The application of three-dimensional seismic spectral decomposition and semblance attribute to characterizing the deepwater channel depositional elements in the Taranaki Basin of New Zealand

In the past few years, three-dimensional（3-D） seismogram has become an essential tool for the interpretation of subsurface stratigraphy and depositional systems. Seismic stratigraphy in conjunction with seismic geomorphology has elevated the degree to which seismic data can facilitate geological interpretation, especially in a deepwater environment. Technologies such as time slicing and interval attribute analysis can enhance geomorphological interpretations, and, when integrated with stratigraphic analyses, can yield insights regarding distribution of seal and reservoir facies. Multiple attributes corendering can further bring out features of geological interest that other technologies may overlook. This method involves corender spectral decomposition components（SDC） with semblance attributes to describe the distribution of deepwater channel elements and the boundaries of deepwater sinuous channel. Applying this technology to four elements is observed：（1） point-bars,（2） migration of channel meander loops,（3） channel erosion/cut, and（4） avulsion. The planview expression of the deepwater channel ranges from low sinuosity to high sinuosity. Furthermore, this technology has enabled interpreters to visualize details of complex depositional elements and can be used to predict net-to-gross ratio in channel systems, which can be incorporated into borehole planning for exploration as well as development needs to improve risk management significantly. The technology is applied to the study area in an effort to illustrate the variety of interpretation technologies available to the geoscientist.

Inverse spectral decomposition using an I_p-norm constraint for the detection of close geological anomalies

An important application of spectral decomposition(SD)is to identify subsurface geological anomalies such as channels and karst caves,which may be buried in full-band seismic data.However,the classical SD methods including the wavelet transform(WT)are often limited by relatively low time-frequency resolution,which is responsible for false high horizonassociated space resolution probably indicating more geological structures,especially when close geological anomalies exist.To address this issue,we impose a constraint of minimizing an lp(0<p<1)norm of time-frequency spectral coefficients on the misfit derived by using the inverse WT and apply the generalized iterated shrinkage algorithm to invert for the optimal coefficients.Compared with the WT and inverse SD(ISD)using a typical l1-norm constraint,the modified ISD(MISD)using an lp-norm constraint can yield a more compact spectrum contributing to detect the distributions of close geological features.We design a 3 D synthetic dataset involving frequency-close thin geological anomalies and the other3 D non-stationary dataset involving time-close anomalies to demonstrate the effectiveness of MISD.The application of 4 D spectrum on a 3 D real dataset with an area of approximately 230 km2 illustrates its potential for detecting deep channels and the karst slope fracture zone.

lp norm inverse spectral decomposition and its multi-sparsity fusion interpretation

Spectral decomposition has been widely used in the detection and identifi cation of underground anomalous features(such as faults,river channels,and karst caves).However,the conventional spectral decomposition method is restrained by the window function,and hence,it mostly has low time–frequency focusing and resolution,thereby hampering the fi ne interpretation of seismic targets.To solve this problem,we investigated the sparse inverse spectral decomposition constrained by the lp norm(0<p≤1).Using a numerical model,we demonstrated the higher time–frequency resolution of this method and its capability for improving the seismic interpretation for thin layers.Moreover,given the actual underground geology that can be often complex,we further propose a p-norm constrained inverse spectral attribute interpretation method based on multiresolution time–frequency feature fusion.By comprehensively analyzing the time–frequency spectrum results constrained by the diff erent p-norms,we can obtain more refined interpretation results than those obtained by the traditional strategy,which incorporates a single norm constraint.Finally,the proposed strategy was applied to the processing and interpretation of actual three-dimensional seismic data for a study area covering about 230 km^(2) in western China.The results reveal that the surface water system in this area is characterized by stepwise convergence from a higher position in the north(a buried hill)toward the south and by the development of faults.We thus demonstrated that the proposed method has huge application potential in seismic interpretation.

Spectral decomposition method for predicting magmatic intrusion into a coal bed

Accurate prediction of magmatic intrusion into a coal bed is illustrated using the method of seismic spectral decomposition.The characteristics of coal seismic reflections are first analyzed and the effect of variable time windows and domain frequencies on the spectral decomposition are examined.The higher domain frequency of coal bed reflections using the narrower STFT time window,or the smaller ST scale factor,are acceptable.When magmatic rock intrudes from the bottom of the coal bed the domain frequency of the reflections is decreased slightly,the frequency bandwidth is narrowed correspondingly,and the response from spectral decomposition is significantly reduced.Intrusion by a very thin magmatic rock gives a spectral decomposition response that is just slightly less than what is seen from a normal coal bed.Results from an actual mining area were used to validate the method.Predicting the boundary of magmatic intrusions with the method discussed herein was highly accurate and has been validated by observations from underground mining.

