ABSTRACT A robust algorithm for the simultaneous estimation of dip, azimuth and curvature in the depth migrated domain is developed. The algorithm makes use of instantaneous-attribute beamforming in small windows aligned with locally coherent migrated events. This is the following two-step procedure: inline and cross-line linear beam stacks to compute the two local dips at image points; 360-degree azimuthal parabolic beamforming to estimate azimuthally dependent curvatures with respect to the plane tangent to the instantaneous-phase surface at the image point. Amplitude and phase content of migrated traces are processed independently using complex trace analysis in order to facilitate this procedure. The instantaneous phase is of central importance since it describes the lateral continuity of events and defines instantaneous dips corresponding to instantaneous apparent phase velocity and group velocity. This attribute is used to compute the instantaneous frequency that defines the beam wavelet at the peak of waveform envelope. The instantaneous amplitude or envelope represents an input to model-based wavefield (Born-Kirchhoff) de-remigration of picked events, useful for dip QC. The QC analysis involves thresholding of modeled migrated amplitudes predicted by Kirchhoff remigration of the Born demigrated wavefield. This also includes simple thresholding of the instantaneous frequency. The analysis is shown to be capable of eliminating undesired events. The algorithm was tested using a 3-D marine streamer dataset with high noise. The success with field migrated data demonstrates that the algorithm is particularly useful for slope-limited tomographic velocity updates and structural interpretation when the signal-to-noise ratio (SNR) is low.

ABSTRACT ABSTRACT: The interpretation of coal seismic data requires a certain precision and accuracy to make the results more reliable. The signature of the seismic wavelet provides a host of valuable geologic information. Subtle features and anomalies, not easily observed in conventional black and white seismic sections, are enhanced through color attribute displays in terms of frequency, amplitude and phase. Coal seam anomalies like sandstone washouts produce a distinct pattern in frequency and amplitude displays due to the change in the net acoustic impedance contrast. Faults produce frequency and amplitude variations due to interference within the Fresnel zone that straddles the fault. The magnitude of displacement is estimated by studying the effects of faults on reflection amplitudes and frequency from computer-generated models. 1 INTRODUCTION Consolidation Coal Company (Consol) and Conoco Inc. initiated a seismic program for coal mining applications in the mid-1970s. During its developmental stages, there were some successes and failures of seismic reflection techniques to detect anomalies at the coal seam horizon. However, the mining industry cannot afford to have an average success rate, especially when safety and productivity are important factors for operating a coal mine. Each seismic survey has to fulfill its objectives. The success of any seismic project depend largely on the three most important processes; namely, field acquisition, data processing and interpretation. In 1987, Consol R&D acquired and developed its own Seismic Inter- active Interpretation Workstation based on a microcomputer system in order to further enhance the seismic program. With some refinements from petroleum applications, the workstation is used to help design the field acquisition parameters and to evaluate the data processing sequence. This process ensures quality control. It is most useful in the interpretation of coal seismic data where computer-generated models are correlated with the processed seismic data. The work- station integrates various sets of geophysical and geological data to form a network of information which is stored in a database. Data sets are retrieved, processed and crosscorrelated to provide the best possible interpretation. The workstation can generate attribute displays of the seismic section to highlight the characteristics of the seismic reflection associated with the target coal seam horizon. The success rate of Consol's seismic program has increased dramatically in recent years due to the introduction and application of state-of-the-art technologies borrowed from the petroleum industry. Transformations of data from one form to another are common in signal analysis. Interpreting data from different points of view often results in new insight and the discovery of relationships not otherwise evident. The transformation of seismic data from the time domain to the frequency domain is the most common example of data rearrangement which is accomplished through Fourier transform. Complex trace analysis is a transform technique which separates the physical characteristics of the waveform that may have significant information about the local geology. It effects a natural separation of amplitude and phase information. The amplitude attribute is called "reflection strength." The phase information is also an attribute and is used to calculate the instantaneous frequency.

