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In this paper, the reverse space cmKdV equation, the reverse time cmKdV equation and the reverse space-time cmKdV equation are constructed and each of three types diverse soliton solutions is derived based on the Hirota bilinear method. The Lax integrability of three types of nonlocal equations is studied from local equation by using variable transformations. Based on exact solution formulae of one- and two-soliton solutions of three types of nonlocal cmKdV equation, some figures are used to describe the soliton solutions. According to the dynamical behaviors, it can be found that these solutions possess novel properties which are different from the ones of classical cmKdV equation. more...

To explore crustal structures using seismic records of earthquakes, we proposed a new seismic reflection imaging method based on reverse time migration (RTM) without source information. In the prop... more...

The severe rugged seabed interfaces bring great difficulties to seismic imaging in the marine environment. To accurately image submarine structures under the rugged seabed interface, an acoustic-el... more...

Migration velocity analysis (MVA) has been widely used for large scale model construction. To make full use of the wavefield information and obtain stable inversion results, wave-equation-based met... more...

Polarity reversal is a well-known problem in elastic reverse time migration, and it is closely related to the imaging conditions. The dot product of source and receiver wavefields is a stable and efficient way to construct scalar imaging conditions for decomposed elastic vector wavefields. However, for PP images, the dot product introduces an angle-dependent factor that will change the polarity of image amplitudes at large opening angles, and it is also contaminated by low-wavenumber artifacts when sharp contrasts exist in the velocity model. Those two problems can be suppressed by muting the reflections with large opening angles at the expense of losing useful information. We have developed an elastic inverse-scattering imaging condition that can retain the initial polarity of the image amplitude and significantly reduce the low-wavenumber noise. For PS images, much attention is paid to the polarity-reversal problem at the normal incidence, and the dot-product-based imaging condition successfully avoids this kind of polarity reversal. There is another polarity-reversal problem arising from the sign change of the PS reflection coefficient at the Brewster angle. However, this sign change is often neglected in the construction of a stacked PS image, which will lead to reversed or distorted phases after stacking. We suggested using the S-wave impedance kernel used in elastic full-waveform inversion but only in the PS mode as an alternative to the dot-product imaging condition to alleviate this kind of polarity-reversal problem. In addition to dot-product-based imaging conditions, we analytically compare divergence- and curl-based imaging conditions and the elastic energy norm-based imaging condition with the presented imaging conditions to identify their advantages and weaknesses. Two numerical examples on a two-layer model and the SEAM 2D model are used to illustrate the effectiveness and advantages of the presented imaging conditions in suppressing low-wavenumber noise and correcting the polarity-reversal problem. more...

Deprimary reverse time migration (RTM) is a newly proposed technology aiming at removing false structures in images computed by RTM. However, a side effect of this new technology is an inability to image steeply dipping structures. We first introduce how to obtain a composite wavefield, including a complete downgoing wavefield and a partial upgoing wavefield, using the combination of an f-k filter and a spatial-wavenumber filter. We next thoroughly analyze the root cause leading to this side effect in the deprimary RTM technology. By using a modified imaging condition accommodating a composite wavefield, we propose a novel flank-preserving deprimary RTM method to maintain the capability of removing false structures and preserve steeply dipping subsurface structures in the final image. We demonstrate the success of this new technology via several examples. Furthermore, we study different perspectives in depth to show that flank-preserving deprimary RTM is a trade-off solution between RTM and deprimary RTM. more...

Pre-stack Q migration can eliminate the absorption effect and accurately image underground structures, which is conducive to subsequent reservoir interpretation and hydrocarbon prediction. However,... more...

The safety and efficiency of tunnel construction depend on the knowledge of complex geologic conditions. Hence, an accurate forward-prospecting technique is required to detect unexpected inhomogeneous geologic structures ahead of tunnel construction. As an accurate method to image geologic heterogeneities, elastic reverse time migration (ERTM) is introduced to the field of tunnel forward prospecting. However, in the tunnel environment, ERTM images may suffer from the interference of crosstalk artifacts, which are caused by converted waves on tunnel surfaces. Therefore, considering the actual influence of the tunnel body, the decoupled nonconversion elastic equation was incorporated into traditional ERTM. This method prevents the generation of converted waves but ensures independent P- and S-wave propagation. In addition, wave-mode separation for raw seismic data is required in our approach. Synthetic examples based on the real geologic environment of tunnels show that our method produces satisfactory results for P-wave and S-wave imaging and the S-wave can produce a better imaging effect in tunnels. Finally, we apply our method to the seismic data obtained from a real highway tunnel construction site to demonstrate its performance in real-world applications. The results indicate that the migrated images can help to accurately constrain the geologic formations ahead of the tunnel face. more...

