenuation based on viscoacoustic finite-difference modeling. We compare energy decay along traveltime curves of reflection and refraction events in the modeled and observed seismic data for a range of attenuation parameters. The best match provides an estimate of the attenuation. First, we estimate only the attenuation of the top layer and study the sensitivity to depth and velocity perturbations. Then, we consider multiple layers. We apply the method to synthetic and real data and investigate the effect of source wavelet and topography. The method is robust against depth and velocity perturbations smaller than 10%. The results are sensitive to the source wavelet. Incorporating the surface topography in the computed traveltimes reduces the uncertainty of the attenuation estimates, especially for deeper layers.

Exact traveltime computation in multi-layered transversely isotropic media with vertical symmetry axis

An approach to calculate the accurate ray paths and traveltimes in multi-layered VTI media (transversely isotropic media with a vertical symmetry axis) is proposed. The expressions of phase velocity, group velocity and Snell’s law used for computation are all explicit and exact. The calculation of ray paths and traveltimes for a given elementary wave is equivalent to that of a transmission problem which is much easier to be treated with the formulae proposed. In the section of numerical examples, the processes of implementation are described at length using a multi-arrival example and a head-wave example. Lastly, the exact and approximate traveltime curves for the same elementary wave are calculated from the exact formulae and Thomsen’s approximations, respectively. The comparison of the curves reveals the increase of errors arising from the repeated use of approximations and indicates the limited applicable range of approximations. It is emphasized that one should keep in mind the applicable range of an approximation when using it.

Depth and morphology of reflectors from the non‐linear inversion of arrival‐time and waveform semblance data. Part I: method and applications to synthetic data

ABSTRACTWe propose a two‐dimensional, non‐linear method for the inversion of reflected/converted traveltimes and waveform semblance designed to obtain the location and morphology of seismic reflectors in a lateral heterogeneous medium and in any source‐to‐receiver acquisition lay‐out. This method uses a scheme of non‐linear optimization for the determination of the interface parameters where the calculation of the traveltimes is carried out using a finite‐difference solver of the Eikonal equation, assuming an a priori known background velocity model. For the search for the optimal interface model, we used a multiscale approach and the genetic algorithm global optimization technique. During the initial stages of inversion, we used the arrival times of the reflection phase to retrieve the interface model that is defined by a small number of parameters. In the successive steps, the inversion is based on the optimization of the semblance value determined along the calculated traveltime curves. Errors in the final model parameters and the criteria for the choice of the best‐fit model are also estimated from the shape of the semblance function in the model parameter space. The method is tested and validated on a synthetic dataset that simulates the acquisition of reflection data in a complex volcanic structure. This study shows that the proposed inversion approach is a valid tool for geophysical investigations in complex geological environments, in order to obtain the morphology and positions of embedded discontinuities.

Crustal stucture of the Barents-Kara Region based on detailed deep seismic sounding

In 1995–1998 and 2003–2005, detailed deep seismic soundings were undertaken in the Barents-Kara Region along geotraverses 1-AR, 2-AR, 3-AR with a total length of over 3000 km. Seismic cross-sections, up to 50 km deep as an average, were obtained using the software package GODOGRAPH designed at the Department of Seismometry and Geoacoustics of the Lomonosov Moscow State University. The study was based on refraction traveltime curves with approximately 100 curves per profile. The sections obtained along the 1-AR and 2-AR traverses were geologically interpreted. The main crustal boundaries, fold-thrust structural features of the lower crust and a suture zone between the North Barents Basin and the Caledonian Orogenic Belt were distinguished. Based on our data, the structure of the suture can be interpreted as an ancient subduction zone. The possible pattern of tectonic movements of the Barents Plate is characterized.