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SUMMARY The detection and characterization of discontinuities such as faults in seismic images can be performed by coherency analysis. I analyze the coherency of the instantaneous phase of the complex seismic trace by using circular statistics and defining a complex-valued correlation. The method, applied to neighbouring seismic traces, can extract at once two seismic attributes: correlation amplitude defining coherency and lateral phase shift relating to dip of events. This technique is computationally inexpensive and does not require any scanning or iteration while the local windowing ensures smooth results. I apply the method on real data from Gulf of Mexico. INTRODUCTION Many interesting seismic attributes are designed to reveal subtle stratigraphic features and to detect discontinuities such as faults and fractures (Chopra and Marfurt, 2007). The first category finds its roots in the instantaneous phase of the complex trace and its derivatives such as instantaneous frequency (Taner et al., 1979; Barnes, 2007). The instantaneous phase contains important information and can be used, for example, in 4D seismic traces matching (Hoeber et al., 2008). When phase is unwrapped, its continuity can be interpreted as a geological horizon leading to the creation of Wheeler diagrams (Stark, 2003). The second category relates to the search for specific dips and azimuths exhibiting some coherency and can be based on semblance (Bahorich and Farmer, 1995), principal component analysis of a local covariance matrix (Marfurt, 2006), or the gradient of the instantaneous phase (Scheuer and Oldenburg, 1988; Luo et al., 1996; Barnes, 2007). While having different names, these methods share common concepts. Balancing the requirement for instantaneous high resolution values and the need for smooth properties suggests a local analysis when deriving seismic attributes (Barnes, 2007; Fomel, 2007). The seminal paper on the complex trace analysis by Taner et al. (1979) exhibited complex-valued cross-correlation of two analytic traces but focused on its amplitude in connection with the power ratio and semblance. Phase shift of complex-valued autocorrelation at zero-lag was exploited later (O’Doherty and Taner, 1992) to effectively compute instantaneous frequency and dip. Marfurt (2006) uses the complex trace in semblance calculation to provide robustness against zero-crossing of seismic reflection events, and mentioned the possibility of complexvalued covariance without further exploiting its properties. I explore in this paper the concept of complex-valued correlation. Complex-valued correlation is connected to circular statistics. Local complex correlation of the instantaneous phase between neighbouring seismic traces produces attributes such as local dip estimate from the phase shift of the correlation, and coherency from its modulus. These attributes are local statistical averages. I first explain the concepts of the method and validate it. I then illustrate the performance of the algorithm on a synthetic model and on real data from Gulf of Mexico, and show that faults and unconformities can be detected. COMPLEX-VALUED CORRELATION Complex seismic trace The complex trace s a (t) enables to analyze a real signal f (t) inside a more convenient mathematical framework by defining the complex-valued variable : where h(t) is the Hilbert transform, or quadrature signal, of the real trace f (t), A(t) is the envelope, and q(t) is the instantaneous phase.

Summary Seismic diffractions carry valuable information related to geological structures and discontinuities. Considering that anti-stationary phase filter is proven to be an effective method to extract diffractions from full wavefield, diffraction imaging based on anti-stationary phase filter plays an important role in detecting small-scale geological objects. However, it is worth noting that construction of reflector dip field is the most important step in this method. In this paper, we propose a new method for constructing reflector dip field using dip-angle response, which can effectively characterize reflector dip field in subsurface medium without the disturbances of diffractions. Comparing to other conventional methods for constructing reflector dip field (e.g. complex trace analysis and plane-wave destruction filter) and their corresponding diffraction images on Sigsbee 2A model, the proposed method shows higher accuracy of subsurface scattering points and faults. Application on 3D field data in Tarim Basin also demonstrates its validity and accuracy. More accurate information of weathering crust and dissolved caves in a carbonate reservoir can be well detected since reflector dip fields in different azimuths are effectively utilized. Introduction Diffractions in principle are the seismic response of small-scale geological objects (e.g. dissolved caves and fractures) in subsurface and their characterization and detection are therefore of significant importance for oil/gas exploration. Although it is tough for diffraction research, many tentative researches have been undertaken using diffractions to find small-scale caved-fractured reservoirs. Among those methods, anti-stationary phase filter has already been proven to be an effective method for diffraction imaging. The idea of this method in a pre-stack migration framework is to apply a weight factor inside the migration loops (Moser and Howard, 2008). It consists of two steps: construction of reflector dip field and pre-stack migration with the weight factor. Undoubtedly, construction of reflector dip field is of highly importance for the accuracy of diffraction imaging. To some extent, the quality of diffraction image depends directly on the accuracy of reflector dip field. There already exist several approaches to obtain reflector dip field from a full wavefield image. Marfurt (2006) showed that complex trace analysis utilized instantaneous frequency and instantaneous wavenumber to calculate the time-domain dip value. Claerbout (2004) proposed that a plane wave in a wave field with one constant slope could be extinguished by plane-wave destruction filter with a partial differential operator. Both these two methods are operated in a full wavefield image so that the reflector dip field can be easily affected by the disturbances of diffractions. These disturbances can directly decrease the accuracy of the reflector dip field, which further influences the results of diffraction imaging.