Steeply dipping structures bring huge challenges in high-resolution imaging. The imaging of the steeply dipping structures can be improved by incorporating the prismatic waves, which has some steep... more...

The Babbage gas field was discovered in 1988 by exploration well 48/2-2 which drilled into the Permian-age lower Leman Sandstone Formation below a salt wall. Seismic imaging is compromised by the presence of this salt wall, which runs east–west across the southern part of the structure, creating uncertainties in depth conversion and in the in-place volumes. Pre-stack depth migration with beam and reverse time migrations appropriate for the complex salt geometry provided an uplift in subsalt seismic imaging, enabling the development of the field, which is located at the northern edge of the main reservoir fairway in a mixed aeolian–fluvial setting. Advances in artificial fracturing technology were also critical to the development: in this area, deep burial is associated with the presence of pore-occluding clays, which reduce the reservoir permeability to sub-millidarcy levels. The Babbage Field was sanctioned in 2008, based on an in-place volume range of 248–582 bcf; first production was in 2010. It produces from five horizontal development wells that were artificially fracced to improve deliverability of gas from the tight matrix. None of the wells has drilled the gas–water contact, which remains a key uncertainty to the in-place volumes, along with depth-conversion uncertainty below the salt wall. more...

In comparison with conventional reverse time migration (RTM), least-squares RTM (LSRTM) can improve imaging resolution and compensate irregular illumination caused by acquisition geometry and compl... more...

The generation of angle-domain common imaging gathers (ADCIGs) from reverse time migration (RTM) is essential for velocity updates, migration quality control and amplitude variation with an...

Anisotropic reverse time migrations (RTMs) using pseudoacoustic or elastic wave equations are tested, and the migrated PP images, obtained using the same data set as input, are compared. In anisotropic elastic RTMs, both divergence operators, and localized low-rank approximations (LLA), are tested and compared for P/S separation. Tests with synthetic data indicate that elastic RTMs have better illumination apertures than pseudoacoustic RTMs in subsalt areas because of the involvement of converted S-waves in the former. Pseudoacoustic RTMs have diamond-shaped S-wave artifacts, which do not exist in elastic RTM images, provided that the P- and S-waves are separated in the elastic wavefields. LLAs provide affordable, accurate P/S separations in anisotropic media, and the separation results are better than those obtained using divergence operators. Anisotropic elastic RTMs with LLA give the best quality images. more...

A bilinearisation-reduction approach is described for finding solutions for nonlocal integrable systems and is illustrated with nonlocal discrete nonlinear Schrodinger equations. In this approach we first bilinearise the coupled system before reduction and derive its double Casoratian solutions; then we impose reduction on double Casoratians so that they coincide with the nonlocal reduction on potentials. Double Caosratian solutions of the classical and nonlocal (reverse space, reverse time and reverse space-time) discrete nonlinear Schrodinger equations are presented. more...

Identifying spawning grounds of Asian carp is important for determining the reproductive front of invasive populations. Ichthyoplankton monitoring along the Illinois Waterway (IWW) has provided information on abundances of Asian carp eggs in the IWW's navigation pools. Post-fertilization times derived from egg development stages and water temperatures can be used to estimate spawning times of Asian carp eggs, but estimating how far these eggs have drifted requires information on river hydraulics. A Fluvial Egg Drift Simulator (FluEgg) program was designed to predict the drift of Asian carp eggs in the riverine environment with egg growth considered. This paper presents a reverse-time particle tracking (RTPT) algorithm for back-casting the spawning location of eggs from their collection site. The RTPT algorithm was implemented as a module in FluEgg. The new version of FluEgg was coupled with an unsteady hydrodynamic model of the IWW to predict the spawning locations for 530 eggs that were collected in June 2015. The results indicate that tailwater sections below the Locks and Dams (L&Ds) in each navigation pool appear to be preferred spawning locations for Silver Carp (a species of Asian carp). From the data analyzed, the most upstream spawning location for the June 2015 spawning period was in the upper Marseilles navigation pool, downstream of the Dresden Island L&D. The RTPT algorithm can efficiently estimate spawning locations for multiple egg samples. more...