Comparison of three different methods in investigating shallow shear-wave velocity structures in Ilan, Taiwan

The Central Weather Bureau (CWB) and National Center for Research on Earthquake Engineering (NCREE) launched a project to build an engineering geological database for strong-motion stations in Taiwan in 2000. The project measures shear-wave velocity using the suspension PS-logging method. In this study, we conduct array measurements of microtremors and apply the stress wave propagation method (SWPM) at seven free-field strong-motion stations in Ilan County to estimate shallow shear-wave velocity structures. We focus on the sediment layers of the top 100 m to compare the shear-wave velocity structures of the three different methods. There are some misfits among the results of the three different methods; so we calculate the values of Vs 30, Vs 100 and plot S-wave travel-time curves of these methods for each site to analyze the misfits effectively. This analysis helped us to prove the efficiency of the microtremor array method in investigating shear-wave velocity structures in the shallow subsurface. Moreover, the horizontal-to-vertical ratios of microtremors for each survey point show the existence of divergence at the same site. We considered this as evidence that misfits are caused by the heterogeneous nature of sediments and also due to the nature of the methods as being one-, two- and three-dimensional. Furthermore, the average shear-wave velocity structure of microtremor arrays may be more representative of the whole site.

A Bayesian hierarchical method for multiple-event seismic location

SUMMARY We formulate the multiple-event seismic location problem as a Bayesian hierarchical statistical model (BAYHLoc). This statistical model has three distinct components: traveltime predictions, arrival-time measurements, and an a priori statistical model for each aspect of the multiple-event problem. The traveltime model is multifaceted, including both phase-specific adjustments to traveltime curves to improve broad-area prediction, as well as path/phase-specific traveltime adjustments. The arrival-time measurement model is decomposed into station, phase, and event components, allowing flexibility and physically interpretable error parameters. The prior model allows all available information to be brought to bear on the multiple event system. Prior knowledge on the probabilistic accuracy of event locations, traveltime predictions, and arrival-time measurements can be specified. Bayesian methodology merges all three components of the hierarchical model into a joint probability formulation. The joint posterior distribution is, in essence, an inference of all parameters given the prior constraints, self-consistency of the data set, and physics of traveltime calculation. We use the Markov Chain Monte Carlo method to draw realizations from the joint posterior distribution. The resulting samples can be used to estimate marginal distributions, for example epicentres and probability regions, as well as parameter correlations. We demonstrate BAYHLoc using the set of Nevada Test Site nuclear explosions, for which hypocentres are known, and phase measurements and traveltimes are well characterized. We find significant improvement in epicentre accuracy using BAYHLoc. Much of the improvement is attributed to the adaptive arrival-time measurement model, which controls data weighting. Regardless of the initial traveltime model, the use of an adjustment to the traveltime curves produces a level of epicentre accuracy that is generally achieved only through meticulous analysis and data culling. Further, we find that accurate hypocentres (including depth and origin-time) are achieved when either accurate traveltime curves with tight priors are used, or when prior information on a small subset of events is utilized.

Upper crust structure of eastern A’nyemaqên suture zone: Results of Barkam-Luqu-Gulang deep seismic sounding profile

Barkam-Luqu-Gulang deep seismic sounding profile runs from north of Sichuan Province to south of Gansu Province. It is located at the northeastern edge of Tibetan Plateau and crosses eastern A’nyemaqen suture zone. The upper crust structures around eastern A’nyemaqen suture zone and its adjacent area are reconstructed based on the arrival times of refracted Pg and Sg waves by using finite difference method, ray tracing inversion, time-term method and travel-time curve analysis. The results show that the depth variation of basement along profile is very strong as indicated by Pg and Sg waves. The basement rose in Zoige basin and depressed in eastern A’nyemaqen suture zone, and it gradually rose again northward and then depressed. The results also indicate that eastern A’nyemaqen suture zone behaves as inhomogeneous low velocity structures in the upper crust and is inclined toward the south. Hoh Sai Hu-Maqen fault, Wudu-Diebu fault and Zhouqu-Liangdang fault are characterized by low velocity distributions with various scales. The distinct variation in basement depth occurred near Hoh Sai Hu-Maqen fault and Zhouqu-Liangdang fault, which are main tectonic boundaries of A’nyemaqen suture zone. Wudu-Diebu fault, located at the depth variation zone of the basement, possibly has the same deep tectonic background with Zhouqu-Liangdang fault. The strongly depressed basement characterized by low velocity distribution and lateral inhomogeneity in A’nyemaqen suture zone implies crushed zone features under pinching action.

