Reflection Traveltimes Research Articles

Coupling adaptive filters with acoustic travel time tomography for indoor climate measurements in occupied room conditions

Acoustic travel time TOMography (ATOM) as a remote sensing technique allows for the measurement of indoor climate parameters, such as air temperature and airflow velocity distributions. The performance of ATOM in monitoring indoor air temperature in empty room conditions was evaluated recently, utilizing a combined analysis approach of room acoustics and tomography. This study shifts focus to the assessment of ATOM in an occupied room condition where fixed objects are introduced to the test area. The presence of objects in a room can result in notable shifts in the travel times of individual reflections. In some cases, these shifts can cause reflections to disappear completely or be replaced by new ones. These partial disruptions in the reflection pattern present challenges in obtaining accurate information about the room's temperature. To ensure the accurate identification of undisturbed reflection paths, an algorithm was developed that can convert distorted signals into a pure reference signal using a suitable adaptive filter. The measurement results confirm the validity of the approach for a temperature interval of 4°C where the system was trained for two temperatures of 20°C and 24°C in a climate chamber.

A three-dimensional immersed boundary method for accurate simulation of acoustic wavefields with complex surface topography

Abstract Irregular topography of the free surface significantly affects seismic wavefield modelling, especially when employing finite-difference methods on rectangular grids. These methods represent the free surface as discrete points, resulting in a boundary that resembles a ‘staircase’. This approximation inaccurately represents surface topography, introducing errors in surface reflection traveltimes and generating artificial diffractions in wavefield simulation. We introduce a stable three-dimensional immersed boundary method (3DIBM) employing Cartesian coordinates to address these challenges. The 3DIBM enables the simulation of acoustic waves in media with complex topography through standard finite difference, extending the two-dimensional immersed boundary approach to compute spatial coordinates for ghost and mirror points in a three-dimensional space. Wavefield values at these points are obtained by three-dimensional spatial iterative symmetric interpolation, specifically through the Kaiser-windowed sinc method. By implicitly implementing the free surface boundary condition in three dimensions, this method effectively reduces artificial diffractions and enhances the accuracy of reflection traveltime. The effectiveness and accuracy of 3DIBM are validated through numerical tests and pre-stack depth migration imaging with simulated data, demonstrating its superiority as a modelling engine for migration imaging and waveform inversion in three-dimensional land seismic analysis.

Weakly anelliptical traveltime analysis: Ambiguity between subsurface and elasticity

The building of a subsurface and (anisotropic) velocity model from a single gather of reflection traveltime (kinematic) data is inherently ambiguous because the processing of such data can only determine a horizontal slowness component, not a vertical one. Based thereon, I derive a simple algorithm that generates an infinite series of combinations of the subsurface-velocity models, all of which will show nearly the same seismic kinematic response, as further demonstrated by simulating wave propagation through a model with different interface dips. This algorithm assumes, first, that all interface dips remain constant over the distance considered and, second, that an approximation of the elasticity model — that is, the linearization of a phase velocity — valid for weak anisotropy can be used. Furthermore, when applied to the classic and analytically solvable case of traveltime analysis for a stack of flat layers with weak transverse isotropy, the algorithm theoretically explains the combination of anisotropy parameters that govern the nonhyperbolic term of a traveltime series: the established [Formula: see text] and its new counterpart [Formula: see text] for a [Formula: see text] and [Formula: see text] wave, respectively.

Eikonal-equation-based characteristic reflection traveltime tomography

Automatically picking reflection traveltimes from the prestack shot gathers and positioning and updating the reflector depths during inversion are challenging in conventional eikonal-equation-based adjoint-state reflection traveltime tomography methods. To solve these problems, we develop an eikonal-equation-based adjoint-state characteristic reflection traveltime tomography (ASCRT) method. This method automatically extracts the reflection traveltimes by sequentially applying characteristic reflector picking in the depth migration section, followed by eikonal-equation-based traveltime calculation and an event-tracking algorithm. We also develop an efficient eikonal-equation-based kinematic imaging method to rapidly position and update the reflector depths. With our ASCRT method, the characteristic reflector positions and the velocity above the reflector are alternately updated. Our ASCRT method is performed with a layer-stripping strategy that sequentially uses selected characteristic reflectors to update the velocity model from shallow to deep. Compared with the wave equation-based reflection traveltime inversion methods, the efficiency of the ASCRT method is improved by several orders of magnitude, and the memory consumption is remarkably reduced. Synthetic and field data examples are presented to demonstrate the effectiveness and efficiency of our method.

