Dariush Nadri

Estimation of stress-dependent anisotropy from P-wave measurements on a spherical sample

Our aim is to understand the stress-dependent seismic anisotropy of the overburden shale in an oil field in the North West Shelf of Western Australia. We analyze data from measurements of ultrasonic P-wave velocities in 132 directions for confining pressures of 0.1‐400 MPa on a spherical shale sample. First, we find the orientation of the symmetry axis, assuming that the sample is transversely isotropic, and then transform the ray velocities to the symmetry axis coordinates. We use two parameterizations of the phase velocity; one, in terms of the Thomsen anisotropy parameters a, b, e, d as the main approach, and the other in terms of a, b, g, d. We invert the ray velocities to estimate the anisotropy parameters a, e, d, and g using a very fast simulated reannealing algorithm. Both approaches result in the same estimation for the anisotropy parameters but with different uncertainties. The main approach is robust but produces higher uncertainties, in particular for g, whereas the alternative approach is unstable but gives lower uncertainties. These approaches are used to find the anisotropy parameters for the different confining pressures. The dependency of P-wave velocity, a, on pressure has exponential and linear components, which can be contributed to the compliant and stiff porosities. The exponential dependence at lower pressures up to 100 MPa corresponds to the closure of compliant pores and microcracks, whereas the linear dependence at higher pressures corresponds to contraction of the stiff pores. The anisotropy parameters e and d are quite large at lower pressures but decrease exponentially with pressure. For lower pressures up to 10 MPa, d always is larger than e; this trend is reversed for higher pressures. Despite the hydrostatic pressure, the symmetry axis orientation changes noticeably, in particular at lower pressures.

Sedimentary cyclicity from X-ray CT images in Campos Basin, Offshore Brazil

Small-scale changes in rock properties, such as those resulting from centimeter-scale depositional layering, are usually undetectable in standard borehole logs (Murphy et al., 1984). Even high-resolution logs with a small sampling interval (e.g., 2 inches) may still have a relatively large investigation volume. This presents a problem when we wish to capture the full variation in physical properties for purposes such as rock physics modeling.

Inversion Based Accuracy Comparison of Non-hyperbolic Moveout Approximations for P-waves in VTI Media

In this study we have quantified the accuracy of six most common non-hyperbolic traveltime approximations for P-waves in VTI media in terms of medium anisotropy and ratio of the maximum source offset to reflector depth. Our analysis is based on the inversion of P-wave traveltimes for VTI anisotropy parameters of the medium as we believe that the accuracy of the inversion results is directly related to the accuracy of traveltime approximation. Our analysis shows that among all, only approximation presented by Fomel and Stovas (2010) has enough accuracy to produce reliable estimates of VTI anisotropy parameters for both a wide range of medium anisotropy and wide offset /depth ratios.

Elasticity tensor inversion from spherical sample measurements

From the P-wave traveltime measurements over a spherical shale sample at 40 MPa we find the symmetry axis. We transform the ray velocities from the measurement coordinate system to the symmetry axis coordinate system. Assuming transverse isotropy symmetry

Estimation of Anisotropy Parameters Using the P-wave Velocities On a Cylindrical Shale Sample

Summary In this paper we present a new approach to the estimation of the Thomsen anisotropy parameters and symmetry axis coordinates from the P-wave traveltime measurements on cylindrical shale samples. Using the tomography-style array of transducers, we measure the ultrasonic P-wave ray velocities to estimate the Thomsen anisotropy parameters for a transversely isotropic shale sample. This approach can be used for core samples cut in any direction with regard to the bedding plane, since we make no assumption about the symmetry axis directions and will estimate it simultaneously with the anisotropy parameters. We use the very fast simulated re-annealing to search for the best possible estimate of the model parameters. The methodology was applied to a synthetic model and an anisotropic shale sample.

