Time-Reassigned Multisynchrosqueezing Generalized S Transform and Its Application in Frequency Decomposition Coherence

This paper presents the design of an improved image compression algorithm based on an optimal spatial and frequency decomposition of images. The use of spatially varying wavelet packets for a generalized wavelet decomposition of images was recently introduced by Asai, Ramchandram and Vetterli. They use a `double tree' algorithm to obtain the optimal set of bases for a given image, through a joint optimization with respect to frequency decomposition by a wavelet packet and spatial decomposition based on a quad-tree structure. In this paper, we present a `double-tree' frequency and spatial decomposition algorithm that extends the existing algorithm in three areas. First, instead of the quad-tree structure, our algorithm uses a more flexible merging scheme for the spatial decomposition of the image. Second, instead of a scalar quantizer, we use a pyramidal lattice vector quantizer to represent each subband of each wavelet packet, which improves the coding efficiency of the representation. Both of these extensions yield an improved rate-distortion (R-D) performance. Finally, our algorithm uses a scheme that gives a good initial value for the slope of the R-D curve, reducing the total computations needed to obtain the optimum decompositions.

Frequency decomposition and forward modelling represent advanced seismic techniques that can be applied to assist hydrocarbon exploration. The Chandon (4TCF) and Yellowglen (net-pay column 137m) gas discoveries in the Exmouth Plateau, North Carnarvon Basin (NCB), Australia (Figure 1) offer an excellent opportunity to test and demonstrate the applicability of these techniques in the search for hydrocarbons, because of the high-quality seismic data available, the textbook-example of gas flat-spot response, the fluvial-dominated reservoir and the existing proven hydrocarbon accumulation (Geoscience Australia, 2014). This study presents a workflow for reservoir characterization based on the integration of seismic interpretation, seismic attribute analysis, core analysis, petrophysical interpretation, rock physics modelling, and synthetic seismic modelling to ultimately mitigate uncertainty. Firstly, the complex tectonostratigraphic history of the petroleum system is resolved using attribute analysis, attribute colour blends, and frequency decomposition. This analysis reveals an extensive set of reservoir features, emphasizing the structural evolution and stratigraphic architecture. Frequency decomposition represents a powerful tool for looking at band restricted frequency volumes of the seismic data, to reveal hidden geological features. The discrete frequency volumes are combined in a Red-Green-Blue (RGB) blend that shows the contribution of and interaction between different frequency bands, highlighting geological features. However, up until now frequency decomposition images have been used rather qualitatively. This study offers a different approach: it uses forward seismic modelling to compare the high definition frequency decomposition (HDFD, see Eckersley et al., 2018) responses of the original data set and the synthetic models (e.g. Han, 2018), in order to validate the model geometries and their rock and fluid property distribution. A 3D seismic cube (Chandon 3D Survey, 875 km2), was used for seismic interpretation which was supplemented by information obtained from four wells (Figure 1). Especially useful logs were the Vertical Seismic Profile and Sonic Scanner logs for rock property estimates and subsequent mechanical layering. Core analysis was available for Yellowglen, Chandon-2&3 wells. Well completion reports, including advanced studies such as special core analysis interpretations, rock physics, formation evaluation, and core photography observations were synthesised as part of the framework for this study. Checkshots were available for three of the four wells to enable accurate well-ties. Published papers on the system assisted in establishing the geological framework for this project.

Geological Expression workflows, involving data conditioning and frequency decomposition can be used to detect subtle changes within the seismic signal, increase the confidence on the seismic interpretation and de-risk exploration and appraisal wells. This paper looks at the application of these workflows to the Permian carbonates in the Gohta discovery (Barents Sea, Norway) and how the results can help to increase the confidence on the proposed appraisal programme. As a preparation for the rest of the workflow, the data was conditioned using post imaging techniques. The first step involved noise cancellation of the seismic data using structurally oriented and edge-preserving algorithms. An area of poor quality data due to shallow gas clouds was identified to the south of the Gohta structure. In this area, a stronger noise attenuation workflow followed by an amplitude normalisation was applied to increase the reflector continuity. Both noise cancellations were then combined and this noise cancelled dataset was used as an input for the spectral enhancement. Two different spectral enhancements were tested using different methods; one involved the enhancement of the low frequencies using a low-pass high-cut filter, and the other one involved an enhancement of both the low and the high frequencies, aiming for a white spectrum. Frequency decomposition and RGB blending were applied on both enhanced datasets, using two different methods: one involving a short window-based Fast Fourier Transform, and the other one involving an adaptive matching pursuit algorithm. The bright colours observed in the blends were interpreted as an indicator of the presence of oil and gas, while colour changes were interpreted as changes in reservoir thickness, lithology or fluid content. The results of this work supported the presence hydrocarbons on the proposed location of the Gohta appraisal well (7120/1- 4 S), which was drilled in 2014 and encountered gas but the testing in the oil zone was inconclusive because of the technical problem of isolating gas flow from the oil zone, proving the validity of this technique as a DHI.

