Reflection Traveltimes Research Articles

Shot- and angle-domain wave-equation traveltime inversion of reflection data: Synthetic and field data examples

Full-waveform inversion requires the accurate simulation of the dynamics and kinematics of wave propagation. This is difficult in practice because the amplitudes cannot be precisely reproduced for seismic waves in the earth. Wave-equation reflection traveltime tomography (WT) is proposed to avoid this problem by directly inverting the reflection-traveltime residuals without the use of the high-frequency approximation. We inverted synthetic traces and recorded seismic data for the velocity model by WT. Our results demonstrated that the wave-equation solution overcame the high-frequency approximation of ray-based tomography, was largely insensitive to the accurate modeling of amplitudes, and mitigated problems with ambiguous event identification. The synthetic examples illustrated the effectiveness of the WT method in providing a highly resolved estimate of the velocity model. A real data example from the Gulf of Mexico demonstrated these benefits of WT, but also found the limitations in traveltime residual estimation for complex models.

A refraction method to detect reservoir velocity and anisotropy

Since its inception in the early 1980s, detection of fractures and stress using P-wave reflection amplitudes and traveltimes has proved to be challenging. A significant amount of theory has been developed, but convincing and calibrated applications of the theory to field data have been lacking. This is mainly because of the physical limitation that P-wave reflection amplitudes sample only a small areal region (Fresnel zone) of the reservoir. Similarly, P-wave reflection traveltimes sample only a limited thickness (twice near-vertical reservoir thickness) compared with total traveltime from the source to the receiver. As a result, estimation of reservoir anisotropy from P-wave reflection data is inherently limited. A new method is used to detect fracturing and stress in addition to reservoir velocity. When available, the use of refracted P-wave traveltimes from a target of interest can provide robust information on reservoir velocity and anisotropy caused by fractures and horizontal stress variations. This is because refracted waves travel horizontally inside the medium under investigation and sample a large section of the target, integrating the anisotropic variation along different azimuths. Azimuthal variation of refraction traveltimes from the investigated medium can be used to invert for velocity and anisotropy. This traveltime method is applied to the highly fractured Joanne reservoir in the U. K. sector of the Central North Sea.

Imaging pre‐existing natural fractures using microseismic data

ABSTRACTIn hydraulic fracturing treatments, locating not only hydraulic fractures but also any pre‐existing natural fractures and faults in a subsurface reservoir is very important. Hydraulic fractures can be tracked by locating microseismic events, but to identify the locations of natural fractures, an additional technique is required. In this paper, we present a method to image pre‐existing fractures and faults near a borehole with virtual reverse vertical seismic profiling data or virtual single‐well profiling data (limited to seismic reflection data) created from microseismic monitoring using seismic interferometry. The virtual source data contain reflections from natural fractures and faults, and these features can be imaged by applying migration to the virtual source data. However, the imaging zone of fractures in the proposed method is strongly dependent on the geographic extent of the microseismic events and the location and direction of the fracture. To verify our method, we produced virtual reverse vertical seismic profiling and single‐well profiling data from synthetic microseismic data and compared them with data from real sources in the same relative position as the virtual sources. The results show that the reflection travel times from the fractures in the virtual source data agree well with travel times in the real‐source data. By applying pre‐stack depth migration to the virtual source data, images of the natural fractures were obtained with accurate locations. However, the migrated section of the single‐well profiling data with both real and virtual sources contained spurious fracture images on the opposite side of the borehole. In the case of virtual single‐well profiling data, we could produce correct migration images of fractures by adopting directional redatuming for which the occurrence region of microseismic events is divided into several subdivisions, and fractures located only on the opposite side of the borehole are imaged for each subdivision.

