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ABSTRACT We propose a stable inversion method to create geologically constrained instantaneous velocities from a set of sparse irregular stacking/RMS picked vertical functions. The method is mainly designed for building the optimal velocity model for curved rays PSTM and an initial macromodel for PSDM and grid-based tomography. It is mainly applicable in regions containing compacted sediments, where the velocity gradually increases with depth and can be laterally varied. Inversion is done in three stages: Establishing a global velocity trend model, applying constrained inversion, and fine mapping. Initially, the velocity trend is assumed an exponential asymptotically bounded function defined locally by three parameters at each lateral node. It is calculated from a reference datum, normally taken as the sea bottom in marine surveys, or the topography or another given reference horizon in land surveys. At each node, the initial trend is defined from a set of vertical functions within a pre-defined area of influence. Velocity picks related to non-sediment rocks, such as salt flanks or basalt boundaries, require different trend functions and therefore are treated differently. The inversion is performed individually for each RMS vertical function, and the lateral and vertical continuities are controlled by the global trend function. Finally, smoothing and mapping are done for the resulting instantaneous velocity, generating a regular fine grid in space and time. This method leads to a stable and geologically plausible velocity model, and can be applied to 3D, 2D single-line and 2D multi-line surveys.
ABSTRACT Shot profile migration provides a convenient framework for implementation of a differential semblance algorithm for estimation of complex, strongly refracting velocity fields. The objective function minimized in this algorithm may measure either focussing of the image in offset or of the image in (scattering) angle. The gradient of this objective is a by-product of a depth marching scheme, an requires a few extra computations beyond those necessary to produce the prestack data volume. A strongly refracting 2D synthetic data example illustrates the excellent image quality obtainable from model-consistent data. Offset and angle variants behave differently, with more rapid convergence for the offset variant, underlining the importance of a mathematically well posed formulation: in 2D, the angle variant is much less well-conditioned than the offset variant.
- Geophysics > Seismic Surveying > Seismic Processing (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling (1.00)
ABSTRACT The time-domain electromagnetic (EM) method such as ground-penetrating radar is a useful tool for civil and environmental engineering fields because of its high resolving power and non-destructive measurements. This paper presents the full-waveform inversion of EM wavefield data for imaging the cross-borehole permittivity structure. The EM full-waveform inversion method uses the conjugate gradient method to minimize an objective function. Frechet derivatives can be calculated by the crosscorrelation at zero lag between the forward propagated wavefield and the backward propagated wavefiled represented by the adjoint Maxwell''s equations. Both the forward and backward propagations are calculated by a same stable finite difference time domain method. The inversion algorithm is validated using a synthetic model having non-uniform permittivity distribution.
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling > Seismic Inversion (1.00)
- Geophysics > Electromagnetic Surveying (1.00)
Concepts and Causes The centroid concept (pressure lateral transform) assumes The term pore pressure can be confusing. Pore pressure is that there is a "center" or mid-point along a dipping predicted in relatively impermeable beds (shale and clay) sequence of seals and reservoirs where the pore pressure in and measured in reservoir quality rocks (sand). However, both are in equilibrium. This observation can hold true in a in many occasions, there is not a direct link between the specific geological setting where a sub-surface depositional pressure in the sand and in the sandwiching shale. The system is still intact. Noteworthy, most of the exploration relationship between predicted (PPP) and measured (MPP) play concepts and prospects are usually subjected to pore pressure is often complicated and establishing the structural deformation and breached seals. This leads to relationship involves analysis of the geologic setting and sub-surface communication between different reservoir compaction disequilibrium gradient (Shaker, 2002).