Summary Spikes in complex trace attributes are caused by reflection interference, discontinuities, and noise. They complicate quantitative interpretation, but they may have qualitative value as stratigraphic and structural markers. Destructive reflection interference is the chief cause of spikes. Spikes caused by interference are a function of the reflection spacing and frequency spectrum of the seismic wavelet. They occur at envelope minima and are associated with reflection tails or weak reflectivity. Spikes do not indicate thin beds or stratigraphic terminations, but they can identify faults. Attributes computed horizontally, such as instantaneous wavenumber magnitude, serve as crude discontinuity measures. Introduction Spikes are ubiquitous in complex trace attributes. Attribute spikes are large, transient values, positive or negative, caused by reflection interference, discontinuities, and noise. Spikes confound quantitative interpretation, but their locations mark stratigraphic and structural boundaries. The initial response to spikes was to remove them. Observing that spikes in instantaneous frequency coincide with minima in the trace envelope, or reflection strength, Taner et al. (1979) suppressed them through envelopeweighted averaging. Bodine (1984) removed spikes through the nonlinear .response frequency. method. Both approaches produce attributes with intuitive meaning as time-variant spectral averages. In this way the problem of spikes in quantitative analysis has long been solved. The second response to spikes was to treat them as markers. Hardage (1987, p. 217) observed that spikes in instantaneous frequency form stratigraphic markers between reflections, and Hardage et al. (1998) argued that they also identify stratigraphic terminations and lateral discontinuities. In related studies, Oliveros and Radovich (1997) implicitly used spikes in the second derivative of the envelope as the basis for a discontinuity attribute, and Taner (2001) suggested that frequency spikes indicate thin beds. Nonetheless, the value of spikes in qualitative analysis remains uncertain. I investigate the nature of spikes in complex seismic trace attributes. I show that spikes caused by reflection interference depend on the seismic wavelet and the reflection spacing, and argue that they do not reveal thin beds or stratigraphic terminations. Finally, I look at how spikes in instantaneous wavenumber and amplitude change highlight faults and other discontinuities. Theory All complex trace attributes that involve differentiation are prone to spikes. This includes instantaneous frequency, instantaneous wavenumber, and relative amplitude changes (Figure 1). Instantaneous frequency is the scaled time rate of change of the instantaneous phase (Taner et al., 1979). Instantaneous wavenumber is defined similarly as the scaled rate of change of the phase in the x or y direction (Scheuer and Oldenburg, 1988). Horizontal wavenumber magnitude is the square root of the sum of the squares of the instantaneous wavenumbers in the x and y directions (Oliveros and Radovich, 1997). Relative amplitude changes are derivatives of the trace envelope normalized by the envelope (Oliveros and Radovich, 1997; Barnes, 2008), and are similar to the coherent amplitude gradients introduced by Marfurt and Kirlin (2000). Destructive reflection interference is the major cause of spikes in complex trace attributes. Such spikes occur between reflections at minima in the trace envelope and are a sensitive function of the reflection spacing and the frequency content of the seismic wavelet.

