Velocity analysis with local event slopes related probability density function

Agood seismic velocity model is required for many routine seismic imaging techniques. Velocity model building from seismic data is often labor intensive and time consuming. The process becomes more complicated by taking nonhyperbolic traveltime estimations into account. An alternative to the conventional time-domain imaging algorithms is to use techniques based on the local event slopes, which contain sufficient information about the traveltime moveout for velocity estimation and characterization of the subsurface geologic structures. Given the local slopes, there is no need for a prior knowledge of a velocity model. That is why the term “velocity independent” is commonly used for such techniques. We improved upon and simplified the previous versions of velocity-independent nonhyperbolic approximations for horizontally layered vertical transverse isotropy (VTI) media by removing one order of differentiation with respect to offset from the imaging kinematic attributes. These kinematic attributes are derived in terms of the local event slopes and zero-offset two-way traveltime (TWTT). We proposed the use of predictive painting, which keeps all the attributes curvature independent, to estimate the zero-offset TWTT. The theoretical contents and performance of the proposed approach were evaluated on synthetic and field data examples. We also studied the accuracy of moveout attributes for shifted hyperbola, rational, three-parameter, and acceleration approximations on a synthetic example. Our results show that regardless of the approximation types, NMO velocity estimate has higher accuracy than the nonhyperbolicity attribute. Computational time and accuracy of the inversion of kinematic attributes in VTI media using our approach were compared with routine/conventional multiparameter semblance inversion and with the previous velocity-independent inversion techniques.

Summary The estimation of local slopes has been an important topic for numerous seismic processing applications. Many local slope algorithms are based on the plane wave destruction approach, using the time derivative of the seismic trace along with a horizontal gradient trace to generate estimates of the dip. Differentiation increases high frequencies in the data, limiting the accuracy of these dip estimates. Alternatively, the plane wave destruction equation may be recast in terms of integration. In this case the original seismic trace is used along with the causal integration of the horizontal gradient trace. Since there is no differentiation to boost high frequency noise, and since numerical integration is itself a smoothing process, this approach leads to better-behaved dip estimates. In both cases, the finite difference approximation of the gradient leads to a biased estimate. However, as long as the local event slopes are not aliased, the dip estimates will be of the correct sign, and an iterative application of the algorithm will lead to accurate local slopes.

An integrated procedure for migration velocity analysis in complex structures of thrust belts

Seismic imaging is a significant technology to provide the image of the subsurface in several fields such as hydrocarbon exploration/production and civil engineering. A fundamental problem in seismic imaging is that both the depth reflectivity and velocity distribution of the subsurface have to be predicted by only seismic events observed at the surface, and it still remains a challenging research topic. Joint migration inversion (JMI) is one of the seismic waveform imaging algorithms that were recently proposed. JMI is capable of simultaneously estimating velocity and reflectivity models of the subsurface by exploiting reflected waves including internal multiples. The seismic modeling algorithm in the JMI process is a method termed full wavefield modeling (FWMod), which is a one-way propagator-based reflection modeling algorithm, including higher-order scattering and transmission effects. In this thesis, two directions to improve the accuracy of seismic imaging based on JMI are discussed. On one hand, an extension of FWMod is proposed to correctly deal with not only reflected waves but refracted/diving waves via one-way propagators in the horizontal direction, and this method is extended to a new JMI algorithm. On the other hand, we assume that only reflected waves including internal multiples are utilized in the imaging based on JMI and present two novel methods for the inversion and pre-processing: 1) iterative reflectivity-constrained velocity estimation, 2) surface amplitude correction via learning from synthetic models for land seismic data. The reflectivity-constrained velocity estimation is employed to improve the accuracy of the estimated velocity by exploiting the estimated reflectivity in the JMI process. The surface amplitude correction process is introduced to mitigate the influence of the amplitude variations caused by source/receiver response sensitivities and the difference of the features between observed land seismic data and the simulated data by the used imaging scheme. The numerical and field data examples for both land and marine cases demonstrate that the proposed approach is capable of effectively estimating reflectivity and velocity model, even though the low frequency components of the observed data are absent.

Summary Anisotropic terms of elastic wave equations make it much more complicated, that is why usually earth is assumed isotropic. Anisotropy effect arising from shale layers (clastic and also unconventional reservoirs) need to be corrected in seismic imaging as a function of travel time and in seismic reservoir characterization as a function of amplitude. In this study the influence of anisotropy on amplitude variation with offset (AVO) is analyzed. In AVO response, the amplitude changes should be evaluated and determine that how much originates from hydrocarbon and how much is due to anisotropy effect. In order to overcome the plausible misleading of interpretation after seismic simultaneous pre-stack inversion, anisotropy correction on seismic data is carried out. To do so, Backus averaging is performed to predict anisotropic parameters. Afterwards, in different seismic angle stacks, amplitude correction is exerted according to the specified incident angle and estimated Thomsen parameters. The inversion results derived from corrected data reduce the uncertainty of hydrocarbon prediction and leads to far more accurate reserve estimation which in turn positively affects on drilling costs.