2D seismic reflection tomography in strongly anisotropic media

Seismic traveltime tomography is an effective method to reconstruct underground anisotropic parameters. Currently, most anisotropic tomographic methods were developed under the assumption of weak anisotropy. The tomographic method proposed here can be implemented for imaging subsurface targets in strongly anisotropic media with a known tilted symmetry axis, since the adopted ray tracing method is suitable for anisotropic media with arbitrary degree. There are three kinds of reflection waves (qP, qSV and qSH waves) that were separately used to invert the blocky abnormal body model. The reflection traveltime tomographiy is developed here because a surface observation system is the most economical and practical way compared with crosswell and VSP. The numerical examples show that the traveltimes of qP reflection wave have inverted parameters successfully. Traveltimes of qSV reflection wave have inverted parameters successfully, with the exception of the since it is less sensitive than other parameters. Traveltimes of qSH reflection wave also have inverted parameters successfully. In addition, we find that the velocity sensitivity functions (derivatives of phase velocity with respect to elastic moduli parameters) and raypath illuminating angles have a great influence on the qualities of tomograms according to the inversion of theoretical models. Finally, the numerical examples confirm that the reflection traveltime tomography can be applied to invert strongly anisotropic models.

Parameter estimation from non‐hyperbolic reflection traveltimes for large aperture common midpoint gathers

ABSTRACTAs far as superficial seismic reflection events are concerned, the classical normal moveout (NMO) process, which leads to the construction of seismic zero‐offset (or stacked) sections, encounters several difficulties due to the large data aperture. One of these difficulties is that the hyperbolic approximation of the reflection traveltime in common midpoint (CMP) gathers is no longer valid when offset largely exceeds the target depth. Recently, Fomel and Kazinnik proposed a novel, multi‐parameter, non‐hyperbolic formula for the traveltime of such reflection events. This formula, which will be referred to here as the FK traveltime after the authors, is exact for reflectors whose shape can be described by a hyperbola, and shows promising accuracy for long offsets and/or curved reflectors. It also depends on the same set of parameters as the common reflection surface (CRS) traveltime. In this paper, we propose strategies for estimating these CRS parameters based on the FK traveltime using large aperture data. However, in contrast to traditional CRS processing, and due to their widespread use, only common midpoint (CMP) gathers will be considered for the parameter searches. We will begin with a sensitivity analysis, showing the impact of each parameter on the traveltime. Based on this analysis, we will propose a two‐step estimation strategy, that could lead to improved seismic images, especially for very shallow, high aperture events. We will then highlight, through synthetic examples and discussions, the strengths and limitations of this strategy.

Structure-coupled joint inversion for magnetotelluric, seismic refraction and reflection traveltime data

SUMMARY A method of joint inversion of Magnetotelluric, seismic refraction and seismic reflection (JIMRR) is developed especially for typical hydrocarbon or hard-rock mineral exploration. JIMRR includes two parts: jointed seismic refraction and seismic reflection; and its combination with Magnetotelluric (MT) method. The objective of the research is to enhance spatial resolution of the three model parameters: electrical resistivity, seismic velocity and reflector depth. Since horizontal coordinates of reflector are not treated as model parameters in existing travel time inversion algorithm, seismic forward modelling may loss the true reflection point locations at the side edges of reflector with limited extension. We developed the technology of extensible reflector to overcome this problem. JIMRR is completed by employing the cross-gradient function as constraints which enforces the structural similarity between the resistivity and the seismic velocities, so as to reduce velocity-depth ambiguity. The cross-gradient constraints are incorporated into the solution through least squares and Lagrange multiplier method. This method results in integrated symmetric square linear matrix that is solved by bi-conjugate gradient method (BiCG). Two example synthetic models show that our joint inversion can significantly enhance the spatial resolution of inversion; and also the velocity-depth ambiguity caused by reflection travel time inversion can be notably reduced by constraints from shallow lithologies.

Wave-equation reflection traveltime inversion with dynamic warping and full-waveform inversion

In reflection seismology, full-waveform inversion (FWI) can generate high-wavenumber subsurface velocity models but often suffers from an objective function with local minima caused mainly by the absence of low frequencies in seismograms. These local minima cause cycle skipping when the low-wavenumber component in the initial velocity model for FWI is far from the true model. To avoid cycle skipping, we discovered a new wave-equation reflection traveltime inversion (WERTI) to update the low-wavenumber component of the velocity model, while using FWI to only update high-wavenumber details of the model. We implemented the low- and high-wavenumber inversions in an alternating way. In WERTI, we used dynamic image warping (DIW) to estimate the time shifts between recorded data and synthetic data. When compared with correlation-based techniques often used in traveltime estimation, DIW can avoid cycle skipping and estimate the time shifts accurately, even when shifts vary rapidly. Hence, by minimizing traveltime shifts estimated by dynamic warping, WERTI reduces errors in reflection traveltime inversion. Then, conventional FWI uses the low-wavenumber component estimated by WERTI as a new initial model and thereby refines the model with high-wavenumber details. The alternating combination of WERTI and FWI mitigates the velocity-depth ambiguity and can recover subsurface velocities using only high-frequency reflection data.