SUMMARY Detection and characterization of faults, unconformities and salt bodies can be conducted by coherency analysis and dip estimation of the seismic images. I use the complex-valued correlation of the instantaneous phase between neighbouring seismic traces to extract two seismic attributes: correlation modulus defining coherency and correlation phase shift relating to dip of events. This method is based on circular statistics concepts. Extracted attributes are neither instantaneous nor global, but estimated smoothly and locally by using shaping regularization. The technique is computationally inexpensive and does not require any scanning but only a single iteration. I apply the method on depth migrated offshore data in West Africa. INTRODUCTION Seismic attributes are designed to reveal subtle stratigraphic features and to detect discontinuities such as faults and fractures (Chopra and Marfurt, 2007). The first category finds its roots in the instantaneous phase of the complex trace and its derivatives such as instantaneous frequency (Taner et al., 1979; Barnes, 2007). The instantaneous phase contains important information and can be used, for example, in 4D seismic traces matching (Hoeber et al., 2008). When phase is unwrapped, its continuity can be interpreted as a geological horizon leading to the creation of Wheeler diagrams (Stark, 2003). The second category relates to the search for specific dips and azimuths exhibiting some coherency and can be based on semblance (Bahorich and Farmer, 1995), principal component analysis of a local covariance matrix (Marfurt, 2006), or the gradient of the instantaneous phase (Scheuer and Oldenburg, 1988; Luo et al., 1996; Barnes, 2007). While having different names, these methods share common concepts. Taner et al. (1979), in their seminal paper on complex trace analysis, exhibited complex-valued cross-correlation of two analytic traces but focused on its amplitude in connection with the power ratio and semblance. Phase shift of complex-valued autocorrelation at zero-lag was exploited later (O’Doherty and Taner, 1992) to effectively compute instantaneous frequency and dip. Marfurt (2006) uses the complex trace in semblance calculation to provide robustness against zero-crossing of seismic reflection events, and mentioned the possibility of complexvalued covariance without further exploiting its properties. A complex discrete wavelet transform can extract dips from the phase (van Spaendonck and Baraniuk, 1999). I explore in this paper the concept of local complex-valued correlation. Local complex correlation of the instantaneous phase between neighbouring seismic traces produces attributes such as local dip estimate from the phase shift of the correlation, and coherency from its modulus. These attributes are estimated smoothly but locally by using shaping regularization (Fomel, 2007). I first explain the concepts of my method based on complex-valued statistics. I then illustrate the performance of the algorithm on a synthetic model and on real prestack depth migrated seismic data from offshore West Africa. Complex-valued circular statistics Cyclic data can be analyzed using circular statistics (Jupp and Mardia, 1989; Jammalamadaka and Sengupta, 2001). Local dip from phase shift Phase measurements are estimates of relative arrival times and are connected to velocity, dip and static time correction (Taner and Koehler, 1969).

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Summary In this study texture attribute analysis application to 3D surface seismic data is presented. This is done by choosing a cubic texel from the seismic data to generate a grey-level occurrence matrix, which in turn is used to compute secondorder statistical measures of textural characteristics. The cubic texel is then successively made to glide through the 3D seismic volume to transform it to a plurality of texture attributes. Application of texture attributes to two case studies from Alberta confirm that these attributes enhance understanding of the reservoir by providing a clearer picture of the distribution, volume and connectivity of the hydrocarbon bearing facies in the reservoir. Introduction A plethora of seismic attributes have been derived from seismic amplitudes to facilitate the interpretation of geologic structure, stratigraphy and rock/pore fluid properties. Complex trace analysis (Taner and Sheriff, 1977) treats seismic amplitudes as analytic signals and extracts various attributes to aid feature identification and interpretation. Computations for these attributes are carried out at each sample of the seismic trace and so have also been dubbed instantaneous attributes . Another class of attributes utilizes the 3D nature of the seismic data by using an ensemble of traces in the inline and crossline directions and using time samples in the computation as well. Coherence attribute computation is done this way. More information on all these attributes can be found in Chopra and Marfurt, 2005. These different attributes have been used for different purposes and have their own limitations. Texture analysis of seismic data was first introduced by Love and Simaan (1984) to extract patterns of common seismic signal character. This inspiration came from the suggestion that zones of common signal character are related to the geologic environment in which their constituents were deposited. These and other similar attempts enjoyed limited success as the outcome was dependent on the signal-to-noise ratio and also because the stratigraphic patterns could not be standardized. More recently, the use of statistical measures to classify seismic textures using grey-level co-occurrence matrices (GLCMs) (West et al, 2002, Gao, 2003) has been introduced. The idea behind texture analysis of surface seismic data is to mathematically describe the distribution of pixel values (amplitude) in a sub-region of the data. Texture analysis has been extensively used in image processing (remote sensing), where individual pixel (picture element) values are used in the analysis. The term texel (texture element) is usually used for reference to the smallest set of pixels (planar for 2D) used for characterizing a texture. For 3D seismic data, a cubic texel is used for texture analysis. The technique used to quantify this utilizes a transformation that generates GLCMs. The GLCMs essentially represent the joint probability of occurrence of grey-levels for pixels with a given spatial relationship in a defined region. The GLCMs are then used to generate statistical measures of properties like coarseness, contrast and homogeneity of seismic textures, which are useful in the interpretation of oil and gas anomalies. GLCMs for seismic data A computed grey-level co-occurrence matrix has dimensions n x n, where n is the number of grey levels.

