Travel-time Shifts Research Articles

Characteristic reflection wavefield-based wave equation traveltime inversion

Introducing a high-precision deep-depth velocity model is essential for accurately imaging seismic data in complex areas such as deepwater and deep depth in oil and gas exploration. Conventional methods, such as reflection full-waveform inversion (RFWI), face challenges, notably the cycle-skipping issue, especially when the initial velocity model is far away from the true model. To address this, we develop a novel wave equation traveltime inversion (WETI) using the characteristic reflection wavefield (CRW) to update the low-wavenumber components of the velocity model. The CRWs are primary reflections in seismic data that contribute significantly to velocity model updates. We implement a multistep approach, including migration, characteristic reflector structure (CRS) picking, and demigration to extract the CRW. This extraction, constrained by CRS, ensures accurate matching between the observed and the simulated CRWs, even with an inaccurate initial velocity model, thus enabling an accurate traveltime shift estimation during inversion. Unlike conventional methods that use all reflection data simultaneously, CRW-WETI strategically selects fewer CRWs, enhancing inversion convexity and avoiding local minima from the cycle-skipping problem. This selective inversion begins with a limited number of CRWs to ensure stability and progressively incorporates more as the WETI process advances, eventually transitioning into conventional RFWI. Moreover, with the CRS constraint, CRW can be selected based on the target region. The target-oriented velocity inversion can also be implemented easily to update a local anomalous velocity model. Numerical examples of synthetic and field data demonstrate the effectiveness and validity of our method.

Transformer Graph Convolutional Network for Relative Travel-Time Shift Prediction

Abstract Predicting surface-wave travel-time shifts is valuable for analyzing potential effects caused by changes in medium properties, station clock errors, instrument response errors, and other factors. Many current neural networks used in seismology are single-station models trained using single-station (pair) data. However, most seismic methods require knowledge of the spatial positions between multiple stations. Multiple stations contain rich interrelationships and spatial information that cannot be exploited by single-station models. We proposed a multistation neural network structure Transformer Graph Convolutional Network (TGCN) that utilizes temporal attention and spatial attention to capture spatiotemporal information for predicting relative travel-time shifts. Before that, we introduced a method that treats station pairs as nodes and constructs a graph with multiple station pairs. We collected original ambient noise waveforms from 2017 to 2019 in the Alaska region and 2010 to 2014 in the southern California region to obtain relative travel-time shift sequences of station pairs for model training and testing. To showcase the improvement of spatial information to the model, we compared TGCN with two other baseline single-station models—temporal convolutional network and long short-term memory. Our proposed method predicted travel-time values more accurately than the two baseline models, and it also exhibited slower decay in performance when predicting over larger intervals. We also found that the number of station pairs has an impact on the model. When there are a sufficient number of station pairs, the model can effectively utilize the rich spatial information and achieve higher accuracy. Our approach, which incorporates spatiotemporal information, provides outputs that are more efficient and accurate compared with the traditional single-station (pair) method that only considers temporal information, suggesting that spatial information does enhance the performance of the model.

Crosscorrelation-based dynamic time warping and its application in wave equation reflection traveltime inversion

Crosscorrelation and dynamic time warping (DTW) are ubiquitous in time-shift estimation. However, the small-shift limitation of crosscorrelation and the instability and high sensitivity to noise of DTW seriously hinder their applications in complex situations. In this study, we develop a method called crosscorrelation-based DTW (CDTW) to address these issues. Our method constructs error matrices by local crosscorrelation instead of Euclidean distance to minimize the sensitivity to noise. The new error matrices are calculated in local windows and contain local structure similarity information of the two input signals. It improves the stability of the algorithm and makes the CDTW method less sensitive to noise and amplitude modulation. Our method estimates the time-varying shift using dynamic programming as the conventional DTW after the new error matrix is formulated. Numerical tests on pairs of signals and seismic images prove that our method can accurately estimate time shifts in cases of time-varying amplitude modulation and strong random noise contamination. Finally, we apply the CDTW method to wave equation reflection traveltime inversion (WRTI) and develop a CDTW-based WRTI method. Synthetic and field applications prove that this method can construct good background velocity models with the reliable reflection traveltime shifts produced by the CDTW method.