Seismic modeling of gas chimneys

We propose a simple acoustic model explaining the main features of gas chimneys. The main elements of the model consist of gas diffusing from a connected fracture network and into the surrounding shale creating an inhomogeneous gas saturation. The gas saturation results in an inhomogeneous fluctuating compressional velocity field that distorts seismic waves. We model the fracture network by a random-walk process constrained by maximum fracture length and angle of the fracture with respect to the vertical. The gas saturation is computed from a simple analytical solution of the diffusion equation, and pressure-wave velocities are locally obtained assuming that mixing of shale and gas occurs on a scale much smaller than seismic wavelengths. Synthetic seismic sections are then computed using the resulting inhomogeneous velocity model and shown to give rise to similar deterioration in data quality as that found in data from real gas chimneys. Also, synthetic common-midpoint (CMP) gathers show the same distorted and attenuated traveltime curves as those obtained from a real data set. The model shows clearly that the features of gas chimneys change with geological time (a model parameter in our approach), the deterioration of seismic waves being smallest just after the creation of the gas chimney. It seems likely that at least some of the features of gas chimneys can be explained by a simple elastic model in combination with gas diffusion from a fracture network.

A case study on the use of ray tracing in removing the effect of near-surface layer and its impact on reservoir imaging

Variation in the thickness and velocity of the weathering layer results in variation in the prestack traveltime for a given reflector and traveltime curves become nonhyperbolic, even for a flat horizon. This obviously will adversely affect our ability to image exploration targets and might even cause a false structural anomaly.

MTCLAB: A MATLAB ®-based program for traveltime quality analysis and pre-inversion velocity tuning in 2D transmission tomography

A MATLAB ®-based computer code that analyses the traveltime distribution and performs quality analysis at the pre-inversion stage for 2D transmission experiments is presented. The core tools of this approach are the so-called mean traveltime curves. For any general recording geometry, the user may select any pair of subsets of contiguous sources and receivers. The portion of the domain swept by the implied rays defines a zone of analysis, and for each source (receiver) the outcoming (incoming) ray fan is named a source (receiver) gather. The empirical mean traveltime curves are constructed, for each zone, by assigning the average and the standard deviation of the traveltimes in the gathers to the positions of the sources (receivers). The theoretical expressions assume isotropic homogeneous velocity inside each zone. The empirical counterparts use the observed traveltimes and make no assumptions. Isotropic velocity in each zone is inferred by least-squares fitting of the empirical mean traveltime curves. The user may refine the analysis considering different zones (multi-zone analysis). Initially the whole domain is modelled as a single zone. The procedure compares empirical versus theoretical curves. In addition, residuals can be plotted using source–receiver positions as plane coordinates. The results are used to unravel the possible presence of anomalous gathers, heterogeneities, anisotropies, etc. Depending on the kind of anomalies, velocity estimation and mean time residuals are different in the source and receiver gather curves. This software helps to grasp a better understanding of the data variability before the inversion and provides to the geophysicist an approximate zonal isotropic model and a range of velocity variation that can be used in the inverse problem as a priori information (regularization term). Its use is described through tutorial examples. A guided user interface leads the user through the algorithm steps.

Estimation of layer parameters for linear P- and S-wave velocity functions

For a horizontally layered medium with isotropic layers with constant P- and S-wave velocity gradients, it is possible to estimate the velocity functions (gradient and velocity at the top of each layer) and thickness of each layer. From large-offset PP seismic reflections, one can estimate three traveltime parameters: the zero-offset two-way traveltime, the NMO velocity, and a heterogeneity coefficient responsible for the nonhyperbolicity of the traveltime curve, using the different traveltime approximations. From large-offset (offset/depth greater than two) PS seismic reflections, one can estimate two traveltime parameters: zero-offset two-way traveltime and NMO velocity. From the estimated traveltime parameters at the top and bottom of a layer, it is possible to compute the thickness and velocity functions of the layer.