IDENTIFICATION OF PIPELINES FROM THE SECONDARY REFLECT WAVE TRAVEL TIME OF GROUND-PENETRATING RADAR WAVES

When using ground-penetrating radar to identify underground pipelines of similar dielectric constants (i.e. PE and PVC), misidentification is quite common. In this study, we apply reflected travel time of radar waves into the PE- and PVC- dielectric constants and the differentiation becomes possible. We have conducted the experiments using the nonmetal PE- and PVC- pipelines as well as the heavy metal (iron) pipelines in a water environment. Based on a travel- time calculation, the dielectric constants of non-metal pipelines with similar composition (PE=2.3 and PVC=3.0) were quite close. The error between the experimental and theoretical values is acceptable in general engineering projects. It is also compliant with the standard error by the U.S. ASTMD4748-98 (the error range is about ± 0.2 inches or ± 0.508 cm). Therefore, the result of this study not only can be applied to detect the metal pipes, but also may be used to distinguish non-metallic pipes in a water environment.

Water-bottom multiple attenuation by Kirchhoff extrapolation

Despite being less general than 3D surface-related multiple elimination (3D-SRME), multiple prediction based on wavefield extrapolation can still be of interest, because it is less CPU and I/O demanding than 3D-SRME and moreover it does not require any prior data regularization. Here we propose a fast implementation of water-bottom multiple prediction that uses the Kirchhoff formulation of wavefield extrapolation. With wavefield extrapolation multiple prediction is usually obtained through the cascade of two extrapolation steps. Actually by applying the Fermat’s principle (i.e., minimum reflection traveltime) we show that the cascade of two operators can be replaced by a single approximated extrapolation step. The approximation holds as long as the water bottom is not too complex. Indeed the proposed approach has proved to work well on synthetic and field data when the water bottom is such that wavefront triplications are negligible, as happens in many practical situations.

The use of low frequencies in a full‐waveform inversion and impedance inversion land seismic case study

ABSTRACTVelocity model building and impedance inversion generally suffer from a lack of intermediate wavenumber content in seismic data. Intermediate wavenumbers may be retrieved directly from seismic data sets if enough low frequencies are recorded. Over the past years, improvements in acquisition have allowed us to obtain seismic data with a broader frequency spectrum. To illustrate the benefits of broadband acquisition, notably the recording of low frequencies, we discuss the inversion of land seismic data acquired in Inner Mongolia, China. This data set contains frequencies from 1.5–80 Hz. We show that the velocity estimate based on an acoustic full‐waveform inversion approach is superior to one obtained from reflection traveltime inversion because after full‐waveform inversion the background velocity conforms to geology. We also illustrate the added value of low frequencies in an impedance estimate.

Building starting models for full waveform inversion from wide‐aperture data by stereotomography

ABSTRACTBuilding an accurate initial velocity model for full waveform inversion (FWI) is a key issue to guarantee convergence of full waveform inversion towards the global minimum of a misfit function. In this study, we assess joint refraction and reflection stereotomography as a tool to build a reliable starting model for frequency‐domain full waveform inversion from long‐offset (i.e., wide‐aperture) data. Stereotomography is a slope tomographic method that is based on the inversion of traveltimes and slopes of locally‐coherent events in a data cube. One advantage of stereotomography compared to conventional traveltime reflection tomography is the semi‐automatic picking procedure of locally‐coherent events, which is easier than the picking of continuous events, and can lead to a higher density of picks. While conventional applications of stereotomography only consider short‐offset reflected waves, we assess the benefits provided by the joint inversion of reflected and refracted arrivals. Introduction of the refracted waves allows the construction of a starting model that kinematically fits the first arrivals, a necessary requirement for full waveform inversion. In a similar way to frequency‐domain full waveform inversion, we design a multiscale approach of stereotomography, which proceeds hierarchically from the wide‐aperture to the short‐aperture components of the data, to reduce the non‐linearity of the stereotomographic inversion of long‐offset data. This workflow which combines stereotomography and full waveform inversion, is applied to synthetic and real data case studies for the Valhall oil‐field target. The synthetic results show that the joint refraction and reflection stereotomography for a 24‐km maximum offset data set provides a more reliable initial model for full waveform inversion than reflection stereotomography performed for a 4‐km maximum offset data set, in particular in low‐velocity gas layers and in the deep part of a structure below a reservoir. Application of joint stereotomography, full waveform inversion and reverse‐time migration to real data reveals that the FWI models and the reverse‐time migration images computed from the stereotomography model shares several features with FWI velocity models and migrated images computed from an anisotropic reflection‐traveltime tomography model, although stereotomography was performed in the isotropic approximation. Implementation of anisotropy in joint refraction and reflection stereotomography of long‐offset data is a key issue to further improve the accuracy of the method.