Characteristic reflector-based wave equation reflection traveltime inversion

Reconstructing the deep background velocity model is crucial for imaging subsurface structures. The reflection traveltime inversion (RTI) is capable of recovering the kinematic information in the velocity model under a limited seismic observation aperture. The estimation of the reflection traveltime residuals between the synthetic and observed seismic waves is the key to the RTI. However, it is difficult to accurately obtain the rapidly changing reflection traveltime shifts in the prestack data domain. Estimating the traveltime difference is especially difficult where the discrepancy between the noisy observed data and demigrated synthetic data includes a waveform distortion, inconsistent reflected events, and so on. To overcome this problem, we have developed a new reflection traveltime residual estimation method. In this method, after identifying a characteristic reflector in the prestack depth migration section with an initial velocity, the demigrated and observed seismic reflections in the data domain corresponding to the characteristic reflector share the same traveltime at the zero offset. Thus, their traveltime residual can be automatically tracked by their crosscorrelation with a modified dynamic programming algorithm based on a zero-offset control point, which can avoid traveltime picking or windowing of relevant reflection arrivals in the prestack seismic data domain. Then, the estimated reflection traveltime residual is applied to the RTI. To improve the inversion accuracy, we have further developed a layer-stripping velocity model-building workflow. Synthetic and field data tests demonstrate that the proposed method can obtain a robust reflection traveltime residual and further achieve a correct low-to-intermediate wavenumber velocity model update.

An Envelope Travel-Time Objective Function for Reducing Source–Velocity Trade-Offs in Wave-Equation Tomography

In conventional cross-correlation (CC)-based wave-equation travel-time tomography, wrong source wavelets can result in inaccurate velocity inversion results, which is known as the source–velocity trade-off. In this study, an envelope travel-time objective function is developed for wave-equation tomography to alleviate the non-uniqueness and uncertainty due to wrong source wavelets. The envelope of a seismic signal helps reduce the waveform fluctuations/distortions caused by variations of the source time function. We show that for two seismic signals generated with different source wavelets, the travel-time shift calculated by cross-correlation of their envelopes is more accurate compared to that obtained by directly cross-correlating their waveforms. Then, the CC-based envelope travel-time (ET) objective function is introduced for wave-equation tomography. A new adjoint source has also been derived to calculate the sensitivity kernels. In the numerical inversion experiments, a synthetic example with cross-well survey is first given to show that compared to the traditional CC travel-time objective function, the ET objective function is relatively insensitive to source wavelet variations and can reconstruct the elastic velocity structures more reliably. Finally, the effectiveness and advantages of our method are verified by inversion of early arrivals in a practical seismic survey for recovering near-surface velocity structures.

Contribution of flows around active regions to the north-south helioseismic travel-time measurements

Context. In local helioseismology, the travel times of acoustic waves propagating in opposite directions along the same meridian inform us about horizontal flows in the north-south direction. The longitudinal averages of the north-south helioseismic travel-time shifts vary with the sunspot cycle. Aims. We aim to study the contribution of inflows into solar active regions to this solar-cycle variation. Methods. To do so, we identified the local flows around active regions in the horizontal flow maps obtained from correlation tracking of granulation in continuum images of the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory. We computed the forward-modeled travel-time perturbations caused by these inflows using 3D sensitivity kernels. In order to compare with the observations, we averaged these forward-modeled travel-time perturbations over longitude and time in the same way as the measured travel times. Results. The forward-modeling approach shows that the inflows associated with active regions may account for only a fraction of the solar-cycle variations in the north-south travel-time measurements. Conclusions. The travel-time perturbations caused by the large-scale inflows surrounding the active regions do not explain in full the solar-cycle variations seen in the helioseismic measurements of the meridional circulation.