Monochromatic wave equation reflection traveltime inversion

Wave equation reflection traveltime inversion (WRTI) is a fundamental method for interrogating the deep subsurface macrovelocity model. The time-domain WRTI calculates the gradient through the crosscorrelation of the source background and receiver scattered wavefields and the crosscorrelation of the source scattered and receiver background wavefields. During the backward propagation of the adjoint source, access to the source background and scattered snapshots of the entire propagation time is required. Because the source and receiver wavefields are extrapolated in opposite temporal directions, these source background and scattered wavefields are either stored in memory or reconstructed by additional wavefield extrapolation. This leads to a heavy memory burden and/or high computational cost. To address these challenges, we develop a new frequency-domain WRTI that is based on a monofrequency. By using the wavenumber coverage and gradient analyses, we prove that the monochromatic WRTI can produce comparable wavenumbers with time-domain and multifrequency-based WRTI. Our method directly stores monochromatic wavefields in memory because only one frequency is used for the gradient calculation. Therefore, our method significantly outperforms the conventional time-domain implementation in terms of memory requirement and computational cost. The accuracy of the monochromatic WRTI method is validated by gradient and result comparisons of several models with different complexities. Finally, we determine the effectiveness of our method by applying it to offshore streamer data.

Converted-wave reflection traveltime inversion with free-surface multiples for ocean-bottom-node data

Advancements in ocean-bottom-node (OBN) technologies have enabled the recording of high-quality multicomponent seismic data, which can provide crucial information about subsurface properties through elastic seismic imaging. However, imaging multicomponent data is challenging due to the requirement for P- and S-wave velocity models. Conventional processing relies on estimating the S-wave velocity model using a primary converted wave (C wave) because the pure S-wave primaries are not available if using standard air-gun sources. When a free surface is present, the C waves recorded with geophones can be contaminated by source-side P-wave multiples, especially water-layer reverberations, which are difficult to remove even using state-of-the-art wavefield decomposition methods. These C-wave multiples can cause significant mismatches between synthetic and observed data during reflection traveltime or waveform inversion if only primary P-to-S (PS) conversions are simulated. To address these issues and reliably build an S-wave velocity model for PS imaging, we develop a C-wave reflection traveltime inversion method that takes source-side free-surface multiples into account. The traveltime misfit of C-wave data is extracted using dynamic image warping to ensure a better match between the synthetic and observed data. The functional gradient of the objective function is derived using the adjoint state method. Based on sensitivity kernel analyses, a convenient gradient preconditioning strategy is developed to robustly separate the contribution of primary and multiple C waves during backpropagation. This strategy can effectively mitigate the high-wavenumber crosstalk associated with nonphysical wavepaths in the gradient and thus allow more accurate updating for the S-wave velocity model. The synthetic data and shallow-water OBN data from the East China Sea indicate that this approach can reliably recover the S-wave macrovelocity structures for PS imaging.

Deep crustal structure and tectonic implications of the Nansha Trough from wide-angle reflection and refraction seismic data

Deep crustal structure of the Nansha Trough (NT) plays a crucial role in understanding its crustal nature and magmatic activity. This study used the data from a wide-angle seismic profile (NDL1), which passes through the Jinghong seamount (JHSM) and Yinqing seamount (YQSM) along the trough. By using 2D forward ray-tracing and joint refraction and reflection travel-time inversion methods, we obtained the velocity structure of the NT. The model results show a thinned continental crust with a thickness of ∼9–18 km in the east of the trough, which is variable drastically below the seamounts. The upper crust slightly varies at a thickness of ∼5 km except at the seamounts, while the lower crust shows lateral variations in thickness and velocity, accompanied by high velocities below the JHSM due to the magmatic addition. Velocity models of the NDL1 also reveal crustal differences between the JHSM and YQSM. Combined with the magnetic anomaly and multichannel seismic data, we infer that the seamounts formed from multiple stages of magmatism after the spreading of the South China Sea and the NT are still active. High velocities in the lower crust result from the mantle upwelling and decompression melting of flexural responses of the NT, which may provide a genesis clue for the formation of the submarine seamounts.