Mapping of thin sandstone reservoirs in bisol field, Niger delta, Nigeria using spectral decomposition technique

This study focuses on using spectral decomposition(SD)technique to characterize complicated reservoirs to understand the structural and stratigraphic variations in the interpreted horizons from Bisol field.The purpose of this study is to use geophysical and well logging data sets to map the thin-bedded sandstone reservoirs and prospect zones within the multiple reservoirs in Bisol field,Niger Delta.The interpretation of faults and horizons was carried out on the seismic section,which was further used to produce the structural maps.Seismic attributes such as trace and variance were used to enhance the truncated structures from the seismic section,while the produced spectra were used to delineate the stratigraphy and thickness of the thin-bedded reservoirs.Thin sandstone reservoirs were identified from well logs and consequently mapped on the seismic section.Fast Fourier Transform workflow was successfully used to image the stratigraphic features in the study area.Three horizons(S1T,S2T and S3T)were delineated from the seismic section,and four reservoirs were mapped and correlated across the wells.Frequency analyses from the seismic sectional view revealed some thin pay sandstone reservoirs,which were characterized by high amplitude.Three new probable zones(Prospect A,B and C)of hydrocarbon accumulation were identified using the SD technique.

Comparison of different spectral decompositions for non-marine deep water sandstone reservoir prediction in the Xingma area

It is difficult to identify and predict non-marine deep water sandstone reservoir facies and thickness,using routine seismic analyses in the Xingma area of the western Liaohe sag,due to low dominant frequencies,low signal-to-noise ratios,rapid lateral changes and high frequencies of layered inter-bedding.Targeting this problem,four types of frequency spectral decomposition techniques were tested for reservoir prediction.Among these,the non-orthogonal Gabor-Morlet wavelet frequency decomposition method proved to be the best,was implemented directly in our frequency analysis and proved to be adaptable to non-stationary signals as well.The method can overcome the limitations of regular spectral decomposition techniques and highlights local features of reservoir signals.The results are found to be in good agreement with well data.Using this method and a 3-D visualization technology, the distribution of non-marine deep water sandstone reservoirs can be precisely predicted.

Application of Wavelet Spectral Decomposition for Geological Interpretation of Seismic Data

Modem oil industry is on the way of complication of the geological structure to use the latest technologies to analyze available geological and geophysical algorithm---continuous wavelet transform in example of synthetic and real data. of the deposits. This trend requires specialists information. The article describes a new

Spectral Decomposition of Weighted Shift Operators

The reseearch on the relation between weighted shift operators on Hilbert spaces and other important class of operators attracted the attention of some mathematicians. For example, the relation between weighted shift operators and subnormal operators has been thoroughly studied by J. Stampfli, R. Gellar and D. A. Herrero, etc. (see reference [1]) But the decomposability of weighted shift operators has not yet attracted enough attention up to now. We made initial research

Angular unconformity in Pennsylvanian strata from 3-D seismic interpretation,Goldsmith Field,West Texas

The Pennsylvanian unconformity,which is a detrital surface,separates the beds of the Permian-aged strata from the Lower Paleozoic in the Central Basin Platform.Seismic data interpretation indicates that the unconformity is an angular unconformity,overlying multiple normal faults,and accompanied with a thrust fault which maximizes the region's structural complexity.Additionally,the Pennsylvanian angular unconformity creates pinch-outs between the beds above and below.We computed the spectral decomposition and reflector convergence attributes and analyzed them to characterize the angular unconformity and faults.The spectral decomposition attribute divides the broadband seismic data into different spectral bands to resolve thin beds and show thickness variations.In contrast,the reflector convergence attribute highlights the location and direction of the pinch-outs as they dip south at angles between 2° and 6°.After reviewing findings from RGB blending of the spectrally decomposed frequencies along the Pennsylvanian unconformity,we observed channel-like features and multiple linear bands in addition to the faults and pinch-outs.It can be inferred that the identified linear bands could be the result of different lithologies associated with the tilting of the beds,and the faults may possibly influence hydrocarbon migration or act as a flow barrier to entrap hydrocarbon accumulation.The identification of this angular unconformity and the associated features in the study area are vital for the following reasons:1)the unconformity surface represents a natural stratigraphic boundary;2)the stratigraphic pinch-outs act as fluid flow connectivity boundaries;3)the areal extent of compartmentalized reservoirs'boundaries created by the angular unconformity are better defined;and 4)fault displacements are better understood when planning well locations as faults can be flow barriers,or permeability conduits,depending on facies heterogeneity and/or seal effectiveness of a fault,which can affect hydrocarbon production.The methodology utilized in this study is a further step in the characterization of reservoirs and can be used to expand our knowledge and obtain more information about the Goldsmith Field.