Monitoring subsurface changes by tracking direct-wave amplitudes and traveltimes in continuous distributed acoustic sensor VSP data

Instrumenting wells with distributed acoustic sensors (DASs) and illuminating them with passive or active seismic sources allows precise tracking of temporal variations of direct-wave traveltimes and amplitudes, which can be used to monitor variations in formation stiffness and density. This approach has been tested by tracking direct-wave amplitudes and traveltimes as part of a carbon capture and storage project where a 15 kt supercritical CO2 injection has been monitored with continuous offset vertical seismic profiling using nine permanently mounted surface orbital vibrators acting as seismic sources and several wells instrumented with DAS cables cemented behind the casing. The results indicate a significant (from 15% to 30%) increase of strain amplitudes within the CO2 injection interval, and traveltime shifts of 0.3–0.4 ms below this interval, consistent with full-wave 1.5D numerical simulations and theoretical predictions. The results give independent estimates of the CO2 plume thickness and the associated P-wave velocity reduction.

Long-Term Variation of Helioseismic Far-Side Images and What Causes It

A new time–distance far-side imaging technique was recently developed by utilizing multiple multi-skip acoustic waves. The measurement procedure is applied to 11 years of Doppler observations from the Solar Dynamics Observatory/Helioseismic and Magnetic Imager, and over 8000 far-side images of the Sun have been obtained with a 12-hour temporal cadence. The mean travel-time shifts in these images unsurprisingly vary with the solar cycle. However, the temporal variation does not show good correlations with the magnetic activity in their respective northern or southern hemisphere, but show very good anti-correlation with the global-scale magnetic activity. We investigate four possible causes of this travel-time variation. Our analysis demonstrates that the acoustic waves that are used for mapping the Sun’s far side experience surface reflections around the globe, where they may interact with surface or near-surface magnetic field and carry travel-time deficits with them. The mean far-side travel-time shifts from these acoustic waves therefore vary in phase with the Sun’s magnetic activity.

Joint wave-equation traveltime inversion of diving/direct and reflected waves for P- and S-wave velocity macromodel building

Full-waveform inversion (FWI) suffers from the local minima problem and requires a sufficiently accurate starting model to converge to the correct solution. Wave-equation traveltime inversion (WETI) is an effective tool to retrieve the long-wavelength components of the velocity model. We have developed a joint diving/direct and reflected wave WETI (JDRWETI) method to build P- and S-wave velocity macromodels. We estimate the traveltime shifts of seismic events (diving/direct waves and PP- and PS-reflections) through the dynamic warping scheme and construct a misfit function using the time shifts of diving/direct and reflected waves. We derive the adjoint wave equations and the gradients with respect to the background models based on the joint misfit function. We apply the kernel decomposition scheme to extract the kernel of the diving/direct wave and the tomography kernels of PP- and PS-reflections. For an explosive source, the kernels of the diving/direct wave and PP-reflections and the kernel of the PS-reflections are used to compute the P- and S-wave gradients of the background models, respectively. We implement JDRWETI by a two-stage inversion workflow: First, we invert the P- and S-wave velocity models using the P-wave gradients, and then we improve the S-wave velocity model using the S-wave gradients. Numerical tests on synthetic and field data sets reveal that the JDRWETI method successfully recovers the long-wavelength components of P- and S-wave velocity models, which can be used for an initial model for the subsequent elastic FWI. Moreover, the JDRWETI method prevails over the existing reflection WETI method and the cascaded diving/direct and reflected wave WETI method, especially when large velocity errors are present in the shallow part of the starting models. The JDRWETI method with the two-stage inversion workflow can give rise to reasonable inversion results even for the model with different P- and S-wave velocity structures.

Analysis of Time–Distance Helioseismology for Detection of Emerging Active Regions

Abstract A time–distance helioseismic technique, similar to the one used by Ilonidis et al., is applied to two independent numerical models of subsurface sound-speed perturbations to determine the spatial resolution and accuracy of phase travel time shift measurements. The technique is also used to examine pre-emergence signatures of several active regions observed by the Michelson Doppler Imager and the Helioseismic Magnetic Imager. In the context of similar measurements of quiet-Sun regions, three of the five studied active regions show strong phase travel time shifts several hours prior to emergence. These results form the basis of a discussion of noise in the derived phase travel time maps and possible criteria to distinguish between true and false-positive detection of emerging flux.