3D Seismic Imaging

Exploration programs in deepwater Tertiary basins (e.g., the Gulf of Mexico) typically rely on bright‐spot and amplitude variation with offset (AVO) technology to help identify oil‐ and gas‐charged sands. The reliance on these attributes, along with the high cost of exploration programs in deepwater environments, has driven the need to examine the limitations of these technologies and to build robust models for the conditions under which AVO is useful as a fluid and/or lithology indicator. We build subregional AVO background trends for both brine‐ and gas‐saturated sands from several wells from the eastern deepwater Gulf of Mexico. These trends are built from the depth dependencies of velocities and densities for both shale and sands (brine saturated). Simple models of AVO gradient and intercept are constructed as a function of depth below the mud line. Sand and shale properties show little velocity contrast, justifying the interpretation of these data in the context of linearized AVO models. In addition to the in‐situ brine response, the response to gas is also calculated. These trend models indicate that the AVO response is suppressed (although still positive) below a depth of approximately 10 000 ft below the mud line. Even optimistic porosity modeling (sand porosity >30°) does not substantially change this conclusion. An important corollary is that the absence of a strong AVO anomaly at these deeper depths cannot be used with confidence when ruling out hydrocarbon presence. This observation also highlights the need to crossplot attributes to best predict hydrocarbon presence. Velocity data collected as part of this study are also used to generate a local shear velocity estimator for sands and shale. These shear estimators are similar in form to other published estimators, but minor differences in coefficients may become important in AVO modeling.

In AVO (Amplitude Variation with Offset) analysis, the amplitudes of reflected waves with different incident angles are studied to deduce lithology information beyond the structure map obtained by seismic imaging algorithms. The quantitative analysis of the amplitude, relies on common-image gathers being flat (or equivalently, at the same depth). But the waves with different incident angles will have different apparent velocities, resulting in different depths for the same image point at different angles, or non-flat common image gathers. In many scenarios, non-flat common-image gather was flattened by trim means at the cost of compromising zero-crossing and polarity-reversal information. This work presents a solution based on the seismic imaging subseries of the inverse scattering series (ISS) that flattens the common image gather without knowing or determining the subsurface velocity, and without any harmful amplitude consequencies.

The velocity of near-surface materials is one of the most important for Ground-Penetrating Radar (GPR). In the study, we evaluate the options for determining the GPR velocity to measure the accuracy of velocity approximations from the acquired GPR data at an experimental site in Hangzhou, China. A vertical profile of interval velocities can be estimated from each common mid-point (CMP) gather using velocity spectrum analysis. Firstly, GPR data are acquired and analyzed using the popular method of hyperbola fitting which generated surprisingly high subsurface signal velocity estimates while, for the same profile, the Amplitude variation with offset (AVO) analysis of the GPR data (using the same hyperbola fitting method) generate a more reasonable subsurface signal velocity estimate. Several necessary processing steps are applied both for CMP and AVO analysis. Furthermore, experimental analysis is conducted on the same test site to get velocities of samples based on dielectric constant measurement during the drilling process. Synthetic velocities generated by AVO analysis are validated by the experimental velocities which confirmed the suitability of velocity interpretations.

The amplitude Variations with Offset (AVO) technique is extensively used in hydrocarbon exploration and production for de-risking of the prospect before drilling. The interpretation of AVO results brings more confidence in the presence or absence of hydrocarbon. The AVO and Direct Hydrocarbon Indicator (DHI) analysis have their own inherent limitations. Therefore, to ensure the presence of true AVO in seismic, other attribute supports are crucial. The present prospect in this study was deposited as a channel-levee complex in the shelf-slope of the Krishna-Godavari basin. There is evidence of false AVO within this complex and thus additional attributes were used in this study to support the AVO analysis. The conventional AVO analysis shows the presence of Class-III AVO for a probable reservoir in seismic. However, it is unable to ensure the presence of hydrocarbon in the stacked reservoir unit. The spectral AVO technique was used to check AVO response at low frequencies for laminated and stacked reservoir units. Additionally, seismic attenuation and dispersion attribute studies were incorporated into the de-risking analysis. The drill result showed two distinct reservoir intervals in this prospect, which validated the predrill interpretation. This integrated approach added significant value in de-risking the prospect using AVO and other seismic attributes in complex geologic setups.