A Comparison of Adaptive Processing Techniques with Nth Root Beam Forming Methods

Summary Small differences in slowness and azimuth for overlapping phases especially where the branches of the travel-time curve are triplicated must be resolved for a meaningful inversion of array data. A computer program package has been written in FORTRAN IV which enables a user to determine, automatically, the apparent azimuth and slowness of any portion of the seismic wavetrain recorded at various arrays if he has the raw data on digital tape and has access to any modern computer. These programs make use of two methods, (i) adaptive processing, and (ii) Nth root beam forming which have been compared to determine the apparent azimuth and slowness of the seismic wavelets. The former method is performed by cross correlating the signal on each channel with a velocity and azimuth filtered trace in an iterative manner until the convergence takes place. In the latter method the operation is done by delaying the various channels to align a group of arrivals with a particular velocity and azimuth; taking the Nth root of the signal; summing and then raising the result to the Nth power. The value of apparent velocity and azimuth which produces a maximum filtered signal is determined. Experiments with clean and noisy synthetic data have shown that the adaptive processing method is more successful for resolving small differences in apparent velocity and azimuth of overlapping wavelets. It also has an advantage that a set of residuals may easily be obtained from the analysis. The Nth root method is extremely powerful in enhancing the signal to noise ratio at the expense of signal distortion. The computation time for both methods is about the same.

Simulation of wave transmission and reception with phased arrays near the sea shelf bottom

The wave field excited by both single sources and a vertically directed phased transmitting array in a shallow-water waveguide with a layered elastic bottom is numerically simulated. The receivers are equispaced vertical arrays with different apertures, which are positioned at different depths in the water layer. The type of vertical distribution and the transformation of the vertical angular spectrum of pulsed signals arriving at a receiving array are demonstrated for different parameters of the medium, different carrier frequencies, and different distances from the source. It is shown that a selective angular reception ensures a better resolution of the travel-time curves of waves used for sounding the bottom. As an example, the possibility of singling out the shear wave refracted by a deep-seated bottom layer from the tone pattern of the travel-time curves is demonstrated. This possibility can be realized by means of angular scanning in the course of transmission and reception with the use of vertically oriented arrays.

Ground-coupled acoustic airwaves from Mount St. Helens provide constraints on the May 18, 1980 eruption

The May 18, 1980 Mount St. Helens eruption perturbed the atmosphere and generated atmosphere-to-ground coupled airwaves, which were recorded on at least 35 seismometers operated by the Pacific Northwest Seismograph Network (PNSN). From 102 distinct travel time picks we identify coherent airwaves crossing Washington State primarily to the north and east of the volcano. The travel time curves provide evidence for both stratospheric refractions (at 200 to 300 km from the volcano) as well as probable thermospheric refractions (at 100 to 350 km). The very few first-hand reports of audible volcano sounds within about 80 km of the volcano coincide with a general absence of ground-coupled acoustic arrivals registered within about 100 km and are attributed to upward refraction of sound waves. From the coherent refracted airwave arrivals, we identify at least four distinct sources which we infer to originate 10 s, 114 s, ∼ 180 s and 319 s after the onset of an 8:32:11 PDT landslide. The first of these sources is attributed to resultant depressurization and explosion of the cryptodome. Most of the subsequent arrivals also appear to be coincident with a source located at or near the presumed volcanic conduit, but at least one of the later arrivals suggests an epicenter displaced about 9 km to the northwest of the vent. This dislocation is compatible with the direction of the sector collapse and lateral blast. We speculate that this concussion corresponds to a northern explosion event associated with hot cryptodome entering the Toutle River Valley.