Temporal Seismic Velocity Variations: Recovery Following From the 2019 Mw 7.1 Ridgecrest, California Earthquake

AbstractWe investigated seismic velocity changes (dv/v) associated with the 2019 Ridgecrest earthquake sequence with high‐frequency autocorrelations of ambient seismic noise data. Daily autocorrelation functions were computed for the entirety of 2019 and the first quarter of 2020 for broadband stations within the region, including the temporary broadband stations installed during the aftershock deployment. Travel time shifts in the daily autocorrelation functions, relative to the mean autocorrelation waveform, were computed to produce dv/v time series, which are sensitive to the evolving material properties of the shallow crust surrounding the Ridgecrest fault zone (RFZ). A short‐term velocity drop follows the Mw 7.1 earthquake at stations in the vicinity of the rupture surface, while those greater than 50 km away showed no such drop. The maximum, absolute changes in seismic velocity are proportional to the logarithm of distance from the fault rupture and to the peak dynamic strain experienced during the earthquake. Near the areas of the highest coseismic slip within the RFZ, seismic velocities recovered over 3 months. However, in the vicinity of the nearby Garlock fault, where triggered slip manifested, and north of the RFZ, seismic velocities recovered within a month. We interpret the seismic velocity changes and their recovery to be largely due to changes in the physical properties of the shallow crust, such as fault zone damage recovery caused by the earthquake rupture process and in response to the large dynamic stresses of passing seismic waves from the mainshock.

Impact of Odd–Even Scheme on Travel Pattern in Delhi

The paper intends to assess the impact of the odd–even scheme on the travel pattern of the daily commuters in Delhi. The objective of the paper is to assess the impact of the odd–even scheme on mode choice for daily work trips, shift in travel patterns – before, during, and post-implementation – of the odd–even scheme, and to understand people perception regarding the odd–even scheme. Based on the primary survey, the paper concludes that the odd–even scheme brought a significant impact in the travel pattern in terms of occupancy, travel cost, travel time, and modal shift, and statistically not so much on the air quality gain. It was observed that the scheme helped increase the occupancy rate in cars as well as ridership of buses and Delhi metro. The scheme had a huge impact on congestion, which was evident from both perception analysis and the change in travel time. The modal shift, with an improvement in public transport services and a reduction in car users, is one of the key successes of the scheme resulting in decrease in air pollution caused by private vehicles. To improve the outcome of the odd–even scheme on air pollution, two-wheelers should not be exempted going forward.

Computing Helioseismic Sensitivity Kernels for the Sun’s Large-scale Internal Flows Using Global-scale Wave-propagation Simulations

Abstract Helioseismic waves observable at the solar surface can be used to probe the properties of the Sun’s interior. By measuring helioseismic travel times between different location on the surface, flows and other interior properties can be inferred using so-called sensitivity kernels that relate the amount of travel-time shift with variations in interior properties. In particular, sensitivity kernels for flows have been developed in the past, using either ray or Born approximation, and have been used to infer solar interior flows such as the meridional circulation, which is of particular interest for understanding the structure and dynamics of the Sun. Here we introduce a new method for deriving three-dimensional sensitivity kernels for large-scale horizontal flows in the solar interior. We perform global-Sun wave-propagation simulations through 784 small flow perturbations placed individually in the interior of a simulated Sun, and measure the shifts in helioseismic travel times caused by these perturbations. Each measurement corresponds to a linear equation connecting the flow perturbation velocities and the sensitivity kernels. By solving the resulting large set of coupled linear equations, we derive three-dimensional sensitivity kernels for horizontal flows, which have a longitudinal component (parallel to the wave’s travel direction) and a transverse component (perpendicular to the wave’s travel direction). The kernels exhibit a “banana” shape, similar to kernels derived using Born-approximation methods, and show that transverse components are not negligible in inversions for interior flows.