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Mudrock > Shale (0.61)
Summary: Gravity gradients often produce a complex pattern of anomalies over their sources. To understand this pattern and to aid in the interpretation of measured gravity gradient data, gravity gradient components of the full gradient tensor are computed starting with the basic gravitational potential, followed by computing the first derivatives and second derivatives of the potential. A diapiric salt model in a geologic setting similar to the US Gulf Coast is used for these computations; the results are displayed in color contour maps on which the model is projected for easy reference and interpretation of the data. Combinations of various gravity gradient components are also presented to enhance the anomalies associated with the model and to aid in the interpretation. It is also noticed that there are similarities between surface variations of the horizontal Gravity and Gravity Gradient components and subsurface variations of vertical Gravity and vertical Gravity Gradient (or anomalous Apparent Density) such as those observed in a borehole. Method: The use of measured gravity gradient data in exploration is becoming more common in recent years (Bell, et. al., 1997 , Pawlowski, 1998). Interpretation of Gravity gradient data, however, is not as easy as the familiar vertical gravity data. For a given source, gravity gradients often produce a complex pattern of anomalies (dipolar, tripolar, or quadropolar) as compared to the simple monopolar gravity anomalies. To understand the complex pattern of anomalies associated with gravity gradients, one starts with the basics, the gravitational potential, computes and examines the following : 1. the first derivatives of the potential in x, y, and z directions (Figure 1), i.e. the horizontal and vertical gravity field components, followed by : 2. the second derivatives of the potential (derivatives of each gravity component), to arrive at the Gravity Gradient components of the full tensor. The model used for this purpose, constructed with GOCAD, is a diapiric salt body placed within a sedimentary section whose density increases with depth. The upper part of the salt is above the “Nil” zone, thus having positive density contrasts with the surrounding sediments, while the lower part of the salt body has negative density contrasts; the “Nil” zone is that zone where the density of the surrounding sediments is identical to that of salt. Results: Figure 1 shows the Cartesian coordinate system convention used. Figure 2 shows color contour maps of the potential (P), and its first x, y, z derivatives (horizontal and vertical gravity components) with the salt model contours projected for reference. The potential shows mainly the broad negative anomaly due to the main salt body; the effect of the shallow part of the salt is not obvious although there is a subtle change in the contour spacing in the northeast direction. The first horizontal derivatives of the potential in x and y directions (P,x ; P,y) produce doublet anomalies, a negative – positive pair along the x and y axes, respectively These are coordinate-dependent and equivalent to the horizontal gravity components that would be measured by a horizontal gravimeter.
Abstract In case that the subsurface is not horizontal layered system, 2d seismic data of one CMP gather are not from the same plane and 2d velocity inversion is not accurate. In order to obtain more accurate interval velocities, this article invests a 3d inversion technique from conventional 2d line profiles. Given a 2d seismic time reflections and stacking velocities (or pre-stack CMP gather), time gradients of stacking velocities along the seismic line and normal to the seismic line are calculated. A 3d time model is then established, rays of the CMP gather extend to 3d space through Snell’s law and interactive modeling and inversion method. Eventually, 3-dimensional interval velocities and reflector positions corresponding to the input stacking velocities are calculated. Results of the synthetic model and real data example show that the 3d inversion technique is more accurate than 2d inversion in the case of 3d structures. In case of dipping multilayered subsurface with different dipping angles and azimuths and with that dipping angles and azimuths don’t change too much within one CMP gather, this method can give minimally biased velocity estimates. Key words: Interval velocity, 3D inversion, CMP gather Introduction Geophysicists are encountering more complicated structures with development of seismic exploration. Velocity model is one of the most important factors for geologists to know more details about complicated subsurface structures. One of the reasons is that seismic velocity determines the quality of seismic image, which is the basis of geologists to understand the geology structures of the whole region. Another reason is that the result map, which gives the closest look into the true subsurface structures, is also dependent closely on the accurate velocity field. So velocity analysis of seismic data through different methods is one of the most important tasks for geophysicists. At present, For a 2d seismic data, the velocity inversion methods only consider seismic waves traveling in 2d space. In the case of 3d multilayered structures, these kinds of methods are inaccurate in velocity inversion estimates. Sorin (1993) proposed a 3d velocity inversion technique which given conventional 2d seismic stack profiles and ray-path parameters of interchanging shot-geophone ray in routine 2D line. In this article, we invests a 3d inversion technique from conventional 2d line profiles and 2D stacking velocity or pre-stack CMP trace gather. Synthetic data example A six layer model with different dipping angles and different azimuths, shown in Figure 1, is established to test the proposed velocity inversion method. In the middle of the model, three seismic lines with 1km interval are designed along north-south and west-east respectively. The map of the seismic lines is shown in Figure 2. Zero-offset time sections of these lines and the stacking velocities at the intersections of the lines are obtained by ray-tracing the synthetic model. The stacking velocities are used to calculate interval velocities with the inversion technique proposed above. Table 1 shows the interval velocities of Line 02 (north-south) at intersect B by 2d and 3d inversion technique.
