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The separation of P- and S-wavefields is considered to be an effective approach for eliminating wave-mode crosstalk in elastic reverse time migration (RTM). At present, the Helmholtz decomposition method is widely used for isotropic media. However, it tends to change the amplitudes and phases of the separated wavefields compared with the original wavefields. Other methods used to obtain pure P- and S-wavefields include the application of the elastic wave equations of the decoupled wavefields. To achieve high computational accuracy, staggered-grid finite-difference (FD) schemes are usually used to numerically solve the equations by introducing an additional stress variable. However, the computational cost of this method is high because a conventional hybrid wavefield (the P- and S-wavefields are mixed together) simulation must be created before the P- and S-wavefields can be calculated. We have developed the first-order particle velocity equations to reduce the computational cost. The equations can describe four types of particle-velocity wavefields: the vector P-wavefield, the scalar P-wavefield, the vector S-wavefield, and the vector S-wavefield rotated in the direction of the curl factor. Without introducing the stress variable, only the four types of particle velocity variables are used to construct the staggered-grid FD schemes; therefore, the computational cost is reduced. We also develop an algorithm to calculate the P and S propagation vectors using the four particle velocities, which is simpler than the Poynting vector. Finally, we apply the velocity equations and propagation vectors to elastic RTM and angle-domain common-image gather computations. These numerical examples illustrate the efficiency of our methods.

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.

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...

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...

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...

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.

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.

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,...

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.

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...

In this paper, we consider the Gevrey problem for a loaded parabolic equation with the direct and reverse time in an unbounded domain. The problem on the solvability of this problem is reduced to the problem on the solvability of a generalized Abel equation in the class of function satisfying the Holder condition.

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.

Fractures and faults were extracted from a reverse time migrated 3D Vertical Seismic Profile (VSP) data acquired over a carbonate reservoir offshore Abu Dhabi in the United Arab Emirates. A specifi...

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.

The adjoint method is known for its efficient calculation of sensitive information. After decades of development, assimilation technology based on adjoint method has gradually become an important tool for emission inversion. On the basis of GRAPES-CUACE aerosol adjoint model, and combined with the optimization algorithm and pollutants observations, the GRAPES-CUACE 3D variational (GRAPES-CUACE-3D-Var) assimilation system was further developed, and was used in the inversion of BC emissions in Beijing-Tianjin-Hebei region. The results show that the newly constructed GRAPES-CUACE-3D-Var assimilation system is reasonable and reliable, and can be applied to the emission inversion in Beijing-Tianjin-Hebei region. Compared to the simulations using the a priori BC emissions, the model simulations driven by the a posterior BC emissions in two inversion schemes are in better agreement with measurements. The correlation coefficient between the simulations and the observations is increased from 0.2 before the inversion to 0.7 and 0.64, respectively, and the NMSE is reduced from 0.38 to 0.22 and 0.24, respectively, and the NMB is decreased from 51.53 % to 43.37 % and 40.90 %, respectively, in the two inversion schemes. The spatial distributions of the a posterior BC emissions in the two inversion schemes are consistent with the distributions of the a priori BC emissions. The high-value areas are mainly located in the south of Beijing, Tianjin, central and southern Hebei, and northern Shandong. On the whole, the inversion scheme with a large observation ratio has better optimization effect. The observation information of the target time has a great influence on the a posterior BC emissions in a short period before the target time, and the influence decreases with the reverse time sequence.

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.

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.

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.

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.

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.

AIM To characterize the survival of cirrhotic patients with Barcelona Clinic Liver Cancer (BCLC) stage C hepatocellular carcinoma (HCC) and to ascertain the factors predicting the achievement of disease control (DC). METHODS The cirrhotic patients with BCLC stage C HCC evaluated by the Hepatocatt multidisciplinary group were subjected to the investigation. Demographic, clinical and tumor features, along with the best tumor response and overall survival were recorded. RESULTS One hundred and ten BCLC stage C patients were included in the analysis; the median overall survival was 13.4 mo (95%CI: 10.6-17.0). Only alphafetoprotein (AFP) serum level > 200 ng/mL and DC could independently predict survival but in a time dependent manner, the former was significantly associated with increased risk of mortality within the first 6 mo of follow-up (HR = 5.073, 95%CI: 2.159-11.916, P = 0.0002), whereas the latter showed a protective effect against death after one year (HR = 0.110, 95%CI: 0.038-0.314, P < 0.0001). Only patients showing microvascular invasion and/or extrahepatic spread recorded lower chances of achieving DC (OR = 0.263, 95%CI: 0.111-0.622, P = 0.002). CONCLUSION The BCLC stage C HCC includes a wide heterogeneous group of cirrhotic patients suitable for potentially curative treatments. The reverse and time dependent effect of AFP serum level and DC on patients’ survival confers them as useful predictive tools for treatment management and clinical decisions.

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.

Summary The development of digital algorithms that allow you to automate certain interpretation tasks makes it much easier to solve geological problems. The main difficulty of automatic algorithms in complex geological conditions is related to the multivariance of interpretation and, as a result, possible errors that can introduce ambiguity in further interpretation. The use of machine learning methods and Reverse Time Holography can help in solving this problem, as well as reduce the amount of work performed manually by the interpreter and improve the accuracy of the results.

Summary Both acoustic and elastic reverse time migrations reconstruct forward and backward wavefields by solving the full wave equation using recorded data as boundary conditions. The wavefield injection and reconstruction are theoretically based on the Kirchhoff integral for acoustic case, and the representation theorem for elastic case, with which accurate wavefields can be reconstructed by complete boundary conditions on a closed surface. However, in most cases, the recording surface is not closed, nor do the recorded data provide complete information to implement the exact Kirchhoff integral/representation theorem. For reflection seismology, usually only pressure is recorded for the acoustic case and displacements are recorded for elastic case. By using a finite-difference propagator, we uniformly inject boundary values based on exact Kirchhoff integral and representation theorem to reconstruct both source-side and receiver-side wavefields for reverse time migration (RTM). Specifically, boundary values are treated as equivalent sources, providing RTMs with an economic source-side wavefield reconstruction strategy using parsimonious memory, where only single-layer boundary values are required. Receiver-side records are injected and time-reversed propagated with correct phases and amplitudes. To investigate how incomplete data can affect the reconstructed acoustic/elastic wavefields, artefacts from incomplete injections are analyzed. Numerical examples verify the effectiveness of the proposed method.

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.