Using onset times from frequent geophysical surveys to understand reservoir fluid flow and to estimate flow properties

Seismic characterization of flow properties is a difficult prospect, due to the indirect relationship between permeability and seismic velocity and attenuation. At best, seismic time-lapse changes can detect the effects of saturation and pressure changes in a reservoir due to fluid flow. Even in this case, the interpretation of the seismic observation in terms of the state of the reservoir depends intimately on the properties of the rock physics model, which are usually poorly known. The onset time, the calendar time of geophysical changes, provides an alternative datum for characterizing properties such as reservoir permeability. The main advantage of an onset time is that it is sensitive to the flow properties of the reservoir yet insensitive to the details of the rock physics model. Two examples of the utility of onset times are discussed: the use of travel time shifts induced by the injection of carbon dioxide between two wells, and the time-lapse time shifts for elastic waves propagating through a reservoir undergoing enhanced oil recovery. In both examples, the onset times are mapped into permeability estimates using a trajectory-based approach akin to seismic tomography.

The Sagnac effect on a scale-dependent rotating BTZ black hole background

In this paper, we investigate the Sagnac effect by calculating the difference in travel time and phase shift observed for photon beams counter-propagating in a rotating interferometer on a BTZ black hole solution in the context of scale-dependent gravity, which describes the field around a massive static and rotating object in 2 + 1 gravity.

Goos–Hänchen induced normal moveout correction for wide-angle reflections

The Goos–Hanchen (GH) lateral shift has been theoretically simulated and observed in lab. GH lateral shift introduces additional traveltime and distance when the incidence angles are larger than the critical angle. For seismic wave, this GH shift is caused by the total reflection of an incident beam of P-wave from low to high impedance medium at near and post-critical angles. Because of its large influences on traveltime and lateral shift displacement, the GH shift should be corrected in normal moveout (NMO) correction for wide-angle reflections in seismic data processing. In this paper, we derive the partial derivatives of reflection coefficients (PP- and PSV-wave) with respect to circular frequency using the Zoeppritz equations. Then, the delay time and NMO correction term with the behavior of GH lateral shift is derived. The characteristics of delay time and GH induced time differences are analyzed. The results show that this GH shift could be either positive or negative and the delay on time has large influences on seismic reflections when the incidence angles are larger than the critical angles. The efficiency of GH induced NMO correction is tested using synthetic seismic data. The GH induced NMO correction should be done for wide-angle reflections during the progress of seismic data processing.

Application of Flow Diagnostics to Rapid Production Data Integration in Complex Grids and Dual-Permeability Models

SummaryStreamline-based methods, as repeatedly demonstrated in multiple applications, offer a robust and elegant framework for reconciling high-resolution geologic models with observed field responses. However, significant challenges persist with the application of streamline-based methods in complex grids and dual-permeability media due to the difficulty with streamline tracing in these systems. In this work, we propose a novel and efficient framework that circumvents these challenges by avoiding explicit tracing of streamlines but exploits the inherent desirable features of streamline-based production data integration in high-resolution geologic models.Our approach features the application of flow diagnostics to inverse problems involving the integration of multiphase production data in reservoir models. Here, time-of-flight as well as numerical tracer concentrations for each well, on the basis of a defined flux field, are computed on the native finite-volume grid. The information embedded in these metrics are used in the dynamic definition of stream-bundles and, eventually, in the computation of analytical water arrival-time sensitivities with respect to model properties. This calculation mimics the streamline-derived analytical sensitivity computation used in the well-established generalized travel-time inversion (GTTI) technique but precludes explicit streamline tracing. The reservoir model property field is updated iteratively by solving the LSQR (sparse least-squares with QR factorization) system composed of the computed analytical sensitivity and the optimal water travel-time shift, augmented with regularization and smoothness constraints.The power and efficacy of our approach are demonstrated using synthetic model and field applications. We first validate our approach by benchmarking with the streamline-based GTTI algorithm involving a single-permeability medium. The flow-diagnostics-derived analytical sensitivities were observed to show good agreement with the streamline-derived sensitivities in terms of correctly capturing relevant spatiotemporal trends. Furthermore, the desirable quasilinear behavior characteristic of the traditional streamline-based GTTI technique was preserved. The flow-diagnostics-based inversion technique is then applied to a field-scale problem involving the integration of multiphase production data into a dual-permeability model of a large naturally fractured reservoir. The results clearly demonstrate the effectiveness of the proposed approach in overcoming the limitations of classical streamline-based methods with dual-permeability systems. By construction, this approach finds direct application in single/multicontinuum models with generic grid designs, both in structured and fully unstructured formats, thereby aiding well-level history matching and high-resolution updates of modern geologic models.This work presents, for the first time, an application of the GTTI to dual-permeability models of naturally fractured reservoirs. This is facilitated by a simplified, yet effective approach to travel-time sensitivity computations directly on finite-volume grids. The proposed approach can be easily applied to subsurface models at levels of complexity identified as challenging for classical streamline-based methods.

