Time–frequency analysis is widely used in the processing and interpretation of seismic data. The fractional-order Fourier transform can process nonstationary data by introducing a rotation angle into the time–frequency plane. To take advantage of the fractional-order Fourier transform and the$W$-transform, we introduce the fractional-order$W$-transform (FrWT) by introducing rotation and scaling parameters in the hope of producing time–frequency spectra with high-energy concentration and resolution. The rotation angle of the time–frequency plane introduces more characteristics into the time–fractional-frequency domain, making the algorithm more applicable to geophysical problems. We also propose a computational strategy to speed up the calculation. Numerical investigation of synthetic and real data shows that the proposed algorithm can achieve a time–frequency spectrum with higher resolution and energy concentration but at the cost of negligible additional computational effort.

In seismic full waveform inversion (FWI), the shot-encoding technique can reduce computational costs. It randomly encodes all individual shot gathers and combines them into a super shot gather. This allows the number of wavefield simulations to be reduced. To mitigate crosstalk noise caused by interference between different shots, shot-encoded FWI requires the shot encoding to be sufficiently random. However, this may destabilize the standard limited memory BFGS (L-BFGS) algorithm and lead to instability and nonconvergence in the interactive inversion of FWI. In this article, we propose the improved L-BFSG (iL-BFGS) method, which uses the formula of the outer product of the Hessian matrix to calculate the gradient difference for the recursive L-BFSG computation. We also redesigned the workflow for shot-encoded FWI to increase the randomness within the shot encoding. We have shown that the proposed method improves the image quality of shot-encoded FWI, especially for intermediate and deep formations, accelerates the convergence of iterative inversion, and improves the ability of FWI to suppress crosstalk effects.

In seismic inversion, the subsurface model can be parameterized by a truncated Fourier series, and the inversion problem is then the inversion of the Fourier coefficients. To improve the efficiency of the evaluation of the Fourier coefficients and the reconstruction of the model from the inverted coefficients, we propose to use the efficient implementation of the fast Fourier transform (FFT) to speed up these two calculations. By using the FFT pair, the computation time for 3D subsurface models with realistic size could be reduced by two to three orders of magnitude compared to conventional methods. When this model parameterization scheme is applied to seismic impedance inversion, we proposed two strategies to further improve the efficiency. One is to invert the Fourier coefficients from small-valued numbers to large-valued numbers, and the other is to divide the seismic data into subgroups and use part of them for the inversion of the Fourier coefficients. Both strategies are helpful for efficient inversion of the Fourier coefficients from the seismic data. Moreover, thanks to this model parameterization scheme, the Fourier coefficients are inverted in a multi-trace manner, and the impedance model reconstructed from the inverted Fourier coefficients has good spatial continuity. The scheme is able to generate stable and continuous impedance models from the inversion of seismic data with missing traces, with affordable computation times.

Estimation of seismic structural correlation can provide useful information for structural interpretation, events correlation enhancement, signal-to-noise ratio (SNR) improvement, subsurface modeling, and geophysical inversion. In this letter, we propose a Shannon entropy-based method to measure seismic local correlation and further enhance the correlation of seismic events. The proposed method is derived from the local plane-wave model and formulated as a Shannon entropy form. The probabilities are calculated along with the coordinate direction of local slope and estimated by solving two least-squares problems in local areas. Application to both synthetic and field data sets demonstrates the superior performance of the Shannon entropy-based method over traditional alternatives.