Prestack time migration by common-migrated-reflector-element stacking

Time migration is an attractive tool to produce a subsurface image because it is faster and less sensitive to velocities errors than depth migration. However, a highly focused time image is only achievable with well-determined time-migration velocities. Therefore, a refinement of the initial time-migration velocities often is required. We introduced a new technique for prestack time migration, based on the common-migrated-reflector-element stack of common scatterpoint gathers, including an automatic update of time-migration velocities. The common scatterpoint gathers are generated using a new formulation of the double-square-root equation that is parametrized with the common-offset apex time. The common-migrated-reflector-element stack is a multiparameter stacking technique based on the Taylor expansion of traveltimes of time-migrated reflections in the paraxial vicinity of the image ray. Our 2D synthetic and field data examples demonstrated that the proposed method provides updated time-migration velocities that are more robust and have higher resolution compared with the initial time-migration velocities. The prestack time migration method also showed a clear improvement of the focusing of reflections for such geologic features as faults and salt structures.

Non‐hyperbolic common reflection surface

ABSTRACTThe method of common reflection surface (CRS) extends conventional stacking of seismic traces over offset to multidimensional stacking over offset‐midpoint surfaces. We propose a new form of the stacking surface, derived from the analytical solution for reflection traveltime from a hyperbolic reflector. Both analytical comparisons and numerical tests show that the new approximation can be significantly more accurate than the conventional CRS approximation at large offsets or at large midpoint separations while using essentially the same parameters.

Georadar‐derived estimates of firn density in the percolation zone, western Greenland ice sheet

Greater understanding of variations in firn densification is needed to distinguish between dynamic and melt‐driven elevation changes on the Greenland ice sheet. This is especially true in Greenland's percolation zone, where firn density profiles are poorly documented because few ice cores are extracted in regions with surface melt. We used georadar to investigate firn density variations with depth along a ∼70 km transect through a portion of the accumulation area in western Greenland that partially melts. We estimated electromagnetic wave velocity by inverting reflection traveltimes picked from common midpoint gathers. We followed a procedure designed to find the simplest velocity versus depth model that describes the data within estimated uncertainty. On the basis of the velocities, we estimated 13 depth‐density profiles of the upper 80 m using a petrophysical model based on the complex refractive index method equation. At the highest elevation site, our density profile is consistent with nearby core data acquired in the same year. Our profiles at the six highest elevation sites match an empirically based densification model for dry firn, indicating relatively minor amounts of water infiltration and densification by melt and refreeze in this higher region of the percolation zone. At the four lowest elevation sites our profiles reach ice densities at substantially shallower depths, implying considerable meltwater infiltration and ice layer development in this lower region of the percolation zone. The separation between these two regions is 8 km and spans 60 m of elevation, which suggests that the balance between dry‐firn and melt‐induced densification processes is sensitive to minor changes in melt.

Joint transmission and reflection traveltime tomography using the fast sweeping method and the adjoint-state technique

SUMMARY We present a joint transmission and reflection traveltime tomography algorithm based on the Fast Sweeping Method and the adjoint-state technique. In contrast to classical ray based tomography, this algorithm utilizes a grid-based Eikonal equation solver to circumvent the non-linearity of conventional ray shooting and bending approaches in complex media. The adjoint-state technique is used to obtain the gradient of the objective function without the explicit estimation of the Frechet derivative matrix, which is usually computationally prohibitive for large-scale problems. When combined with Huygens’ Principle, the tomographic inversion can simultaneously use direct and reflected arrivals to optimize a final velocity model, further mitigate the ambiguity of the inverse problem and reveal deeper structures not visible to transmission tomography alone. In this paper, we describe the theoretical basis of our algorithm, evaluate its performance on synthetic models, and then apply it to a 20 km long 2-D seismic survey acquired in the Mackenzie Delta, Northwest Territories of Canada. The subsurface at that location is characterized by a thick permafrost (600 m) comprising high- and low-velocity areas associated with thermokarst lakes. Our results show the potential of the joint tomography in characterizing multi-scale heterogeneous velocity structures within the permafrost.