Michael Baumbach 1953-2006

After a long illness, Michael Baumbach, one of the most talented and appreciated colleagues of the GeoForschungsZentrum Potsdam, Germany, passed away at the early age of 52.⇓ ![][1] Michael Baumbach, summer 1998 Michael was born on 17 December 1953 in Dessau, a town in the eastern part of Germany. He went to school there between 1960 and 1972 and earned his university-entrance diploma “with distinction.” He studied physics at the Lomonossov University in Moscow and specialized in seismology under the guidance of professors E. F. Savarensky, L. P. Vinnik, and E. M. Chesnokov. In 1978 he defended his diploma thesis, “Seismic Anisotropy of the Oceanic Lithosphere and its Influence on the Travel-Time Curves of Seismic Waves,” … [1]: /embed/graphic-1.gif

Downhole Receiver Function: a Case Study

Receiver function is defined as the spectral ratio of the radial component and the vertical component of the ground motion. It is used to characterize converted waves. We extend the use of the receiver function to downhole data using waves recorded in a borehole, excited by an earthquake of magnitude 4.0 near San Fran- cisco, California, on 26 June 1994. The focal depth of the event was 6.6 km and the epicenter was located at a distance of 12.6 km from the borehole array. Six three- component sensors were located at different depths in a borehole. To extract a co- herent response of the near-surface from the incoherent earthquake waves, we de- convolve the waves recorded by the sensors at different depths with the waves recorded by the sensor on the surface. Deconvolution applied to the waves in the S- time window recorded by the radial component result in an upgoing and adowngoing wave propagating with S-wave velocity. For the waves in the P-time window re- corded by the radial component, deconvolution also gives an upgoing and a down- going wave propagating with S-wave velocity. This interesting result suggests a P- to-S conversion at a depth below the deepest sensor. To diagnose this we compute the receiverfunction forthe borehole recording of the earthquakewaves.Thereceiver function shows an upgoing wave with an arrival close to time t ! 0 for the deepest sensor. The agreement of the upgoing wave in the receiver function with the travel- time curve for the P-to-S converted wave, calculated using the P- and the S-wave velocity profile, supports the hypothesis of a pronounced P-to-S conversion. We present a synthetic example to illustrate that the first arrival of the receiver function applied to borehole data gives the upward-propagating P-to-S converted wave. To corroborate the observation of the mode conversion, we apply receiver function to a different earthquake data recorded by the same borehole array in 1998. The focal depth of the event was 6.9 km and the epicenter was located at a distance of 13 km from the borehole array. The receiver function for these data also show an upgoing wave with a pulse close to time t ! 0 at the deepest sensor. The moveout of the upgoing wave agrees with the travel-time curve for the P-to-S converted wave, hence supporting our observation of the mode conversion.

A three-dimensional model of the Baltic Shield crust from data of deep seismic studies

A 3-D velocity structure of the crust has been constructed for almost the entire Baltic Shield area from data of extensive deep seismic studies on the shield. The construction involved a revision of all primary data (record sections and observed traveltime curves) obtained in this region over 50 years of research. Comparative analysis of wave fields revealed that three reference reflectors traceable throughout the shield area are K1 (a boundary velocity of 6.4–6.5 km/s), K2 (∼6.8 km/s), and the mantle surface M (8.0–8.2 km/s). The resulting 3-D velocity structure is represented in the form of structural maps of these surfaces and a velocity distribution scheme in the upper crust. Using this general basic model, seismic cross sections are constructed by means of mathematical modeling along all profiles. They showed that, in addition to the main layers and reflectors above the K1 boundary, a lower velocity layer is traceable almost everywhere and the majority of deep faults flatten out toward this layer. On the whole, lateral variations in the velocity structure of the crust are small up to a depth of 40 km. The variations are most significant in the M topography: its average depth being 40–45 km, two deep (down to 50–60 km) depressions exist in southern Finland and the Baltic region. The origin of this depression filled with high velocity (7.2–7.4 km/s) rocks remains unclear.