Summary Gradient structure tensor is extensively used in attributes extraction, such as dip, azimuth, and discontinuity detection. However, the existing faults and other discontinuous structures would affect the precision of dip/azimuth estimation. In this abstract, we propose to combine gradient structure and multi-window technology to estimate the dip and azimuth. The results of synthetic example and fielddata example show the correctness and validity of our method. Introduction The dip and azimuth, which reflects the orientations of seismic events in 3D seismic cubes, is the most important geometric attributes, and also plays the crucial role in seismic interpretation. For instance, they can be used in shaded relief projections (Barnes, 2003). In addition, the dip and azimuth can be utilized to derive other useful attributes. The significant curvature attribute can be obtained by calculate the partial derivatives of dip (Al- Dossary and Marfurt, 2006). Barnes (2000b) also developed a suite of computer-generated textures based on an underlying estimate of dip and azimuth. The dip also plays an important role in dip-steered coherence (Marfurt et al, 1999) and structure-oriented filter (Luo et al, 2002; Wang, 2008, 2012). Therefore, estimating the dip is a worthwhile endeavor. Several methods have been developed to estimate the dip and azimuth. Picou and Utzmann (1962) used a 2D unnormalized cross-correlation scan over dips on 2D seismic lines. Marfurt et al (1998) generalized a semblancebased scan to estimate 3D dip. Barnes (1996, 2000a) presented an dip estimating method based on 3D complex trace analysis, while the estimate based on gradient structure tensor (GST) is also presented (Bakker et al, 1999). Luo proposed dip estimation based on weighted structure method (Luo, 2006). In order to reduce the effect of amplitude's lateral changes, Wang analyzed the relation between partial derivative of complex trace and partial derivative of instantaneous amplitude (IA) / instantaneous phase (IP), and constructed GST on IP to estimate dip (Wang, 2014).

SUMMARY We proposed a new technique for seismic noise attenuation by applying nonstationary polynomial fitting. We suppress random noise on common midpoint (CMP) gather after normal move out (NMO), and to subtract the linear coherent noise in radial trace (RT) domain. Nonstationary polynomial fitting can estimate the coherent component from seismic data. For random noise attenuation on CMP gather after NMO, we directly estimate seismic coherent signal. For linear coherent noise subtraction, we first estimate coherent noise using nonstationary polynomial fitting in radial trace domain, and then subtract it. Nonstationary polynomial fitting method doesn’t need assume the estimated coherent component has constant amplitude. Synthetic and field data examples show that the proposed method can attenuate seismic noise effectively. INTRODUCTION The recovery of the signal and attenuation of the noise are crucial in seismic processing. Seismic stacking is an effective method for seismic noise attenuation (Mayne, 1962; Liu et al., 2009). Such a technique can obtain post stack data with higher signal-noise ratio. Sometimes we need to get prestack data for seismic data analysis, for example, amplitude versus offset (AVO) analysis, velocity analysis, prestack seismic migration, etc. Many methods have been developed and used in practice for prestack seismic noise attenuation. Ristau and Moon (2001) compared several adaptive filters, which they applied in reducing random noise in seismic data. Guitton (2002) proposed an inversion method for coherent noise attenuation using prediction-error filters (PEFs), which approximated the inverse covariance matrices with PEFs. Karsli et al. (2006) applied complex-trace analysis to seismic data for random noise suppression. Bekara and Baan (2009) devised a new filtering technique for random and coherent noise attenuation by applying empirical mode decomposition. Some transform methods were used to eliminate seismic random noise and coherent noise, e.g., seislet transform (Fomel, 2006; Liu et al., 2009), curvelet transform (Neelamani et al., 2008). The polynomial fitting (PF) method has been used successfully to enhance seismic signals and to suppress random noise (Xue and Chen, 2009; Lu and Lu, 2009) and coherent noise (Lu et al., 2006). These methods use sliding window to estimate local linear coherent components. Radial trace (RT) transform has been proposed and used in coherent noise attenuation. Henley (2003) described the principles and practical application details for coherent noise suppression in RT domain. Fomel (2009) developed a general method of nonstationary regression with shaping regularization (Fomel, 2007). The nonstationary polynomial fitting (NPF) was presented in Fomel’s paper, which allows the coefficients of polynomial to become smoothly nonstationary without the need to break the input signal into local windows. Nonstationary regression has been used in multiple subtraction and timefrequency representation (Liu et al., 2009). In this paper, we use nonstationary polynomial fitting to estimate coherent components, and achieve noise attenuation. We review first the theory of nonstationary polynomial fitting. Then we describe respectively the methods of random noise attenuation in CMP gather and coherent noise attenuation in RT domain. We demonstrate the success of this method with synthetic and real data examples.