RGB colour blending is a powerful technique of co-visualization of different band-limited magnitude volumes created by frequency decomposition. The aims of this study were to investigate the impact of changes in geometry and acoustic impedance on what we observe in a blend of frequency magnitude volumes, and to examine how sensitive different methods of frequency decomposition are to these variations. We present a comparison of frequency decomposition methods applied to the Hermod Member submarine fan system, a well understood fan system from the Northern North Sea, and to simple synthetic models. Observations made from RGB imaging are compared to equivalent results from synthetic models created using well measurements and systematic variations in reservoir parameters. We show that thickness variations between events are the dominant factor controlling RGB colour response and that subtle lithological changes, presented as differences in acoustic impedance, are a second order effect. Furthermore, when the source frequency and decomposition bands of a synthetic wedge model are matched to a real dataset, we can relate colour values directly to thicknesses. In doing so we extend the classical tuning wedge for use as a calibration tool for frequency decomposition colour blends.

ABSTRACTSpectral decomposition is a widely used technique in analysis and interpretation of seismic data. According to the uncertainty principle, there exists a lower bound for the joint time–frequency resolution of seismic signals. The highest temporal resolution is achieved by a matching pursuit approach which uses waveforms from a dictionary of functions (atoms). This method, in its pure mathematical form can result in atoms whose shape and phase have no relation to the seismic trace. The high‐definition frequency decomposition algorithm presented in this paper interleaves iterations of atom matching and optimization. It divides the seismic trace into independent sections delineated by envelope troughs, and simultaneously matches atoms to all peaks. Co‐optimization of overlapping atoms ensures that the effects of interference between them are minimized. Finally, a second atom matching and optimization phase is performed in order to minimize the difference between the original and the reconstructed trace. The fully reconstructed traces can be used as inputs for a frequency‐based reconstruction and red–green–blue colour blending. Comparison with the results of the original matching pursuit frequency decomposition illustrates that high‐definition frequency decomposition based colour blends provide a very high temporal resolution, even in the low‐energy parts of the seismic data, enabling a precise analysis of geometrical variations of geological features.

Frequency decomposition methods have been applied to a seismic dataset which images the late Palaeocene Hermod Fm. submarine fan system which occurs within the Viking Graben in the Northern North Sea. Conventional bandpass decomposition methods are compared to HD frequency decomposition – a technique based on matching pursuit of wavelets and the sensitivities of each method are discussed. Red-Green-Blue colour blending is shown to image in great detail channels, levees and splays. In order to understand the controlling factors determining the colour, contrast and amplitude shown in the RGB blends produced using each decomposition method, synthetic models of a Hermod splay has been produced. Within these models thickness and acoustic impedance are varied to investigate which has a larger effect. Frequency decomposition and blending of the synthetic models closely resembles blends created from the original data and it is likely that thickness changes, within the Hermod fan, which varies from above the tuning thickness in the channel core, to below tuning in the distal splays is mainly responsible for colour, amplitude and constrast changes within the blends.

Spatial and Frequency Decomposition for Image Compression

We present a new algorithm for calculating an image of dispersive energy in the frequency-velocity (f-v) domain. The frequency decomposition is first applied to a shot gather in the offset-time domain to stretch impulsive data into pseudo-vibroseis data or frequency-swept data. Because there is a deterministic relationship between frequency and time in a sweep used in the frequency decomposition, the first step theoretically completes the transform from time to frequency. The slant stacking is then performed on the frequency-swept data to complete the transform from offset to velocity. This simple two-step algorithm generates an image of dispersive energy in the f-v domain. The straightforward transform only uses offset information of data so that this algorithm can be applied to data acquired with arbitrary geophone-acquisition geometry. Examples of synthetic and real-world data demonstrate that this algorithm generates accurate images of dispersive energy of the fundamental as well as higher modes.

The study focuses on detailed imaging of the seabed and the shallow sub-seabed sequences of a deep water area particularly affected by seabed features such as pockmarks, faults, carbonate hardgrounds and hydrate mounds. Three workflows that were applied to achieve this objective are discussed: noise cancellation, spectral enhancement and standard frequency decomposition with RGB blending. Noise cancellation was successful in attenuating much of the coherent and random noise present in the original data set. Vertical resolution, reflector continuity and event separation was improved by spectral enhancement. Frequency decomposition and RGB blending revealed a wide range of geological features on and under the seabed. With the help of these techniques one can distinguish the seabed features and identify and map different elements, such as faults, channels and pockmarks, as well as submarine landslides, mass transport complexes, outrunner blocks of varying sizes and corresponding glide tracks below the seabed. The results confirm that volumetric frequency decomposition and RGB blending lead to an improved and more reliable assessment of shallow geohazards by assisting interpreters to identify a wide range of geological features in unparalleled detail, in a reasonable amount of time.