An analysis of SS precursors using spectral-element method seismograms

SUMMARY The traveltimes of underside shear wave reflections (i.e. SS precursors) are widely used data for mapping the topography of mantle discontinuities in the upper mantle. Here, we examine the accuracy of ray theory in estimating the contribution of shear velocity heterogeneity in the mantle to SS–S400S, SS–S670S and S400S–S670S traveltimes. We analyse stacks of spectral-element method waveforms computed for 34 shallow earthquakes and 16 020 globally distributed virtual seismometers. The waveforms are computed for three versions of shear velocity model S20RTS with variable strengths of the volumetric shear velocity perturbations within the layered structure of the Preliminary Reference Earth Model. We find that ray-theoretical corrections account for only 50 per cent of the traveltime variation due to large-scale velocity heterogeneity. For current tomographic models, as represented by S20RTS, this translates into unpredictable long- and short-wavelength errors in maps of mantle discontinuity depths of about 5 km. This amounts to roughly 10 per cent of published variations in mantle discontinuity depths. However, relative errors will be significantly larger if ray-theoretical traveltime corrections are based on (forthcoming) models of shear velocity with much stronger heterogeneity at the smallest scales.

Joint transmission and reflection traveltime tomography in imaging permafrost and thermokarst lakes in Northwest Territories, Canada

We propose an application of joint tomographic inversion using both transmitted and reflected arrivals to map velocity structures in thick permafrost areas of the Mackenzie Delta, Northwest Territories of Canada. Our tomography algorithm combines a grid-based solver of the eikonal equation, Huygens' principle, and the adjoint method. The grid-based solver assigns a traveltime to each grid point and avoids the shadow-zone problem in classical ray tracing and is well-adapted for parallelization. The adjoint method used in the inversion provides the gradient of a given objective function without explicitly estimating the Fréchet derivative matrix. When combined with Huygens' principle, the tomographic inversion can simultaneously use first and later arrivals to optimize a final velocity model. We first demonstrate the performance of the joint tomography algorithm on a two-dimensional synthetic model with velocity variations typical of permafrost. The method is then applied to a 2D seismic survey covering over 20 km with offsets up to 4 km, acquired in the Mackenzie Delta. The subsurface at that location is characterized by a thick permafrost (600 m) comprising high-velocity and low-velocity areas associated with thermokarst lakes. Our results show the potential of the joint tomography in characterizing multiscale heterogeneous velocity structures within the permafrost.

On the footprint of anisotropy on isotropic full waveform inversion: the Valhall case study