In the last few years new imaging methods have been introduced. One of the most important and powerful procedure for seismic time imaging is Common Reflection Surface stack (CRS stack) method. In contrast to the conventional methods like NMO/DMO stack and pre-stack time migration which are based on velocity information, the CRS stack method is independent of a velocity model. In this study we perform a stacked section without any velocity analysis using CRS move out formula. In contrast to the conventional stacking process, signal-to-noise ratio and continuity of signal along the events are improved significantly using CRS stack method. In this study we use this method for 2D land data by inhomogeneous layers.

The limited-view angle problem is one of the difficulties in seismic diffraction tomography. In the configuration of seismic data acquisition systems, the exploring wave cannot probe the object from all directions. This limitation will lead to incomplete coverage in the wavenumber domain. If we ignore this incomplete data by assigning zero to the blind area and use the ordinary reconstruction algorithms, poor resolution will be introduced. Thus, it is important to estimate the missing data in the spectrum in order to improve the resolution. In this paper, POCS (Projections Onto Convex Sets) is applied to the cross-hole seismic diffraction tomography in order to solve the limited-view angle problem in this configuration. The algorithm that combines POCS with direct Fourier transform and bilinear interpolation in the wavenumber domain is proposed. POCS can incorporate many kinds of convex-type a priori knowledge about the object function as constraints and its estimate is superior to that of G-P extrapolation. INTRODUCTION In cross-hole seismic tomography, the sources and geophones are deployed in the two bore-holes respectively and it is very difficult to probe the object in the subsurface from all directions. This problem is known as the limited-view angle problem and it will lead to large patches of “blind area” in the wavenumber domain. Up to now, most seismic diffraction tomography methods have bypassed this problem by assigning zero to the “blind area” where data are not available. The reconstruction directly from the limited-view data is the so-called zero-order or “naive” solution and the image is often blured and distorted because the data in the blind area are not actually zero. In this paper, we combine the convex projections and direct Fourier transform to estimate the blind area data for cross-hole seismic diffraction tomography. The limited-view angle problem is an underdetermined problem in which only a small number of projections is available. Artifacts such as streaking and geometric distortion are inevitable in the reconstructed image. This lack of information, however, may be made up in part by adequate a priori knowledge about the image. Such knowledge may be used to impose constraints on the solutions or the reconstruction procedure in an attempt to regularize the ill-posed problem. POCS offers two note-worthy advantages: 1) it enables any number of a priori convex-type constraints to be incorporated in the algorithm; and 2) it guarantees convergence: weak in general, strong in practice. It is a recursive technique that finds a solution consistent with the measured data and a priori known constraints in both the space and Fourier domain. Because of these advantages, POCS has found applications in image restoration and X-ray CT image reconstruction, etc. In this paper, it is used in seismic diffraction tomography. BASIC EQUATIONS OF SEISMIC DIFFRACTION TOMOGRAPHY Consider the case of the acoustic wave equation with constant density. The object is described by the velocity distribution where is the position vector. The background medium has a velocity The wave equation in the source-free region is

The occurrence of gas hydrate has been inferred from the presence of Bottom-Simulating Reflectors (BSRs) along the western continental margin of India. In this paper, we assess the spatial and vertical distribution of gas hydrates by analyzing the interval velocities and Amplitude Versus Offset (AVO) responses obtained from multi-channel seismics (MCSs). The hydrate cements the grains of the host sediment, thereby increasing its velocity, whereas the free gas below the base of hydrate stability zone decreases the interval velocity. Conventionally, velocities are obtained from the semblance analysis on the Common Mid-Point (CMP) gathers. Here, we used wave-equation datuming to remove the effect of the water column before the velocity analysis. We show that the interval velocities obtained in this fashion are more stable than those computed from the conventional semblance analysis. The initial velocity model thus obtained is updated using the tomographic velocity analysis to account for lateral heterogeneity. The resultant interval velocity model shows large lateral velocity variations in the hydrate layer and some low velocity zones associated with free gas at the location of structural traps. The reflection from the base of the gas layer is also visible in the stacked seismic data. Vertical variation in hydrate distribution is assessed by analyzing the AVO response at selected locations. AVO analysis is carried out after applying true amplitude processing. The average amplitudes of BSRs are almost constant with offset, suggesting a fluid expulsion model for hydrate formation. In such a model, the hydrate concentrations are gradational with maxima occurring at the base of hydrate stability zone.

We perform seismic diffraction imaging and velocity analysis by separating diffractions from specular reflections and decomposing them into slope components. We image slope components using extrapolation in migration velocity in time-space-slope coordinates. The extrapolation is described by a convection-type partial differential equation and implemented efficiently in the Fourier domain. Synthetic and field data experiments show that the proposed algorithm is able to detect accurate time-migration velocities by automatically measuring the flatness of events in dip-angle gathers.

Anisotropic P-wave velocity analysis and seismic imaging in onshore Kutch sedimentary basin of India