Summary Stratigraphic interpretation of seismic data requires careful interpretation of the amplitude, phase and frequency so as to gauge the geologic subsurface detail. Sometimes the interpretation of the changes in amplitudes is not easy and the equivalent phase is difficult to comprehend. In such cases seismic attributes are utilized to provide additional information that could aid the interpretation. One of the earliest set of ‘instantaneous’ attributes was based on complex trace analysis, and instantaneous phase has been used for interpretation of stratigraphic features such as pinchouts and discontinuities as well as fault edges. In this study, we demonstrate that the interpretability of seismic data can be enhanced with the use of spectral phase components derived during spectral decomposition. As there are different methods for decomposing seismic data into its component frequencies and phase within the seismic bandwidth, we consider two of the common methods in our analysis here, namely the continuous wavelet transform and the matching pursuit methods. We also show that the principal component analysis of spectral magnitude and phase components yields additional insight into the data. The first principal component ‘churned’ out of the phase components shows clarity in the features of interest and compares favourably with the discontinuity attributes commonly used for the purpose. Introduction The strength of seismic reflections carry subsurface information sensitive to absorption and scattering, propagation through fluids and complex interference patterns from stacked stratigraphy. Quantitative interpretation requires that the seismic amplitudes be as ‘true’ as possible, and are not contaminated with noise or other distortions of the acquisition process. In addition to its reflection strength, seismic events are characterized by their frequency and phase. Thin bed interference often increases the high frequency and decreases the low frequency components of the seismic wavelet. For adjacent reflectors having equal but opposite reflection coefficients, the peak amplitude occurs or "tunes" at the quarter wavelength frequency. This latter thin bed tuning phenomena also gives rise to a 90° change in phase. Linear increases and decreases in impedance that may be associated with upward fining or coarsening also give rise to a 90° phase change, as does the reflection from an interface between two units of equal impedance but a finite change in attenuation, or 1/Q . While changes in reflection strength are easy to see, the recognition of such phase and frequency changes are subtle and more easily overlooked on large 3D seismic data volumes. Seismic attributes quantify such subtle changes.

Summary If the earth’s surface has a complex geometry, the implementation of the grid method for solving the eikonal equation will become difficult. In fact, in this case we must first solve the following six problems, namely (1) how to describe the curved earth’s surface, (2) how to divide the surface into discrete pieces, (3) how to describe the medium directly near the surface, (4) how to divide the medium directly near the surface into discrete elements, (5) how to compute the local traveltime, and (6) how to capture and to propagate the local wavefront near the curved earth’s surface or interface. Previously, for solving the problems (1) to (5), we used a second order upwind finite difference scheme that uses nonuniform grid spacing in the regions near the earth’s surface or the interface (Sun et al., 2011). For solving the problem (6), we modified the fast marching method (FMM) based on the narrow band technique by introducing new point types, namely the surface point, the point above the surface, the interface point, and the point under the interface (Sun et al., 2011). Here, for solving the problems listed above we present a method that uses a hybrid grid and that combines the linear interpolation method and the FMM. Specifically, the surface is approximated by broken lines (2D cases) and the medium directly near the surface is divided by an irregular grid that is composed of rectangular and triangular grid elements. For the local travetime computation and the local wavefront propagation, we use the linear interpolation method and the modified FMM, respectively. Furthermore, for constructing rays from the computed traveltimes, we search the point from which a ray comes from in reversed direction, i.e., from the bottom of the model to the top. Numerical results show that the method presented here not only can flexibly approximate the traveltimes, but also can give accurate ray trajectories in the models with strong heterogeneities.