A challenging outstanding problem in reverse time extrapolation is recovering accurate amplitudes at reflectors from the receiver wavefield. Various migrations have been developed to produce accurate image locations rather than correct amplitude information because of inadequate compensation of attenuation, dispersion, and transmission losses. We have evaluated the requirements, and determined the theoretical feasibility, of true amplitude recovery of 2D acoustic and elastic seismic data by using the analytic Zoeppritz equations for plane-wave reflection and transmission coefficients. Then, we used synthetic acoustic and elastic wavefield data generated by elastodynamic finite differences to verify the recovery, in the reverse time propagation, of spherical waves and illustrated the salient differences between the incident wavefields reconstructed from reflection data only and from the combination of reflection and transmission data. These examples quantitatively verify that recovering an incident plane or a spherical wave requires the reverse time propagation of all reflections and transmissions in a model with the correct velocity and density. Accurate reconstruction of an incident wave is not possible by backward propagation of only reflections. As an application, we removed downgoing internal multiple reflections generated by upgoing waves incident at reflectors shallower than a horizontal well, in which geophones are deployed. The subtraction of the downgoing reflection involves wavefield reconstruction at depths shallower than the horizontal well and separation of upgoing and downgoing wavefields. This approach assumes that the correct acoustic (or elastic) velocity and density models are available in, and shallower than, the layer where the horizontal well is located. Incident-wave reconstruction works equally well for smooth models, as for models with sharp boundaries. Uncertainties in the model used for reconstruction, and incompleteness of the data aperture are propagated into the equivalent uncertainties, and incompleteness of the reconstruction. more...

In this paper, we suggest a new measure for testing reversibility of time series which combines two different tools: the visibility algorithm and the inversion number. First, the visibility algorithm maps the time series to the network according to a geometric criterion. After that, the degree of irreversibility of the time series can be estimated by the relative asynchronous index (RAI), based on the inverse number, between out and $$\hbox {out}^*$$ degree sequences of the network (out and $$\hbox {out}^*$$ represent the outgoing sequence of forward time series and reverse time series, respectively). This method does not need to rely on additional parameters, so it can avoid the error caused by parameter estimation. In addition, we also study the multiscale RAI and find that the optimal scale selection for detection time irreversibility is 1–4. Different types of time series are used to confirm the validity of this metric. Finally, we apply the method to financial time series and find that the financial crisis can be detected by RAI. more...

Inspired by the idea of Ablowitz and Musslimani, a reverse-time nonlocal nonlinear self-dual network equation is proposed under certain nonlocal symmetry reduction. N -fold Darboux transformation technique is used to construct discrete unstable and stable multi-soliton solutions in zero seed background for this system. Based on the asymptotic and graphic analysis, structures of one-, two- and three-soliton solutions are shown graphically. It is found that the individual components in this nonlocal equation show unstable temporal soliton structures whereas the combined potential terms exhibit stable soliton structures. Dynamical behaviors for one-soliton solutions are investigated via numerical simulations. It is worth noting that the solutions of this nonlocal equation are clearly different from those of its corresponding local part. Results obtained in this paper may be helpful for the explanation of the propagation of electrical signals. more...

The simultaneous-source shooting technique can accelerate field acquisition and improve spatial sampling but it will cause strong interferences in the recorded data and artifacts in the final image. The previously proposed structural smoothing operator can effectively attenuate artifacts for relatively simple reflection structures during least-squares inversion, but it will cause damage to complicated reflection events such as discontinuities. To preserve discontinuities in a seismic image, we apply the singular spectrum analysis (SSA) operator to attenuate artifacts during least-squares inversion. Considering that global SSA cannot deal with overcomplicated data very well, we use local SSA to remove noise and to better preserve the steeply dipping components. The local SSA operator corresponds to a local low-rank constraint applied in the inversion process. The migration operator used in the study is the reverse time migration (RTM) operator. Tests using the Marmousi model showed the superior performance of the proposed algorithm in preserving the discontinuities of seismic images. more...

In this paper, we present and evaluate a novel multilevel hybrid-chaotic oscillator. The proposed generalized multilevel-hybrid chaotic oscillator (GM-HCO) was created by combining a multilevel discrete function generated from user data with a continuous function having a damping factor greater than ln(2) to achieve variable rates and adaptive carrier frequencies. Improved spectral efficiency and lower complexity of the transceiver compared with differentially coherent systems were achieved by multilevel signals at the transmitter and a matched filter at the receiver. An exact analytical solution for the generalized fixed basis function and the impulse response of the matched filter were also derived. The bit error rate (BER) expression of the GM-HCO was derived for two levels. It was found that the noise performance of the proposed system was better than a hybrid chaotic system based on forward time and differential chaos shift keying (DCSK). A comprehensive set of simulations were carried out to evaluate the performance of the proposed system with chaotic communication systems in the presence of additive white Gaussian noise (AWGN). The performance of the proposed system was comparable with that of conventional communication systems. The results demonstrate that the proposed system can offer better noise performance than existing chaotic communication systems, and it also offers variable transmitter frequencies and improved spectral efficiency. Noise-like behavior of the chaotic signals provides an additional layer of security at the physical layer compared with conventional (sinusoidal) communication systems. more...