Second-order optimization for multiparameter reflection waveform inversion in acoustic VTI media

SUMMARY The seismic wave velocity in subsurface formations typically varies both spatially and directionally, resulting in a heterogeneous and anisotropic medium. To successfully image complex structures and potential reservoirs using multichannel seismic data, high-resolution interval velocity models are required. However, most controlled-source seismic recordings lack wide-angle signals, such as diving and refracted waves that propagate through deep formations. Consequently, geophysicists rely on the traveltimes and waveforms of reflections or back-scatterings in finite-frequency and finite-offset seismograms to estimate velocity and account for possible anisotropy. Recently, wave-equation based reflection waveform inversion (RWI) has emerged as an active research topic due to its ability to recover intermediate-wavelength model components that cannot be retrieved in reflection traveltime tomography. Nevertheless, the widely used gradient-type local optimization suffers from multiparameter trade-off and slow convergence of RWI in anisotropic media. Analysis of the Fréchet derivative reveals that the sensitivity of reflections to changes in long-to-intermediate wavelengths of the anisotropic velocities is jointly controlled by the specular reflection on the interface and the radiation pattern of scattered fields concerning the model parameters along the wave paths. Anatomy of the approximate Hessian reveals characteristics of parameter coupling and spatial resolution in the context of multiparameter RWI, inspiring the development of a matrix-free Gauss–Newton algorithm based on the second-order adjoint-state method for large-scale applications. Synthetic and real data examples demonstrate that the proposed approach can appropriately handle overburden heterogeneities and anisotropies, and thus improve imaging of underlying complex structures such as dipping and small-scale faults in the deep parts.

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.

A robust array geometry inversion method for a deep-towed multichannel seismic system with a complex seafloor

Deep-towed multichannel seismic exploration technology has better applicability and more development potential when utilized to invert the geoacoustic properties of deep-sea sediment. The accurate geometric inversion results of the receiving array are crucial for fine submarine sediment imaging and physical property parameter inversion based on deep-towed multichannel seismic data. Thus, this study presents an array geometry inversion method suitable for complex seafloors to address the challenge of precise source-receiver positioning. The objective function of the deep-towed seismic array geometry inversion is built using the shortest path algorithm according to the traveltimes of direct waves and seafloor reflections, and the particle swarm optimization algorithm is used to achieve high-precision inversion of the source-receiver position. The results showed that the proposed method is shown to have incomparable applicability and effectiveness in obtaining exact source-receiver positions for deep-towed multichannel seismic systems. Regardless of the complexity of the seabed morphology, seismic image processing techniques using the source-receiver position data obtained by the suggested method produce fine seismic imaging profiles that clearly and accurately reflect the structural characteristics of sediments. These findings provide insights for the accuracy and reliability of the proposed geometric shape inversion method for deep-towed seismic arrays in practical applications to meet the requirements of near-bottom acoustic detection for fine imaging of deep-sea seabed strata and precise inversion of geoacoustic parameters.

Wide‐spectrum reconstruction of a velocity model based on the wave equation reflection inversion method and its application

AbstractMost seismic data used for conventional exploration lack far‐offset signals and effective low‐frequency components. This makes it difficult for conventional full waveform inversion methods to recover the low‐wavenumber components of mid‐ and deep‐layer models. To resolve the bottleneck of ray‐theoretical reflection traveltime tomography, wave equations, such as reflection inversion methods, are receiving increasing attention. We reconstructed a wide‐spectrum velocity model based on the multiscale wave‐equation reflection inversion method for model decomposition. First, using the dynamic image warping method to obtain reflection traveltime residuals, the wave‐equation reflection traveltime inversion was used to recover the low‐wavenumber components of the background model, which also solved the cycle‐skipping problem. Second, the medium‐wavenumber component of the model is then supplemented by the reflection waveform inversion, while the reflectivity model is obtained relying on the least‐squares reverse time migration method. Based on this method, the background and perturbation models are updated alternately and iteratively. At the same time, the stratum structural tensor information was extracted using the perturbed model image to construct a preconditioned operator for the stratum structural constraint, suppress unreasonably high‐wavenumber components in the generalized gradient and improve the geological consistency of the inversion results. Testing of the model using the Sigsbee2b model and seismic field data from the East China Sea showed that, compared with the conventional reflection traveltime tomography method based on prestack depth migration, the wave‐equation reflection inversion strategy with well‐matched information from traveltimes to waveforms significantly improved the accuracy of the middle and deep velocity modelling and enhanced the imaging quality of the whole body.

