Preserved amplitude migration based on the one way wave equation in the angle domain

Traditional pre-stack depth migration can only provide subsurface structural information. However, simple structure information is insufficient for petroleum exploration which also needs amplitude information proportional to reflection coefficients. In recent years, pre-stack depth migration algorithms which preserve amplitudes and based on the one- way wave equation have been developed. Using the method in the shot domain requires a deconvolution imaging condition which produces some instability in areas with complicated structure and dramatic lateral variation in velocity. Depth migration with preserved amplitude based on the angle domain can overcome the instability of the one-way wave migration imaging condition with preserved amplitude. It can also offer provide velocity analysis in the angle domain of common imaging point gathers. In this paper, based on the foundation of the one-way wave continuation operator with preserved amplitude, we realized the preserved amplitude prestack depth migration in the angle domain. Models and real data validate the accuracy of the method.

Traveltime tomography and prestack depth migration for vertical seismic profiling of an angle-domain walkaway on a complex surface

Walkaway VSP cannot obtain accurate velocity field,as it asymmetrically reflects ray path and provides uneven coverage to underground target,thereby presenting issues related to imaging quality.In this study,we propose combining traveltime tomography and prestack depth migration for VSP of an angle-domain walkaway,in a bid to establish accurate two-dimensional and three-dimensional(3 D)velocity models.First,residual curvature was defined to update velocity,and an accurate velocity field was established.To establish a high-precision velocity model,we deduced the relationship between the residual depth and traveltime of common imaging gathers(CIGs)in walkaway VSP.Solving renewal velocity using the least squares method,a four-parameter tomographic inversion equation was derived comprising formation dip angle,incidence angle,residual depth,and sensitivity matrix.In the angle domain,the reflected wave was divided into up-and down-transmitted waves and their traveltimes were calculated.The systematic cumulative method was employed in prestack depth migration of a complex surface.Through prestack depth migration,the offset-domain CIGs were obtained,and dip angle was established by defining the stack section horizon.Runge–Kutta ray tracing was employed to calculate the ray path from the reflection point to the detection point,to determine the incident angle,and to subsequently calculate the ray path from the reflection point to the irregular surface.The offset-domain residual depths were mapped to the angle domain,and a new tomographic equation was established and solved.Application in the double complex area of the Tarim Basin showed the four-parameter tomographic inversion equation derived in this paper to be both correct and practical and that the migration algorithm was able to adapt to the complex surface.

Kirchhoff PSDM angle-gather generation based on the traveltime gradient

Angle-domain common-image gathers（ADCIGs） are the basic data in migration velocity analysis（MVA） and amplitude variation with angle（AVA） analysis. We propose a common-angle gather-generating scheme using Kirchhoff PSDM based on the traveltime gradient field. The scheme includes three major operations：（1） to calculate the traveltime field of the source and the receiver based on the dynamic programming approach;（2） to obtain the refl ection angle according to the traveltime gradient field in the image space; and（3） to generate the ADCIGs during the migration process. Because of the computation approach, the method for generating ADCIGs is superior to conventional ray-based methods. We use the proposed ADCIGs generation method in 3D large-scale seismic data. The key points of the method are the following.（1） We use common-shot datasets for migration,（2） we load traveltimes based on the shot aperture, and（3） we use the MPI and Open Mp memory sharing to decrease the amount of input and output（I/O）. Numerical examples using synthetic data suggest that the ADCIGs improve the quality of the velocity and the effectiveness of the 3D angle-gather generation scheme.

Improved H-infinity channel estimator based on EM for MIMO-OFDM systems

H-infinity estimator is generally implemented in timevariant state-space models, but it leads to high complexity when the model is used for multiple input multiple output with orthogo- hal frequency division multiplexing （MIMO-OFDM） systems. Thus, an H-infinity estimator over time-invariant system models is pro- posed, which modifies the Krein space accordingly. In order to avoid the large matrix inversion and multiplication required in each OFDM symbol from different transmit antennas, expectation maximization （EM） is developed to reduce the high computational load. Joint estimation over multiple OFDM symbols is used to resist the high pilot overhead generated by the increasing number of transmit antennas. Finally, the performance of the proposed estimator is enhanced via an angle-domain process. Through performance analysis and simulation experiments, it is indicated that the pro- posed algorithm has a better mean square error （MSE） and bit error rate （BER） performance than the optimal least square （LS） estimator. Joint estimation over multiple OFDM symbols can not only reduce the pilot overhead but also promote the channel performance. What is more, an obvious improvement can be obtained by using the angle-domain filter.

THE COUPLING OF NBEM AND FEM FOR QUASILINEAR PROBLEMS IN A BOUNDED OR UNBOUNDED DOMAIN WITH A CONCAVE ANGLE

Based on the Kirchhoff transformation and the natural boundary element method, we investigate a coupled natural boundary element method and finite element method for quasi-linear problems in a bounded or unbounded domain with a concave angle. By the principle of the natural boundary reduction, we obtain natural integral equation on circular arc artificial boundaries, and get the coupled variational problem and its numerical method. Moreover, the convergence of approximate solutions and error estimates are obtained. Finally, some numerical examples are presented to show the feasibility of our method. Our work can be viewed as an extension of the existing work of H.D. Han et al..

Health status assessment of axial piston pump under variable speed

The axial piston pump usually works under variable speed conditions.It is important to evaluate the health status of the axial piston pump under the variable speed condition.Aiming at the characteristic signals obtained under different wear levels of the port plate,a feature signal extraction method under variable speed conditions is proposed.Firstly,the combination of complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN)energy spectrum and fast spectral kurtosis principle is used to accurately extract the intrinsic mode function(IMF)component containing the sensitive information of the degraded feature.Then,the aspect ratio analysis method of the angle domain variational mode decomposition(VMD)is used to process the feature index containing the sensitive information of the degraded feature.In order to evaluate the health status of the axial piston pump under variable speed,the vibration reliability analysis method for axial piston pump based on Weibull proportional failure rate model is proposed.The experimental results show that the proposed method can accurately evaluate the health status of the axial piston pump.

Amplitude Compensation for One-Way Wave Propagators in Inhomogeneous Media and its Application to Seismic Imaging

TheWKBJ solution for the one-waywave equations inmediawith smoothly varying velocity variation with depth,c(z),is reformulated from the principle of energy flux conservation for acoustic media.The formulation is then extended to general heterogeneous media with local angle domain methods by introducing the concepts of Transparent Boundary Condition(TBC)and Transparent Propagator(TP).The influence of the WKBJ correction on image amplitudes in seismic imaging,such as depth migration in exploration seismology,is investigated in both smoothly varying c(z)and general heterogeneous media.We also compare the effect of the propagator amplitude compensation with the effect of the acquisition aperture correction on the image amplitude.Numerical results in a smoothly varying c(z)medium demonstrate that theWKBJ correction significantly improves the one-way wave propagator amplitudes,which,after compensation,agree very well with those from the full wave equation method.Images for a point scatterer in a smoothly varying c(z)medium show that the WKBJ correction has some improvement on the image amplitude,though it is not very significant.The results in a general heterogeneous medium(2D SEG/EAGE salt model)show similar phenomena.When the acquisition aperture correction is applied,the image improves significantly in both the smoothly varying c(z)medium and the 2D SEG/EAGE saltmodel.The comparisons indicate that although theWKBJ compensation for propagator amplitude may be important for forward modeling(especially for wide-angle waves),its effect on the image amplitude in seismic imaging is much less noticeable compared with the acquisition aperture correction for migration with limited acquisition aperture in general heterogeneous media.