- Geophysics > Seismic Surveying > Seismic Processing (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling > Seismic Inversion (1.00)
A New Modular Sonic Tool Provides Complete Acoustic Formation Characterization
Pistre, V. (Schlumberger) | Plona, T. (Schlumberger) | Sinha, B. (Schlumberger) | Kinoshita, T. (Schlumberger) | Tashiro, H. (Schlumberger) | Ikegami, T. (Schlumberger) | Pabon, J. (Schlumberger) | Zeroug, S. (Schlumberger) | Shenoy, R. (Schlumberger) | Habashy, T. (Schlumberger) | Sugiyama, H. (Schlumberger) | Saito, A. (Schlumberger) | Chang, C. (Schlumberger) | Johnson, D. (Schlumberger) | Valero, HP. (Schlumberger) | Hsu, CJ. (Schlumberger) | Bose, S. (Schlumberger) | Hori, H. (Schlumberger) | Wang, C. (Schlumberger) | Endo, T. (Schlumberger) | Yamamoto, H. (Schlumberger) | Schilling, K. (Schlumberger)
Abstract An improved estimation of sonic slownesses and a Comprehensive mechanical characterization of the wellbore Rockrely on a complete characterization of the Compressional and shear slowness in terms of their radial, azimuthal, and axial variations. The new modular sonic tool accomplishes this by incorporating improved monopole and cross-dipole transmitter technology while featuring an extensive receiver array incorporating 13 axial levels of 8 azimuthal sensors each.Each receiver is individually digitized resulting in 104 waveforms per transmitter firing leading to an extremely reliable and accurate slowness estimation. This comes about through improved borehole mode extraction/rejection and enhanced wave number resolution at all frequencies. Formations exhibit wide, and sometimes complex, Acoustical behaviors ranging from isotropic, anisotropic With its various mechanisms and significant radial slowness gradients. Radial rock property variations arise because of non-uniform stress distributions and mechanical or chemical near-wellbore alteration due to the drilling process. Anisotropy can be caused by intrinsic shale properties or external differential stresses. The critical data required to invert for these rock parameters underlying these acoustic behaviors are derived from the new tool through the use of broadband dispersion curves associated with propagating borehole acoustic modes. In this paper, we highlight tool features that have an important impact on seismic, borehole seismic, and sonic applications. The acquired high quality waveforms and advanced processing techniques lead to improved compressional and shear slowness estimates, radial profiling of shear and compressional slowness, enhanced anisotropy detection and mechanism identification, and reliable through casing slowness measurements. Examples are shown from several wells in Norway and Mexico. Introduction
- North America > Mexico (0.50)
- Europe > Norway (0.35)
Introduction Summary I have derived a new approach to the iterative velocity updating procedure presented by Swan (2001). The moveout-corrected seismic gather parameterized by time vs. sinqmay be viewed as a broadband signal recorded across a linear receiver array. Velocity errors in this domain resemble plane waves impinging from a non-zero arrival angle. The direction of arrival is determined from the apparent instantaneous frequency of the recorded time slice. This estimated angle provides a measure of the velocity error for the time slice, and the velocity may then be easily updated for every time sample. Instantaneous frequency for a narrowband function is estimated by the derivative of the function divided by the function itself. The conventional AVO slope and intercept traces are used as the required estimates of the function and its derivative, respectively. One implementation of this method results in an algorithm equivalent to Swan’s, but a modified implementation results in an updating procedure without expensive Hilbert transforms or the determination of a frequency-related parameter. Seismic attributes from amplitude variation with offset have received much attention in recent years, most of which are based on the two-term approximation to the Zoeppritz equations (Shuey, 1985) r(t,q) = a(t) + b(t) sinqwhere r(t,q) is a gather of reflectivity vs. angle, a(t) and b(t) consist of the least squares linear regression intercepts and