A workflow for processing mono‐channel Chirp and Boomer surveys

AbstractAcquiring seismic data with multichannel, multiple‐streamer and even multi‐componentsystems at sea provides excellent images of the Earth. However, the cost and complexity of operations prevent their use in busy areas such as ports or in sensitive environments such as lagoons. In the latter cases, mono‐channel Chirp or Boomer systems are the most viable instruments for marine surveys. The lack of multiple offsets prevents the use of standard tools for amplitude‐versus‐offset and velocity analysis, which are necessary for the lithological characterization of rocks, especially for the shallow sediments in offshore engineering. In this paper, we present a few recent techniques that exploit the traveltime and amplitude of multiple reflections to compensate for the offset limitation, including a new algorithm for the joint tomographic inversion of direct arrivals, primaries and multiples. We have developed a cost‐effective workflow for mono‐channel surveys based on a data‐driven, physically consistent philosophy that attempts to approximately extract lithological parameters, such as P velocity, anelastic absorption, acoustic impedance and even density. We applied the proposed workflow to a real field experiment and obtained a semi‐quantitative estimate for shallow sediments that can be used by offshore engineers.

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.

Neogene stratigraphic architecture and three-dimensional velocity structure beneath the Gulf of İzmir (western Anatolia) from reflection traveltime tomography

Neogene stratigraphic architecture and three-dimensional velocity structure beneath the Gulf of İzmir (western Anatolia) from reflection traveltime tomography

Inversion of Deep-Water Velocity Using the Munk Formula and the Seabed Reflection Traveltime: An Inversion Scheme That Takes the Complex Seabed Topography Into Account

The sound speed of seawater is not constant. It varies with season, day time, depth and range. This variation was not considered in marine seismic data processing and imaging before deep-water seismic acquisition became a routine activity. As a result, non-ignorable errors may be contained in the final migrated-image of deep-water seismic data. To eliminate such errors, we propose here a scheme for inverting the seawater velocity under the condition that the seabed has a complex topography. In this scheme, the seabed topography is represented by step grids constrained by measured water depth data, and the sound profile is assumed to be the one satisfying the Munk formula. Thus, only the parameters appearing in the Munk formula need to be inverted. This is quite different from the conventional inversion schemes that take the velocity as the inversion target. We use the conjugate gradient method to minimize the objective function given as the sum of squares of traveltime differences. Tests on synthetic common-shot data set show that our scheme presented here works as expected. Applications to real marine data set further validates the reasonability and feasibility of our scheme under complex seabed topography. To investigate the reliability of our inversion scheme, we migrate the real 2D data set using the Kirchhoff migration with the inverted Munk profile as the velocity model. The corresponding results show that the seawater velocity obtained by our inversion scheme improves the imaging quality of underwater structures.

Preconditioned transmission + reflection joint traveltime tomography with adjoint‐state method for subsurface velocity model building

AbstractAdjoint‐state‐based transmission and reflection traveltime inversion are promising approaches for reconstructing a macro velocity field in both shallow and deep depths. However, the contaminated gradient by the uneven illumination impedes the recovery of an optimal velocity model and results in slow convergence rate in inversion. To mitigate this issue, we propose a novel preconditioned transmission + reflection joint traveltime tomography method with transmission and reflection illumination compensation. The proposed illumination compensation operator is theoretically demonstrated as the diagonal elements of the approximated Hessian, which can be efficiently computed in a way similar to gradient calculation. The proposed method can construct a more accurate velocity model compared to the uncompensated counterpart. Convergence is also accelerated by the relatively uniform velocity updates from the shallow to the deep parts. Furthermore, velocity updating and reflector imaging are simultaneously iterated during the inversion. Synthetic numerical example based on the inclusion model indicates that the proposed preconditioned method can result in uniform gradient values of both transmitted and shot/receiver‐side reflected traveltime. The complex foothill model test shows the improved inversion accuracy of the proposed method with an increased convergence rate and improved reflection traveltime predictions using the inverted velocity model. Experiment on the small foothill model indicates that the reflector and velocity can be updated simultaneously, and the inversion accuracy can be significantly improved by selecting multi reflectors. Finally, the effectiveness and practicality of the proposed method are demonstrated by a field data application in East China Sea.