This study investigates using a combination of seismic forward modelling with frequency decomposition (FD) and colour blending analysis with the aim of better understanding what the major controlling factors on the frequency response are and how this impacts the spectral interference colour patterns observed in FD colour blends. Examples are provided using data from the Scarborough giant gas accumulation, offshore Northwest Australia. Forward modelling of reflectivity is common practice in the oil and gas industry, generally used to provide information on amplitude and phase changes which may occur in response to changes in a model. By incorporating frequency decomposition and red-green-blue (RGB) colour blending into the workflow there may be potential to detect subtle changes within the data, since the interplay between three band-restricted frequency volumes produces a colour blend which is extremely sensitive to frequency change and can often highlight features or trends not seen in full frequency or bandpass volumes. Increasing understanding of FD colour blends may aid in supporting or disproving interpretations made using other lines of evidence, as well as potentially allowing additional geological insights to be made, such as identification of facies, fluids, thicknesses and other changes in reservoir characteristics based on frequency response.

This paper develops a predictive repetitive control algorithm based on frequency decomposition. In particular, the periodic reference signal is first represented using a frequency sampling filter model and then the coefficients of the model are analyzed to determine its dominant frequency components. Using the internal model control principle, the dominant frequency components are embedded in model used to obtain the predictive repetitive control algorithm such that the periodic reference is followed with zero steady-state error. The design framework here is based on predictive control using Laguerre functions and hence plant operational constraints are naturally incorporated in the design and its implementation.

The low accuracy of wind power scheduling influences the grid dispatch adversely, increasing the demand for spinning to reserve capacity and obstructing the grid frequency regulation. Considering the throughput characteristics of energy storage system, which can be used to compensate for wind farm power scheduling deviations, and smooth the grid power fluctuations, the hybrid energy storage (HES) is employed to enhance the dispatch ability of wind power generation. As one of the key techniques, desirable energy storage capacity configuration (ESCC) and control methods would accelerate the application of energy storage in the field of new resource. Combined with statistics and frequency decomposition of scheduling power deviation, HES capacity configuration and online dynamic power allocation method are proposed. First, by analysis of grid assessment indexes of wind power, scheduled wind power data are produced by improved adaptive error factor correction particle swarm optimization back-propagation neural network (AEFC-PSO-BPNN) prediction followed by wavelet packet smooth (WPS). After comparing with actual power, scheduling deviation statistics and frequency decomposition are applied in capacity and power configuration of energy storage, as well as dynamic power distribution control. With wind/storage simulation platform, then, feasibility of energy storage embedded in grid wind power scheduling deviation, regulation is verified under several combined methods, and the proposed ESCC methods are tested in application case by grid wind power indexes of root-mean-square error rate (RMSE), average volatility (AV), maximum throughout power and current (MTP, MTC), actual supercapacitor (SC), battery consumption capacity, and the number of crossings of state of charge (SOC) of HES. Finally, analyses and comparison of energy storage capacity requirements are carried out on different scheduling deviation control methods so as to explore the significant factors influencing capacity allocation. Applying these methods can improve the scheduling accuracy of grid wind power, reduce power fluctuations at the power common connected (PCC) point, and minimize the impact of accessed wind power to the grid as much as possible.

Summary Geological expression techniques including frequency decomposition are very powerful tools in understanding and risking reservoirs. A cognitive approach in visualising responses of different band-limited frequency volumes is through red-green-blue (RGB) colour blending. The non-unique colour responses are subject to a variety of complex interference patterns that are related to a number of geological factors: bed thickness, lithology, porosity, fluid content. This study presents a joint seismic forward modelling and frequency decomposition workflow on the Thebe gas discovery, offshore NW Australia to isolate and quantify the effects of hydrocarbon saturation on colour blends. Observations from real life blends are compared to equivalent synthetic models created through comprehensive rock physics modelling at two well locations; Thebe-1 and Thebe-2. Primary gas-bearing sand units within the Triassic Mungaroo Formation have been identified and are associated with a unique combination of high intensity frequency responses surrounded by a low frequency zone related to a pronounced gas-water contact. Sensitivity analysis through forward modelling has confirmed that fluid effects play a significant role in the frequency responses, and yield unique interference patterns in gas saturated sands. Frequency responses were used to establish spatial distribution of these gas-bearing sands to identify locations of ‘sweet-spots’ and de-risk development plans.

We present a new algorithm of calculating an image of dispersive energy in the frequency‐velocity domain. The frequency decomposition (Coruh, 1985) is first applied to a shot gather in the offset‐time domain to stretch impulsive data into pseudo‐vibroseis data or frequency‐swept data. Because there is a deterministic relationship between frequency and time with a sweep that is used in the frequency decomposition, the first step theoretically completes the transform from time to frequency. The slant stacking is then performed on the frequency‐swept data to complete the transform from offset to velocity. This simple two‐step algorithm generates an image of dispersive energy in the domain. The straightforward transform only uses offset information of data so that this algorithm can be applied to data acquired with arbitrary geophone‐acquisition geometry. This algorithm breaks new ground for true 3D surface‐wave analysis. Examples of synthetic and real‐world data demonstrate that this algorithm generates accurate images of dispersive energy of the fundamental mode as well as higher modes.

Geophysical consultant Dick Dalley argues that the seismic interpretation community could learn a lot about frequency decomposition from parallels with colour photography first explored in the nineteenth century.