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SUMMARY We present a new method of surface-wave mitigation using polarization filtering. The method evolves from the polarization-analysis technique developed by Diallo et al., (2006) and introduces new constraints to effectively detect and mitigate surface waves without damaging the signal. Straightforward application of polarization filtering without these constraints results in ineffective filtering or damage to the signal, due to the complexity of surface-wave wavetrains. We illustrate the performance of the method with examples from multicomponent seismic data, and demonstrate the superiority of the filtering compared to the unconstrained approach. INTRODUCTION Polarization filtering exploits the fact that P-waves, S-Waves, Love and Rayleigh waves have distinct polarization patterns, which can be used to discriminate these different wave types. In practice, this turns out to be quite challenging because, in heterogeneous media, surface waves are strongly dispersive, and their polarization attributes are time, frequency and mode dependent. Furthermore, because of interferences, it is very difficult to recover the polarization attributes of individual wave types in either the time or the frequency domain. To overcome some of these limitations, Diallo et al., (2006) derived analytical expressions that relate the multicomponent signal to its polarization attributes in the time-frequency domain using the wavelet transform. A method using these expressions can effectively separate signal from surfacewave noises when clear time-frequency boundaries exist between these wave types. Often, however, it is not the case that such clear boundaries exist. We use an improved method to attenuate surface-wave noises without damaging the signal. The method combines information, including polarization attributes, amplitude, and velocity, to analytically constrain the application of polarization filtering to the part of the time-frequency domain most dominated by surface waves. We demonstrate the effectiveness of the method using field data. THEORY In this section, we highlight some key results from Diallo et al., (2006), which uses complex trace analysis. DETECTION OF TIME-FREQUENCY BOUNDARIES OF SURFACEWAVES We now develop an extension to the method described above. The extension automatically determines a zone in the time-frequency domain where polarization filtering is to be applied, thus constraining the filter and improving protection of signal. We propose two schemes to delineate the time-frequency domain where the surface waves are predominant. Detection based on the instantaneous amplitude From the modulus of the wavelet transform of the complex seismic trace, we identify the portion of the T-F domain that corresponds to surface-wave arrivals. An initial step in detecting the boundary, referred to here as a ridge (which should not be confused with rigorous definition of the ridge as known in the wavelet community), consists of scanning the frequency axis for each given time to find the maximum of the wavelet transform modulus. The resulting curve R(t) represents the frequency f at which the modulus of the wavelet transform is maximum for each time t. At far offsets where surface waves are weak, the curve R(t) is associated with the reflection arrivals. At the near offset where surface wave energy is predominant the curve R(t) gives the frequency of maximum amplitude of the predominant, surface-wave arrivals at each time.

INTRODUCTION Summary Volumetric attributes computed from 3D seismic data are powerful tools in the prediction of fractures and other stratigraphic features. Geologic structures often exhibit curvature of different wavelengths. Curvature images having different wavelengths provide different perspectives of the same geology. Tight (short-wavelength) curvature often delineates details within intense, highly localized fracture systems. Broad (long wavelength) curvature often enhances subtle flexures on the scale of 100-200 traces that are difficult to see in conventional seismic, but are often correlated to fracture zones that are below seismic resolution, as well as to collapse features and diagenetic alterations that result in broader bowls. Such multi-spectral volumetric estimates of curvature are very useful for seismic interpreters and we depict a number of example demonstrating such applications. Computation of volumetric curvature attributes is a significant advancement in the field of attributes. Initial curvature applications were limited to picked 3D seismic horizons. In addition to delineating faults (Sigismundi and Soldo) and subtle carbonate buildups (Hart, 2003), horizonbased curvature has been correlated to open fractures measured on outcrops (Lisle, 1994) and to production data (Hart et al., 2002). Horizon-based curvature is limited not only by the interpreter’s ability to pick, but also the existence of horizons of interest at the appropriate level in 3D seismic data volumes. Horizon picking can be a challenging task in datasets contaminated with noise and where rock interfaces do not exhibit a consistent impedance contrast amenable to human interpretation. To address this issue, Al-Dossary and Marfurt (2006) generated volumetric estimates of curvature generated from volumetric estimates of reflector dip and azimuth. Such reflector dip and azimuth estimates can be calculated using a complex trace analysis (Barnes, 2000), a gradient-structure tensor, discrete semblance-based searches (Marfurt 2006), or plane-wave destructor techniques (Fomel, 2008). Computing derivatives of the volumetric reflector dip components provides a full 3D volume of curvature values. However, since their formation, such fractures may have been cemented (Rich, 2008), filled with overlying sediments (Nissen, 2006) or diagenetically altered (Nissen et al., 2007). Furthermore, the present-day direction of minimum horizontal stress may have rotated from the direction at the time of deformation, such that previously open fractures are now closed, while previously closed fractures may now be open. For this reason, prediction of open fractures requires not only images of faults and flexures provided by coherence and curvature coupled with an appropriate model of deformation, but also measures of present day stress provided by breakouts seen in image lots and seismic anisotropy measures. Many workers will prefer using maximum and minimum curvature (e.g. Sigismundi and Soldo, 2003; Klein et al., 2008), while others (including the authors) have preferred using the most-positive and most-negative curvatures. In this paper, we propose simply using the principal curvatures, k1 and k2 , which we describe below. In addition to faults and fractures, stratigraphic features such as levees and bars and diagenetic features such as karst collapse and hydrothermally altered dolomites also appear to be welldefined on curvature displays. Channels appear when differential compaction has taken place.