A new data-domain reflection full-waveform inversion method based on common-image-point gathers

The migration velocity analysis (MVA) based on the common-image gathers (CIGs) in the image domain is an effective approach for evaluating the seismic background velocity, a crucial index for the full-waveform inversion (FWI) and migration. Compared with cumbersome conventional MVA methods, differential semblance optimization (DSO) is a variation of image-domain wavefield tomography that avoids interactive manual picking but increases the computation cost tremendously. In recent years, the reflection waveform inversions have been studied in depth to construct the background velocity, matching reflection travel time or waveform in the data domain, which requires expensive Born simulations based on accurate imaging results. This study performs a new reflection full-waveform inversion method in the image domain based on the flatness of arbitrarily selected common-image-point (CIP) gathers and their Born simulations. According to the relationship between imaging and background model, the flatness of CIP gathers under the L1 norm is measured. Afterwards, we construct the objective function to update the background model without manual picking or wave-equation migration in an extended dimension. The inversion accuracy is controlled by balancing the density of the imaging points and the computation capability. The whole procedure is implemented in the frequency domain, so the main computation comes from the LU decomposition in the frequency-domain wave-equation simulation, in which way, the proposed data-domain reflection full-waveform inversion achieves complete automation with lower costs. The objective function analysis shows a better convex, proving the weak dependence on the starting model of this method. Besides, synthetic experiments verify the validity and the field data test demonstrates its effectiveness.

Sound speed profile estimation in a thick mud layer from travel time data

The sound speed profile in a surficial mud layer is of importance because it controls what is acoustically illuminated within and below the mud layer. A variety of estimates have been made at the New England Mud Patch (NEMP) with some near-surface sound speed gradients as large as 10 s−1 and larger. Here, single bounce seabed reflection travel time data are used to infer what mud sound speed gradients are and are not plausible near the central NEMP region where the mud thickness is ∼10 m. Time series data were collected on a moored hydrophone from a broadband source with a 1 second repetition rate as the tow ship transited on a radial from the hydrophone to a distance of ∼1 km at a speed of 2 m/s. The water column was essentially isovelocity and grazing angles ranged from 4.5° to 84°. It is known that at the base of the mud, there is a mud-sand transition layer (of order 1 m thick) where sound speed gradients can be large. However, above this layer, the travel time data clearly indicate that a mud 10 s−1 sound speed gradient is too large. [Research supported by ONR Ocean Acoustics Program.]

Seismic reflection waveform inversion based on Gauss–Newton optimization

Abstract Owing to the lack of long-offset signals and effective low-frequency components, it is extremely difficult for classical full-waveform inversion (FWI) to obtain the long-wavelength components of medium and deep elastic parameter models. Considering ray theory, reflection traveltime tomography is restricted by resolution, and the reflection waveform inversion (RWI) method of the wave equation, and its practicability, has received greater attention. However, previous studies into RWI have primarily used first-order optimization methods, in which convergence and resolution still need substantial improvement. Based on the second-order optimization inversion theory, we deduced the reflection wave-sensitive kernel, objective function gradient and Hessian operator of background and perturbation model. Additionally, we revealed the de-fuzzification effect of the Hessian matrix on the gradient of inversion and the working mechanism of background velocity updating on direction optimization and inversion resolution improvement. Experiments on the SEG/EAGE overthrust model showed that an RWI with the Gauss–Newton method using an approximate Hessian matrix significantly improved convergence and wide-spectrum modeling capability compared with the conjugate gradient method. On the streamer seismic data of the East China Sea, the second-order optimization RWI method surpassed the commonly used reflection traveltime tomography based on pre-stack depth migration. In addition, the RTM of inversion model can depict the complex fault system in the Changjiang sag with a high resolution, which improves the imaging quality of the deep basement.

Reflection-based traveltime and waveform inversion with second-order optimization

Reflection-based inversion that aims to reconstruct the low-to-intermediate wavenumbers of the subsurface model, can be a complementary to refraction-data-driven full-waveform inversion (FWI), especially for the deep target area where diving waves cannot be acquired at the surface. Nevertheless, as a typical nonlinear inverse problem, reflection waveform inversion may easily suffer from the cycle-skipping issue and have a slow convergence rate, if gradient-based first-order optimization methods are used. To improve the accuracy and convergence rate, we introduce the Hessian operator into reflection traveltime inversion (RTI) and reflection waveform inversion (RWI) in the framework of second-order optimization. A practical two-stage workflow is proposed to build the velocity model, in which Gauss-Newton RTI is first applied to mitigate the cycle-skipping problem and then Gauss-Newton RWI is employed to enhance the model resolution. To make the Gauss-Newton iterations more efficiently and robustly for large-scale applications, we introduce proper preconditioning for the Hessian matrix and design appropriate strategies to reduce the computational costs. The example of a real dataset from East China Sea demonstrates that the cascaded Hessian-based RTI and RWI have good potential to improve velocity model building and seismic imaging, especially for the deep targets.