The validity of isotropic approximation to perform acoustic full waveform inversion (FWI) of real wide-aperture anisotropic data can be questioned due to the intrinsic kinematic inconsistency between short- and large-aperture components of the data. This inconsistency is mainly related to the differences between the vertical and horizontal velocities in vertical-transverse isotropic (VTI) media. The footprint of VTI anisotropy on 2-D acoustic isotropic FWI is illustrated on a hydrophone data set of an ocean-bottom cable that was collected over the Valhall field in the North Sea. Multiscale FWI is implemented in the frequency domain by hierarchical inversions of increasing frequencies and decreasing aperture angles. The FWI models are appraised by local comparison with well information, seismic modelling, reverse-time migration (RTM) and source-wavelet estimation. A smooth initial VTI model parameterized by the vertical velocity V0 and the Thomsen parameters δ and ∈ were previously developed by anisotropic reflection traveltime tomography. The normal moveout () and horizontal () velocity models were inferred from the anisotropic models to perform isotropic FWI. The VNMO models allows for an accurate match of short-spread reflection traveltimes, whereas the Vh model, after updating by first-arrival traveltime tomography (FATT), allows for an accurate match of first-arrival traveltimes. Ray tracing in the velocity models shows that the first 1.5 km of the medium are sampled by both diving waves and reflections, whereas the deeper structure at the reservoir level is mainly controlled by short-spread reflections. Starting from the initial anisotropic model and keeping fixed δ and ∈ models, anisotropic FWI allows us to build a vertical velocity model that matches reasonably well the well-log velocities. Isotropic FWI is performed using either the NMO model or the FATT model as initial model. In both cases, horizontal velocities are mainly reconstructed in the first 1.5 km of the medium. This suggests that the wide-aperture components of the data have a dominant control on the velocity estimation at these depths. These high velocities in the upper structure lead to low values of velocity in the underlying gas layers (either equal or lower than vertical velocities of the well log), and/or a vertical stretching of the structure at the reservoir level below the gas. This bias in the gas velocities and the mispositioning in depth of the deep reflectors, also shown in the RTM images, are required to match the deep reflections in the isotropic approximation and highlight the footprint of anisotropy in the isotropic FWI of long-offset data. Despite the significant differences between the anisotropic and isotropic FWI models, each of these models produce a nearly-equivalent match of the data, which highlights the ill-posedness of acoustic anisotropic FWI. Hence, we conclude with the importance of considering anisotropy in FWI of wide-aperture data to avoid bias in the velocity reconstructions and mispositioning in depth of reflectors. Designing a suitable parameterization of the VTI acoustic FWI is a central issue to manage the ill-posedness of the FWI.

An adaptive phase space method with application to reflection traveltime tomography

In this work, an adaptive strategy for the phase space method for traveltime tomography (Chung et al 2007 Inverse Problems 23 309–29) is developed. The method first uses those geodesics/rays that produce smaller mismatch with the measurements and continues on in the spirit of layer stripping without defining the layers explicitly. The adaptive approach improves stability, efficiency and accuracy. We then extend our method to reflection traveltime tomography by incorporating broken geodesics/rays for which a jump condition has to be imposed at the broken point for the geodesic flow. In particular, we show that our method can distinguish non-broken and broken geodesics in the measurement and utilize them accordingly in reflection traveltime tomography. We demonstrate that our method can recover the convex hull (with respect to the underlying metric) of unknown obstacles as well as the metric outside the convex hull.

Seismic evidence for the presence of Jurassic oceanic crust in the central Gulf of Cadiz (SW Iberian margin)

We investigate the crustal structure of the SW Iberian margin along a 340 km-long refraction and wide-angle reflection seismic profile crossing from the central Gulf of Cadiz to the Variscan continental margin in the Algarve, Southern Portugal. The seismic velocity and crustal geometry model obtained by joint refraction and reflection travel-time inversion reveal three distinct crustal domains: the 28–30 km-thick Variscan crust in the north, a 60 km-wide transition zone offshore, where the crust abruptly thins ~ 20 km, and finally a ~ 7 km-thick and ~ 150 km-wide crustal section that appears to be oceanic in nature. The oceanic crust is overlain by a 1–3 km-thick section of Mesozoic to Eocene sediments, with an additional 3–4 km of low-velocity, unconsolidated sediments on top belonging to the Miocene age, Gulf of Cadiz imbricated wedge. The sharp transition between continental and oceanic crust is best explained by an initial rifting setting as a transform margin during the Early Jurassic that followed the continental break-up in the Central Atlantic. The narrow oceanic basin would have formed during an oblique rifting and seafloor spreading episode between Iberia and Africa that started shortly thereafter (Bajocian) and lasted up to the initiation of oceanic spreading in the North Atlantic at the Tithonian (late Jurassic-earliest Cretaceous). The velocity model displays four wide, prominent, south-dipping low-velocity anomalies, which seem to be related with the presence of crustal-scale faults previously identified in the area, some of which could well be extensional faults generated during this rifting episode. We propose that this oceanic plate segment is the last remnant of an oceanic corridor that once connected the Alpine-Tethys with the Atlantic ocean, so it is, in turn, one of the oldest oceanic crustal fragments currently preserved on Earth. The presence of oceanic crust in the central Gulf of Cadiz is consistent with geodynamic models suggesting the existence of a narrow, westward retreating oceanic slab beneath the Gibraltar arc-Alboran basin system.