Performance of Continuous Wavelet Transform over Fourier Transform in Features Resolutions

This study presents a comparative analysis of two image enhancement techniques, Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT), in the context of improving the clarity of high-quality 3D seismic data obtained from the Tano Basin in West Africa, Ghana. The research focuses on a comparative analysis of image clarity in seismic attribute analysis to facilitate the identification of reservoir features within the subsurface structures. The findings of the study indicate that CWT has a significant advantage over FFT in terms of image quality and identifying subsurface structures. The results demonstrate the superior performance of CWT in providing a better representation, making it more effective for seismic attribute analysis. The study highlights the importance of choosing the appropriate image enhancement technique based on the specific application needs and the broader context of the study. While CWT provides high-quality images and superior performance in identifying subsurface structures, the selection between these methods should be made judiciously, taking into account the objectives of the study and the characteristics of the signals being analyzed. The research provides valuable insights into the decision-making process for selecting image enhancement techniques in seismic data analysis, helping researchers and practitioners make informed choices that cater to the unique requirements of their studies. Ultimately, this study contributes to the advancement of the field of subsurface imaging and geological feature identification.

Seismic low-frequency-based calculation of reservoir fluid mobility and its applications

Low frequency content of seismic signals contains information related to the reservoir fluid mobility. Based on the asymptotic analysis theory of frequency-dependent reflectivity from a fluid-saturated poroelastic medium, we derive the computational implementation of reservoir fluid mobility and present the determination of optimal frequency in the implementation. We then calculate the reservoir fluid mobility using the optimal frequency instantaneous spectra at the low-frequency end of the seismic spectrum. The methodology is applied to synthetic seismic data from a permeable gas-bearing reservoir model and real land and marine seismic data. The results demonstrate that the fluid mobility shows excellent quality in imaging the gas reservoirs. It is feasible to detect the location and spatial distribution of gas reservoirs and reduce the non-uniqueness and uncertainty in fluid identification.

The optimal fractional Gabor transform based on the adaptive window function and its application

We designed the window function of the optimal Gabor transform based on the time-frequency rotation property of the fractional Fourier transform. Thus, we obtained the adaptive optimal Gabor transform in the fractional domain and improved the time-frequency concentration of the Gabor transform. The algorithm first searches for the optimal rotation factor, then performs the p-th FrFT of the signal and, finally, performs time and frequency analysis of the FrFT result. Finally, the algorithm rotates the plane in the fractional domain back to the normal time-frequency plane. This promotes the application of FrFT in the field of high-resolution reservoir prediction. Additionally, we proposed an adaptive search method for the optimal rotation factor using the Parseval principle in the fractional domain, which simplifies the algorithm. We carried out spectrum decomposition of the seismic signal, which showed that the instantaneous frequency slices obtained by the proposed algorithm are superior to the ones obtained by the traditional Gabor transform. The adaptive time frequency analysis is of great significance to seismic signal processing.

Fractional S-transform-part 2:Application to reservoir prediction and fluid identification

The fractional S-transform （FRST） has good time-frequency focusing ability. The FRST can identify geological features by rotating the fractional Fourier transform frequency （FRFTfr） axis. Different seismic signals have different optimal fractional parameters which is not conducive to multichannel seismic data processing. Thus, we first decompose the common-frequency sections by the FRST and then we analyze the low-frequency shadow. Second, the combination of the FRST and blind-source separation is used to obtain the independent spectra of the various geological features. The seismic data interpretation improves without requiring to estimating the optimal fractional parameters. The top and bottom of a limestone reservoir can be clearly recognized on the common-frequency section, thus enhancing the vertical resolution of the analysis of the low-frequency shadows compared with traditional ST. Simulations suggest that the proposed method separates the independent frequency information in the time-fractional-frequency domain. We used field seismic and well data to verify the proposed method.

Argo floats revealing bimodality of large-scale mid-depth circulation in the North Atlantic

Analysis of Argo float trajectories at 1 000 m and temperature at 950 m in the North Atlantic between November 2003 and January 2005 demonstrates the existence of two different circulation modes with fast transition between them. Each mode has a pair of cyclonic - anticyclonic gyres. The difference is the location of the cyclonic gyre. The cyclonic gyre stretches from southeast to northwest in the first mode and from the southwest to the northeast in the second mode. The observed modes strongly affect the heat and salt transport in the North Atlantic. In particular, the second mode slows down the westward transport of the warm and saline water from the Mediterranean Sea.