Path‐integral seismic imaging

ABSTRACTA new type of seismic imaging, based on Feynman path integrals for waveform modelling, is capable of producing accurate subsurface images without any need for a reference velocity model. Instead of the usual optimization for traveltime curves with maximal signal semblance, a weighted summation over all representative curves avoids the need for velocity analysis, with its common difficulties of subjective and time‐consuming manual picking. The summation over all curves includes the stationary one that plays a preferential role in classical imaging schemes, but also multiple stationary curves when they exist. Moreover, the weighted summation over all curves also accounts for non‐uniqueness and uncertainty in the stacking/migration velocities. The path‐integral imaging can be applied to stacking to zero‐offset and to time and depth migration. In all these cases, a properly defined weighting function plays a vital role: to emphasize contributions from traveltime curves close to the optimal one and to suppress contributions from unrealistic curves. The path‐integral method is an authentic macromodel‐independent technique in the sense that there is strictly no parameter optimization or estimation involved. Development is still in its initial stage, and several conceptual and implementation issues are yet to be solved. However, application to synthetic and real data examples shows that it has the potential for becoming a fully automatic imaging technique.

Crustal Structure in Southern Korea from Joint Analysis of Regional Broadband Waveforms and Travel Times

Regional broadband waveforms and travel times of seismic phases are combined to model crustal structure in regions where the signal-to-noise ratio (snr) of waveforms is low. The utilization of travel-time data enables us to overcome the problem occurring in waveform inversion with low snr data: the distortion of deep velocity structure. The genetic algorithm (ga) adopted as a search algorithm is useful in regions where there is little a priori information about crustal structure. After verifying the robustness of the joint inversion technique by numerical tests, we applied the technique to southern Korea in order to get a simple one-dimensional average crustal model, using broadband waveforms bandpassed between 0.03 and 0.3 Hz and travel times of Pg , PmP , and Pn waves recorded at ten broadband and five short-period stations from the 2 June 1999 Gyeongju earthquake ( M L 3.4), Korea. The P -wave velocities in the resulting three-layered crustal model are 5.67 ± 0.06, 6.05 ± 0.05, 6.67 ± 0.02, and 7.88 ± 0.02 km/sec from the top layer to the half- space, respectively, and the depths of layers are 5.1 ± 0.8, 16.7 ± 1.0, and 31.9 ± 1.0 km. Synthetic waveforms and travel-time curves corresponding to the resulting velocity model fit observed seismograms generally well. The synthetics are preceded by the observed waveforms in the southwestern part of Korean Peninsula, inferring the presence of a high-velocity zone in that area.

Geodynamic processes in seismically active areas of the Tien Shan from monitoring data with the use of nuclear explosions

Recent geodynamic processes in the Tien Shan region are studied by the analysis of time series of effective velocities and traveltime delays relative to the IASPEI-91 traveltime curve of the weakly refracted wave P n from nuclear explosions at the Semipalatinsk test site over the period of 1968–1989. The time series were constructed for 10 seismic stations located at distances of 800–1200 km from the test site in the regions of the Northern, Central, and Southern Tien Shan. The twenty-year period of observations at stations in the North Tien Shan showed a significant decrease in traveltime delays by 0.20–0.76 s, which corresponds to a 0.2–0.7% increase in seismic velocities. An opposite pattern is observed at stations of the Central and Southern Tien Shan: traveltime delays increased by 0.2–0.5 s and, accordingly, seismic velocities dropped by 0.2–0.5%. These results suggest the predominance of compression processes in the crust and upper mantle during the period of observations in Northern Tien Shan and extension processes in the Central and Southern Tien Shan. The series of velocities and traveltime residuals are characterized by the presence of rhythmic oscillations of various amplitudes and periods against a linear trend. A correlation between variations in kinematic parameters and yearly numbers of earthquakes is observed at all stations. Diagrams of the spectral time analysis reveal rhythms with periods of 2–3 and 5–7 yr. The data obtained in this study are consistent with results of studying the stress-strain state of the Tien Shan crust from focal mechanisms of earthquakes and the velocities of recent crustal movements from GPS data. It is found that the amplitude of variations in kinematic parameters of the P wave at stations located in seismically active regions (the Tien Shan, Kopet Dagh, the Caucasus, Altai, and Sayany) is two to five times higher compared to aseismic regions (the Russian and Kazakh plains).