We develop a fractional Laplacian viscoacoustic wave equation-based full waveform inversion (FWI) method. The main novelty is efficient reconstruction of the source wavefields in gradient computation by the adjoint state method. Our FWI is based on Fourier pseudo-spectral time-domain (PSTD) numerical solutions of the fractional Laplacian viscoacoustic wave equation, which can describe the frequency independent${Q}$(quality factor) behaviors of seismic waves accurately. The presented wavefield reconstruction strategy utilizes reverse time-marching formulae to compute the source wavefields backward in time, including an implicit formula in the interior domain and an explicit one in the perfectly matched layer (PML) absorbing domains. Since the wavefields in the entire domain are recovered, our method does not require storing massive boundary values like conventional reconstruction methods. To avoid numerical instability in reverse time reconstruction, we design a global-local checkpointing technique. When reverse time reconstruction encounters numerical instability, the forward propagation restarts from the nearest global checkpoint and proceeds to the unstable time step. Then, the reverse time reconstruction continues. The local checkpoints help to delay the numerical instability in the PML domains. Numerical examples verify the feasibility of our reconstruction strategy and the efficiency gain achieved by using this strategy in FWI.

For shot-encoded seismic waveform tomography, the restarted limited-memory BFGS (L-BFGS) algorithm is an effective technique to suppress the crosstalk effect among encoded seismic shots. It restarts the L-BFGS calculation at each iteration segment, consisted of a group of iterations, and recodes the individual shots randomly not only at the beginning but also at the inside of the iteration segment. Here, we simplified this scheme using an invariant shot-encoding within each iteration segment and recoding individual shots only at the beginning of the segment. This simplification did compromise the image quality at the early stage of inversion, as the crosstalk effect appeared on the inversion result of the low-frequency data. However, it eventually achieved both the computation efficiency and the good quality for a multiscale inversion procedure, which inverts the seismic data from low-frequency components to high-frequency components in sequence.

The interpolation based on prediction-error filter (PEF) is one of the most effective approaches recently proposed for seismic data reconstruction. However, the number of effective regression equations for estimating the filter coefficients will be much less when missing many seismic traces, which makes the estimated filter coefficients inaccurate or even impossible to be estimated. To improve the accuracy of filter coefficients, in this paper, we design a multiscale and multidirectional PEF, in which the number of effective regression equations can be increased much more, and use it to seismic data reconstruction. First, we estimate the adaptive different directional PEFs using the known data in different scales. The known data can be regularly sampled with randomly or regularly missing, or even both of them. Then, we interpolate missing seismic traces using estimated PEF and the sparse known traces. The regularization in least-squares inversion controls the adaptivity of multiscale multidirectional PEF. The use of more effective regression equations in inversion makes the filter coefficients more accurate. In addition, the multiscale filter can conveniently deal with the case of the simultaneous existence of randomly and regularly missing, while the conventional methods have to be treated separately for randomly and regularly missing. The applicability and effectiveness of the proposed method are examined by synthetic and field data examples.

In this paper, we study the source mobility problem that exists in the current named data networking (NDN) architecture and propose a proxy-based mobility support approach named PMNDN to overcome the problem. PMNDN proposes using a proxy to efficiently manage source mobility. Besides, functionalities of the NDN access routers are extended to track the mobility status of a source and signal Proxy about a handoff event. With this design, a mobile source does not need to participate in handoff signaling which reduces the consumption of limited wireless bandwidth. PMNDN also features an ID that is structurally similar to the content name so that routing scalability of NDN architecture is maintained and addressing efficiency of Interest packets is improved. We illustrate the performance advantages of our proposed solution by comparing the handoff performance of the mobility support approaches with that in NDN architecture and current Internet architecture via analytical and simulation investigation. We show that PMNDN offers lower handoff cost, shorter handoff latency, and less packet losses during the handoff process.

To enhance seamless provider mobility support in NDN, we propose a Novel Locator Based mobility support Approach (NLBA). In this approach, we assign an unique locator to each Access Router (AR) in NDN networks, and further modify the outgoing faces field in AR's original Forwarding Information Base (FIB), to record the mobility status and the current locator of the provider. Besides, we append an optional field to the original NDN packet, and further extend the AR with additional functionalities, such as caching or forwarding Interest packets on behalf of the provider. Our analytical investigations indicate that NLBA has lower handover cost and shorter handover latency, compared with other existing rendezvous/indirection point based mobility support approach.