gradients, respectively, of the time slice corresponding to time t . The common denominator of the many attributes is that they all rely on accurate amplitude vs. offset (AVO) measurements of gradient and intercept. The most important requirement for accurate measurements is that the seismic gathers are flat, i.e. that the moveout velocities are correct. It has been well documented that errors in velocity lead to spurious responses in the AVO gradient which are in phase quadrature with the intercept (Spratt, 1987) (Figure 1b, 1d), and that these responses might be used to correct the velocity (Corcoran, et.al., 1991). A more robust velocity updating approach, using the analytic gradient and intercept traces, was introduced by Swan (2001). Implementation Residual Velocity from Plane Wave Dip The moveout curves for reflection times with velocity errors are linear with sinqThus, a window of an NMOcorrected gather with velocity error may be interpreted as a broadband plane wave recorded across a linear receiver array parameterized by distance c=sinq , with the magnitude of the error proportional to the dip (Figure 3). Taking each frequency separately, the windowed gather may be considered a composition of narrowband signals impinging across a linear receiver, where the “frequency” is measured spatially with respect to c. The recorded time slices are also narrowband, with an apparent spatial frequency that depends upon the “direction of arrival” (DOA), or plane wave dip (Figure 4). Equation (16) may be implemented in several ways, leading to different velocity updating schemes. The approach taken by Corcoran, et. al. starts with the recognition that the derivative A’ ?(w)=iwA(w)
Summary In the vicinity of Late Cretaceous mafic volcanic rocks the Ilhabela sandstones of the Santos Basin contain a high percentage of erosional products from these volcanics. This causes a complex mineral composition and diagenetic history that differs from the basin trend and results in completely different elastic properties. An enhanced AVO model is presented that takes these differences into account. Introduction A number of exploration wells in the Santos Basin offshore Brazil have penetrated the Late Cretaceous Ilhabela shallow marine deposits, a part of the Senonian Itajai Açu Formation. Most of the sandstones have a complex and immature mineralogical composition, and have been altered by multiple diagenetic processes. In addition to complex reservoir rock, the bounding lithologies include shale, siltstones and volcanic rocks, making interpretation of preand post-stack seismic reflection data difficult and problematic. The understanding of the petrophysical and especially the elastic properties of the Ilhabela sandstones, related to their genesis in conjunction with a sound regional geological model, is progressing. The results of currently ongoing exploration will contribute to the generation of a predictive seismic model, as the refined model will help to lower the exploration risk. Original AVO model and seismic observation Prior to drilling, a series of AVO models was generated from several nearby wells. One well, which had encountered the target formation at 4200m (Ilhabela deltaic sandstones, water bearing with approximately 12-15% porosity), was chosen to be representative of the target area of the pending well. The sandstone exhibits a higher velocity than the bounding shale, but a significantly lower density. As there were no measured shear wave data available, the Greenberg-Castagna relationship for Vp/Vs ratios in mixed lithologies was used for the model. The fluid substitution modelling showed that, in the brine and oil case, no observable AVO effects should occur, whereas the gas case shows a subtle class III AVO (negative intercept, and weak negative AVO gradient). Modelling has also shown that a decrease in Vshale and corresponding increase in porosity enhances the AVO effect. The analysis of partial stacks and prestack seismic data around the prospect area showed clear sandstone geometries (channels and stacked terminal lobes), and a subtle class III AVO anomaly. This anomaly appeared to match our gas model for a quartz sandstone with 12-15% porosity. Well results The well was drilled, and encountered a thick sand