Summary Thin bed thickness can be predicted by peak instantaneous frequency when the thin bed response has small interference effects from other layers. Based on a simple wedge model, the peak instantaneous frequency is inversely proportional to the layer thickness such that thinner layers exhibit a higher peak instantaneous frequency. However, when the top and bottom reflection coefficients are different, this inverse trend becomes more complicated for layers less than one eighth wavelength thick. We use 3D seismic data from Fort Worth basin with 16 wells to calibrate this method to predict the thickness of the Pennsylvanian age Caddo limestone. We find the peak instantaneous frequency to be well-correlated with the layer thickness measured in the wells. We then use this simple inverse linear trend d to predict Caddo limestone thickness. Introduction Widess (1973) showed that we can estimate the thickness of thin layer (less than the tuning thickness) by exploiting the linear relation between thickness and reflection amplitude. In addition, the tuning thickness itself is inversely proportional to the peak spectral frequency of a broadband spectral response. Robertson and Nogami (1984) discussed the combination of envelope and instantaneous frequency to predict thin bed thickness. Chuang and Lawton (1995) studied four different wedge models to show that peak frequency slowly decreases as layer thickness increases. Based on instantaneous attributes (Taner et al., 1979), Partyka (2002) compared Widess’s amplitude method simple measurements of peak to trough travel time as well as discrete Fourier transform (spectral decomposition) components to predict thickness. Nissen (personal comm., 2002) demonstrated the relationship between instantaneous frequency and “D” sand thickness of Sooner unit in Colorado. Unfortunately, the instantaneous frequency obtained using complex trace analysis can become be unstable and unreliable when seismic data has a low signal to noise ratio. Instead, we propose using peak instantaneous frequency to predict thin bed thickness. Peak instantaneous frequency is calculated in a small window which is around the thin bed response. We assume that thin bed reservoir’s thickness is below or around tuning thickness. We constructed two simple wedge models to verify the relation between peak instantaneous frequency and thin bed thickness. The general trend is that thicker thin bed has lower peak instantaneous frequency, while thinner bed has higher peak instantaneous frequency. One limestone layer in Fort Worth basin is used to test this trend. Caddo limestone thickness came from 16 wells has good matches with computed peak instantaneous frequency from 3-D seismic data. A linear trend is used to approximately predict Caddo limestone thickness. Wedge model example We built two wedge models to test our method. The top and bottom reflection coefficients of the first wedge model have the same magnitude but opposite polarity (-0.01 and +0.01). The second wedge model has different magnitude top and bottom reflection coefficients (-0.01 and +0.009).The input wavelet is a zero-phase Ricker wavelet with peak frequency 35 Hz. Both wedge thicknesses increase from 0.3 m (first trace) to 25 m (last trace).

Summary With the development of 3D seismic exploration techniques, not only in the quality control of seismic acquisition, but also in the preprocessing of seismic data, abnormal traces identification must be automated due to vast amounts of seismic data. Conventional method based on the comparison of the energy of adjacent traces can detect abnormal traces to some extent, but the identification result is poor due to the diversity and complexity of seismic data. By means of the ideological of weighted clustering, and study the different attributes of seismic data, then process fuzzy clustering analysis on these characteristics and attributes, it is better to identify abnormal traces. The actual data and model test show that this method can achieve better effect. Introduction With the development of seismic apparatus and high density seismic acquisition technology, seismic exploration has made great progress, which directly makes the quantity of seismic data so much. Therefore, abnormal traces identification fully relied on artificial have been unable to meet the objective needs of the massive seismic monitoring and processing of data quality. Currently, some of the seismic acquisition quality control system mainly use the combination of artificial and energy compare of adjacent traces to recognize abnormal traces. Although this method can identify abnormal traces with large amplitude, however, continuous abnormal amplitude and main frequency anomalies, and continuous missing traces can not be better identified. With the sharply increase of seismic data, it is necessary to identify abnormal traces automatically, accurately and practically. In this paper, by means of ideological weighted clustering, first extract attributes of seismic data and construct attribute characteristic matrix, then strike the main direction of the seismic data and calculate the distance between each trace to the main direction. If the distance of one trace to the main direction is larger than the predetermined threshold value, it can be considered to be an abnormal trace. The actual data show that this method can quickly and accurately identify abnormal trace automatically.

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