The Barik, Miqrat and Amin formations are deep, tight reservoirs of the Haima Supergroup that provide the majority of gas production in the Sultanate of Oman. The Miqrat formation is a feldspathic sand/shale sequence with complex pore structure and occasional bitumen presence. In the area of interest, it occurs at a depth of approximately 5000 m. Average porosity varies from 5 to 9%, average permeability for Lower Miqrat does not exceed 0.1 mD. In general, Archie equation derived saturation in low porosity rocks is subject to medium to high uncertainty. Therefore the most common challenge in the petrophysical evaluation of tight reservoirs is the determination of gas saturation and fluid type identification. In an effort to improve the reliability of saturation calculation and fluid typing, several different methods were tested including cased-hole Pulsed Neutron Logs (PNL). The classical sigma interpretation was found to be too sensitive to input parameters and did not provide significant improvement to saturation determination in the complex Haima lithologies. An important breakthrough was made when the dynamics of the mud filtrate invasion process in these reservoirs was understood. During open-hole logging usually very little or no gas effect is observed on logs with negligible or no density-neutron separation. The reason is considered to be deep mud filtrate invasion pushing moveable gas beyond the depth of investigation of radioactive logs. One or two months later, the filtrate in the invasion zone dissipates with gas returning to the near wellbore formation. The best match between log calculated moveable gas saturation and production test data was obtained using a reverse time-lapse technique, with PNL cased-hole logs compared to baseline open-hole neutron measurements. The changes in neutron porosity with time can be attributed to moveable gas saturation. Careful neutron log quality control and normalization across non-reservoir and known water-bearing sections is required. Knowing the hydrogen index of gas, we can calculate the moveable gas saturation from the difference in neutron log response. In contrast to the sigma approach, an accurate rock matrix model is not required. This paper describes the Reverse Time-Lapse technique: a novel application of the classic time-lapse technique between open-hole neutron and cased-hole PNL. The case studies demonstrate that this technique is applicable for completion decision making and field-scale development planning. more...

Causal asymmetry is one of the great surprises in predictive modelling: the memory required to predict the future differs from the memory required to retrodict the past. There is a privileged temporal direction for modelling a stochastic process where memory costs are minimal. Models operating in the other direction incur an unavoidable memory overhead. Here we show that this overhead can vanish when quantum models are allowed. Quantum models forced to run in the less natural temporal direction not only surpass their optimal classical counterparts, but also any classical model running in reverse time. This holds even when the memory overhead is unbounded, resulting in quantum models with unbounded memory advantage., Comment: Journal reference included, 7 pages, 4 figures plus appendices, comments welcome more...

In reverse time migration (RTM) or full-waveform inversion (FWI), forward and reverse time propagating wavefields are crosscorrelated in time to form either the image condition in RTM or the misfit gradient in FWI. The crosscorrelation condition requires both fields to be available at the same time instants. For large-scale 3D problems, it is not possible, in practice, to store snapshots of the wavefields during forward modeling due to extreme storage requirements. We have developed an approximate wavefield reconstruction method that uses particle velocity field recordings on the boundaries to reconstruct the forward wavefields during the computation of the reverse time wavefields. The method is computationally effective and requires less storage than similar methods. We have compared the reconstruction method to a boundary reconstruction method that uses particle velocity and stress fields at the boundaries and to the optimal checkpointing method. We have tested the methods on a 2D vertical transversely isotropic model and a large-scale 3D elastic FWI problem. Our results revealed that there are small differences in the results for the three methods. more...

One way to deal with the storage problem for the forward source wavefield in reverse time migration and full-waveform inversion is the reconstruction of that wavefield during reverse time stepping along with the receiver wavefield. Apart from the final states of the source wavefield, this requires a strip of boundary values for the whole time range in the presence of absorbing boundaries. The width of the stored boundary strip, positioned in between the interior domain of interest and the absorbing boundary region, usually equals about half that of the finite-difference stencil. The required storage in 3D with high frequencies can still lead to a decrease in computational efficiency, despite the substantial reduction in data volume compared with storing the source wavefields at all or at appropriately subsampled time steps. We have developed a method that requires a boundary strip with a width of just one point and has a negligible loss of accuracy. Stored boundary values over time enable the computation of the second and higher even spatial derivatives normal to the boundary, which together with extrapolation from the interior provides stability and accuracy. Numerical tests show that the use of only the boundary values provides at most fourth-order accuracy for the reconstruction error in the source wavefield. The use of higher even normal derivatives, reconstructed from the stored boundary values, allows for higher orders as numerical examples up to order 26 demonstrate. Subsampling in time is feasible with high-order interpolation and provides even more storage reduction but at a higher computational cost. more...