CAUCHY PROBLEM FOR LINEARIZED NON-CUTOFF BOLTZMANN EQUATION WITH DISTRIBUTION INITIAL DATUM

In this article, we study the Cauchy problem for the linearized spatially homogeneous non-cutoff Boltzamnn equation with Maxwellian molecules. By using the spectral decomposition, we solve the Cauchy problem with initial datum in the sense of distribution, which contains the dual space of a Gelfand-Shilov class. We also prove that this solution belongs to the Gelfand-Shilov space for any positive time.

Entangled States in a Single-Qubit Structure with SQUID Coupled with a Super-conducting Resonator

In this paper, the number-phase quantization scheme of the mesoscopic circuit, which consists of a singlequbit structure with superconducting quantum interference device coupled with a super-conducting resonator, is given. By introducing a unitary matrix and by means of spectral decomposition, the Hamiltonian operator of the system is exactly formulated in compact forms in spin-l/2 notation. The eigenvalues and the eigenstates of the system are investigated. It is found that using this system the entangled states can not only be prepared, but also be manipulated by tuning the magnetic flux through the super-conducting loop.

Quantization of the double-qubit structure and quantum computation

The quantization scheme of a double-qubit structure with superconducting quantum interference devices （SQUIDs） is given. By introducing unitary matrices and using spectral decompositions, the Hamiltonian operator of the system is exactly formulated in compact forms in spin-1/2 notation. A scheme of designing controlled-phase-shift （CPS） gates is also proposed by using this circuit system.

Two Combinations of Unitary Operators and Frame Representations

In this paper, we prove that the norm closure of all linear combinations of two unitary operators is equal to the norm closure of all invertible operators in B(H). We apply the results to frame representations and give some simple and alternative proofis of the propositions in 'P. G. Casazza, Every frame is a sum of three (but not two) orthonormal bases-and other frame representations, J. Fourier Anal. Appl., 4(6)(1998), 727-732.'

Quantifying spectral thermal transport properties in framework of molecular dynamics simulations:a comprehensive review

Over the past few decades,significant progress has been made in micro-and nanoscale heat transfer.Numerous computational methods have been developed to quantitatively characterize the thermal transport in bulk materials and across the interfaces,which benefit the thermal management design in microelectronics and energy conversion in thermoelectrics largely.In this paper,the methods and studies on quantifying thermal transport properties using molecular dynamics simulations are comprehensively reviewed.Two classical methods based on molecular dynamics simulations are first introduced,i.e.,equilibrium molecular dynamics and nonequilibrium molecular dynamics,to calculate the thermal transport properties in bulk materials and across the interfaces.The spectroscopy methods are then reviewed,which are developed in the framework of equilibrium molecular dynamics(i.e.,time domain normal mode analysis,spectral energy density,Green-Kubo modal analysis) and methods proposed based on the nonequilibrium molecular dynamics(i.e.,time domain direct decompose method,frequency domain direct decompose method and spectral heat flux method).In the subsequent section,the calculations of spectral thermal conductivities using these computational methods in various systems are presented,including simple crystals,low-dimensional materials,complex materials and nanostructures.Following that,spectral thermal transport across the interfacial systems is discussed,which includes solid/solid interfaces,solid/solid interfaces with interfacial engineering and solid/liquid interfaces.Some fundamental challenges in molecular dynamics simulations,such as including quantum effects and quantifying the anharmonic contributions,are discussed as well.Finally,some open problems on spectroscopy thermal transport properties in the framework of molecular dynamics simulations are given in the summary.

Visualization and selection of Dynamic Mode Decomposition components for unsteady flow

Dynamic Mode Decomposition(DMD)is a data-driven and model-free decomposition technique.It is suitable for revealing spatio-temporal features of both numerically and experimentally acquired data.Conceptually,DMD performs a low-dimensional spectral decomposition of the data into the following components:the modes,called DMD modes,encode the spatial contribution of the decomposition,whereas the DMD amplitudes specify their impact.Each associated eigenvalue,referred to as DMD eigenvalue,characterizes the frequency and growth rate of the DMD mode.In this paper,we demonstrate how the components of DMD can be utilized to obtain temporal and spatial information from time-dependent flow fields.We begin with the theoretical background of DMD and its application to unsteady flow.Next,we examine the conventional process with DMD mathematically and put it in relationship to the discrete Fourier transform.Our analysis shows that the current use of DMD components has several drawbacks.To resolve these problems we adjust the components and provide new and meaningful insights into the decomposition:we show that our improved components capture the spatio-temporal patterns of the flow better.Moreover,we remove redundancies in the decomposition and clarify the interplay between components,allowing users to understand the impact of components.These new representations,which respect the spatio-temporal character of DMD,enable two clustering methods that segment the flow into physically relevant sections and can therefore be used for the selection of DMD components.With a number of typical examples,we demonstrate that the combination of these techniques allows new insights with DMD for unsteady flow.