unit, covered by relatively high impedance shale (Fig.1). This sand unit is poorly sorted, and consists of a complex mixture of clays, quartz, feldspar, lithic fragments, volcanic rock fragments, and diagenetic minerals. Importantly, thin section analysis shows this sand seems to obtain a pseudo matrix build of thick diagenetic chlorite rimes. Beneath this main sand unit (Fig. 1), the well encountered a 50 meter thick, high impedance basaltic unit. Underlying this volcanic unit, a clean sandstone layer was encountered, composed predominantly of quartz, with lesser amounts of feldspar and calcite; this unit appears to be grain supported. This lower sand unit was not predicted from the 3D seismic for three reasons:
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Sandstone (1.00)
- Geology > Geological Subdiscipline (1.00)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Mudrock > Shale (0.84)
- South America > Brazil > Brazil > South Atlantic Ocean > Santos Basin (0.99)
- North America > United States > Texas > Permian Basin > Area Formation (0.99)
Summary The presence of wavelet stretch due to imaging presents serious difficulty in AVO or inversion analysis, especially for 3-term wide-angle analysis. Wavelet stretch significantly alters the gradient and wide-angle coefficient and reduces resolution of stacks. In this paper we present a method for correcting wavelet stretch that is exact for any v(z) (layered) medium. It does not depend on an underlying AVO/AVA approximation and is therefore applicable for 2- or 3-term AVA analysis. The required input is an extracted wavelet from any known reflection angle. The resulting correction operator is stationary over the time coordinate of the angle domain and is robustly implemented by a Weiner-Levinson method. This filter corrects angle gathers for wavelet stretch, producing improved resolution in subsequent angle stacks or gradient computations. Wavelet stretch correction is essential for linear inversion for density. Introduction The effect of imaging on a seismic wavelet, otherwise known as wavelet stretch, has been known for a long time (Buchholtz, 1972; Dunkin and Levin, 1973). The presence of wavelet stretch not only degrades stack resolution, it also poses a major difficulty in AVO/AVA studies that involve angles larger than 30 degrees. Wavelet stretch produces inaccurate gradients in 2-term AVA analysis as well as inaccurate densities in 3-term prestack inversion. Different authors have tried to correct for frequency loss due to wavelet stretch in different ways. Lazaratos and Finn (2004), and Dunkin and Levin (1973) correct for the loss by a linear filter that converts the stretched wavelet spectra to its unstretched counterpart. Lazaratos and Finn (2004) derive a stretch factor empirically through modeling. Their implementation is complicated since the stretch factor changes continuously as a function of time and offset and is therefore non-stationary. Swan (1997), Dong (1999), and Lin and Phair (1993) discuss offset-dependent tuning corrections for AVO analysis that can also be viewed as stretch corrections. With these methods the underlying AVO model only allows for correcting the gradient. In this paper we introduce a method to correct for wavelet stretch in the angle domain using a stationary operator for each angle. This method is exact for any v(z) media and does not require any AVO/AVA model assumption. The correction is exact for angle stacks with wide aperture (e.g. 45-60 degrees) and is beneficial for wide-angle inversion and AVA analysis as well as stack resolution enhancement. Theory The amount of stretch that a wavelet undergoes due to imaging appears to depend on the intercept time t, the source-receiver separation x, the interval velocity of the medium v and the rate at which the velocity varies with t. This is illustrated in Figure 1, which shows moveout curves converging as source-receiver separation (offset) increases. The differential intercept time d reduces to dt at an offset x. The application of an imaging operator (including a normal moveout correction) stretches dt back to dt. The goal of this paper is to calculate at a given offset x. This is the reciprocal of the stretch due to imaging for a v(z) (layered) medium.