An improved method for internal multiple elimination using the theory of virtual events

Compared with first-order surface-related multiples from marine data,the onshore internal multiples are weaker and are always combined with a hazy and occasionally strong interference pattern.It is usually difficult to discriminate these events from complex targets and highly scattering overburdens,especially when the primary energy from deep layers is weaker than that from shallow layers.The internal multiple elimination is even more challenging due to the fact that the velocity and energy difference between primary reflections and internal multiples is tiny.In this study,we propose an improved method which formulates the elimination of the internal multiples as an optimization problem and develops a convolution factor T.The generated internal multiples at all interfaces are obtained using the convolution factor T through iterative inversion of the initial multiple model.The predicted internal multiples are removed from seismic data through subtraction.Finally,several synthetic experiments are conducted to validate the effectiveness of our approach.The results of our study indicate that compared with the traditional virtual events method,the improved method simplifies the multiple prediction process in which internal multiples generated from each interface are built through iterative inversion,thus reducing the calculation cost,improving the accuracy,and enhancing the adaptability of field data.

Suppression of internal multiples based on virtual events

In practical seismic exploration, internal multiples generated when the wave impedance of medium is strong, and seismic records are recorded. The method of virtual event repress internal multiples is to move scattered points from underground to the surface, similar to the method of the surface-related multiple elimination (SRME). The method of SRME belongs to the prediction-subtraction approaches to eliminate internal multiples, prediction method is based on building a brand new way of seismic wave propagation (virtual reflection and virtual event), so that it has forward and backward wave propagation, and through convolution with significant wave to predict the internal multiples. Due to required data needing field information of full-wave, the authors use Seislet transform interpolating the missing data to ensure the premise of internal multiples prediction. The test data show that the above method has achieved good results.

Multiple internal resonances of rotating composite cylindrical shells under varying temperature fields

Composite cylindrical shells,as key components,are widely employed in large rotating machines.However,due to the frequency bifurcations and dense frequency spectra caused by rotation,the nonlinear vibration usually has the behavior of complex multiple internal resonances.In addition,the varying temperature fields make the responses of the system further difficult to obtain.Therefore,the multiple internal resonances of composite cylindrical shells with porosities induced by rotation with varying temperature fields are studied in this paper.Three different types of the temperature fields,the Coriolis forces,and the centrifugal force are considered here.The Hamilton principle and the modified Donnell nonlinear shell theory are used to obtain the equilibrium equations of the system,which are transformed into the ordinary differential equations(ODEs)by the multi-mode Galerkin technique.Thereafter,the pseudo-arclength continuation method,which can identify the regions of instability,is introduced to obtain the numerical results.The detailed parametric analysis of the rotating composite shells is performed.Multiple internal resonances caused by the interaction between backward and forward wave modes and the energy transfer phenomenon are detected.Besides,the nonlinear amplitude-frequency response curves are different under different temperature fields.

Nonlinear study of the dynamic behavior of a string-beam coupled system under combined excitations

In this paper,the nonlinear dynamic behavior of a string-beam coupled system subjected to external,parametric and tuned excitations is presented.The governing equations of motion are obtained for the nonlinear transverse vibrations of the string-beam coupled system which are described by a set of ordinary differential equations with two degrees of freedom.The case of 1：1 internal resonance between the modes of the beam and string,and the primary and combined resonance for the beam is considered.The method of multiple scales is utilized to analyze the nonlinear responses of the string-beam coupled system and obtain approximate solutions up to and including the second-order approximations.All resonance cases are extracted and investigated.Stability of the system is studied using frequency response equations and the phase-plane method.Numerical solutions are carried out and the results are presented graphically and discussed.The effects of the different parameters on both response and stability of the system are investigated.The reported results are compared to the available published work.

Interface Controlled Multiple Elimination by Sparsity Inversion

Removing internal multiples remains an important but challenging problem in seismic processing.The generalized Estimation of Primaries by Sparsity Inversion(EPSI)method minimizes data residuals between the calculated and observed wave-form using the sparse constraint of primary impulse responses to predict multiples and remove them directly,instead of using the conventional adaptive subtraction method.Even though the generalized EPSI method provides a good estimate of the primaries and multiples when they overlap,it is limited by intensive computational cost.In this paper,we introduce two strategies to improve computational efficiency.First,the interface-controlled strategy is introduced by only selecting high-amplitude primary responses related to the interfaces with strong impedance contrasts to estimate multiples.The computational time is approximately proportional to the number of involved reflectors and usually,most of the internal multiple energy in the data is only related to a few strong reflectors.Therefore the modified method can remove most of the internal multiples in fewer computations than in the generalized EPSI,which loops through all the interfaces.Next,an approximate formula for estimating primary impulse responses is proposed by neglecting a computationally intensive term which corresponds to the primary responses estimated from internal multiples.According to our analyses and experiments,in most cases,the contribution of this term is negligible because the internal multiples are weak.Therefore,the computational efficiency can be improved without significantly losing quality when estimating most primaries and multiples.In order to demonstrate this,multiple elimination of a two-layered simple data and the Pluto data are implemented.We find that the modified method can yield reliable results that require fewer computations.The improvements of the modified method may encourage the use of the generalized EPSI method in industry.

Global Disturbance Rejection of Switched Nonlinear Systems with Switched Internal Model

This paper investigates the problem of global disturbance rejection for a class of switched nonlinear systems where the solvability of the disturbance rejection problem for subsystems is not assumed. The disturbances are assumed to be sinusoidal with completely unknown frequencies, phases and amplitudes. First, as an extension of the classic concept of internal model for non-switched systems, a switched internal model is proposed. Second, in order to solve the problem under study, an adaptive control method is established on the basis of the multiple Lyapunov functions method. Also,adaptive state-feedback controllers of subsystems are designed and incorporated with a switching law to asymptotically reject the unknown disturbances. Finally, an example is provided to demonstrate the effectiveness of the proposed design method.