Time-lapse seismic analysis of overburden water injection at the Ekofisk field, southern North Sea

On 7 May 2001, a seismic event occurred in the southern North Sea in the vicinity of the Ekofisk platform area. Analysis of seismological recordings of this event indicated that the epicenter is likely within the northern part of the field and its hypocenter lies in the shallow sedimentary layer. Further investigation in this same area revealed a small seabed uplift and identified an unintentional water injection in the overburden. The injection presumably caused the seabed uplift in addition to stress changes in the overburden. To better understand the consequences of this water injection, we analyze marine seismic data acquired before and after the seismological event. The 4D analysis reveals a clear traveltime shift close to the injection well, as well as a weak amplitude difference. We find that these measured time shifts correspond reasonably well with modeled time shifts based on a simple geomechanical model. The modeling also correlates well with the observed bathymetry changes at the seabed and with global positioning system measurements at the platforms. Although no explicit amplitude sign of the seismic event could be detected in the seismic data, the modeled stress changes, combined with the effect of decades of production-induced reservoir compaction, suggest a source mechanism for the far-field seismological recordings of the May 7th event.

On the measurement of seismic traveltime changes in the time–frequency domain with wavelet cross-spectrum analysis

SUMMARY The spatial distribution of temporal variations in seismic wavespeed is key to understanding the sources and physical mechanisms of various geophysical processes. The imaging of wavespeed changes requires accurate measurements of traveltime delays with both high lapse-time and frequency resolutions. However, traditional methods for time-shift estimation suffer from their limited resolutions. In this paper we propose a new approach, the wavelet method, to measure the traveltime changes in the time–frequency domain. This method is based on wavelet cross-spectrum analysis, and can provide optimal time–frequency joint resolution while being computationally efficient. It can deal not only with coda but also dispersive surface waves even in the presence of cycle skipping. Using synthetic coda, we show that the wavelet method can retrieve traveltime shifts more stably and accurately than traditional methods. An application at Salton Sea Geothermal Field indicates that the wavelet method is less affected by spectral smearing and better discriminates dv/v variations at different frequencies. Furthermore, upon investigations on synthetic coda, we illustrate that the bias on dv/v measurements due to changes in source frequency content is likely to be negligible, either with traditional methods or with the new wavelet method. The wavelet method sheds lights on applications of seismic interferometry that aim to locate changes in space.

The Seismic Response to Injected Carbon Dioxide: Comparing Observations to Estimates Based Upon Fluid Flow Modeling

AbstractTime‐lapse seismic amplitude differences and travel time shifts, obtained while monitoring enhanced oil recovery at Cranfield, Mississippi, reveal coherent changes that are associated with the injection of carbon dioxide. Rock physics modeling highlights the importance of the oil, brine, and gas content of pore fluids prior to the injection of carbon dioxide. For example, compressional velocity changes due to the injection of carbon dioxide can drop from 300 m/s to less than 100 m/s as the percentage of oil increases from 1% to 50%. Predictions based upon a new technique for modeling wave propagation in a poroelastic medium containing an arbitrary number of fluids, coupled with multicomponent numerical reservoir modeling at Cranfield, reproduce the general pattern of observed seismic amplitude changes and travel time shifts. In particular, time‐lapse amplitude changes suggest a significant and widespread lowering of compressional velocities due to the injection of CO2 into an aquifer bounding the oil rim of the reservoir. It appears that the large‐scale variations in preexisting pore fluid content have a major influence on seismic velocity changes, even in the highly heterogeneous reservoir at Cranfield.