Inversion of Nonhyperbolic P-wave Traveltimes for Interval Transverse Isotropy Parameters

In this study, we analyse the accuracy of layer-stripping method to use P-wave reflection traveltimes in transverse isotropic media with vertical axis of symmetry (VTI) to estimate interval anisotropic parameters that are required for seismic processing. We also present a synthetic Walkaway VSP example in which a comparison can be made between the results of layer-stripping method and conventional method of using P-wave slownesses measured in a borehole. In the error analysis part, we quantify the errors of estimating interval Thomsen parameters, Epsilon and Delta for a horizontal VTI layer underneath a VTI overburden using noise free traveltimes computed by anisotropic ray tracing. Our analysis shows that both the parameters can be well constrained using traveltimes corresponding to maximum offset to depth ratio equal to 1 and overburden anisotropy plays no significant role in the accuracy of the inversions. On the other hand, parameter estimation using synthetic VSP data shows that an accurate and stable inversion requires traveltimes taken from spreads with maximum offset to depth ratio equal to 1.4 for Delta estimation and 4 for Epsilon estimation. The presented layer stripping-method also compares well with slowness based inversion using VSP data.

Tube Wave removal from vertical seismic profiling (VSP) surveys

Summary This paper presents a processing workflow to attenuate the strong tube waves from VSP surveys acquired in Perth, Western Australia. An array of 24 hydrophones spaced at 10 metre intervals is attached to a cable run down the borehole. The hydrophones were unclamped, so they record significant amount of the tube waves which entirely mask the upgoing waves. F-K filtering was used for wavefield decomposition of flattened downgoing waves. Linear moveout correction was applied to flatten the tube waves and removed unusual aliased energy due to shot depth variations and hydrophone positioning errors through the F-K filtering. The flattened data were transformed to tau-pi domain using a very narrow window slowness to produce a model of tube waves. An adaptive wavefield subtraction algorithm was used to subtract the tube wave model using a matching filter from the input data. The result was processed through a F-K filter and moderate tau-pi filter to remove the residual undesired energy. After attenuating the multiple energy and true amplitude recovery, pre stack depth migration, a CDP-VSP mapping and stacking were applied to produce CDP equivalent depth and time images.

An Estimation of Sonic Velocities in Shale Using Clay and Silt Fractions from the Elemental Capture Spectroscopy Log

Anisotropic differential effective medium approach is used to simulate elastic properties of shales from elastic properties and volume fractions of clay and silt constituents. Anisotropic elastic coefficients of the wet clay pack are assumed to be independent of mineralogy and to be linearly dependent on clay packing density (CPD), a fraction of clay in an individual wet clay pack. Simulated compressional and shear velocities normal to the bedding plane and are shown to be in a good agreement with measured sonic velocities. Further, elastic coefficients of shales, and , calculated from the log sonic velocities, calibrated porosity and clay fraction obtained from the mineralogy tool are used to invert for elastic constants of clays, C33 and C44. The obtained elastic coefficients of clays show lower scatter than the original elastic coefficients of shales. The noticeable increase of the clay elastic coefficients with the depth increase is shown to result from the positive trend of the CPD with depth. Being interpolated to the same CPD = 0.8, elastic coefficients of clays show no depth dependency. Our findings show that the CPD and silt fraction are the key parameters that can be used for successful modelling of elastic properties of shales.

Estimation of Thomsen Anisotropy Parameters Using the P-wave Velocities on a Cylindrical Shale Sample

In this paper we present a new approach to the estimation of Thomsen anisotropy parameters from laboratory data on cylindrical rock samples. Using tomography-style transducers array, ultrasonic P-wave ray velocities are measured on a transversely isotropic shale sample. This approach is applied to core samples cut along and normal to the bedding plane. Synthetic and actual laboratory data from an anisotropic shale specimen are used as examples. The fast simulated re-annealing method is used to search for the anisotropy parameters.

Estimation of elasticity tensor from the inversion of traveltimes in spherical shale samples

Due to sedimentation pattern of clay minerals, shal e formations generally show transverse isotropy (TI) with vertical axis of symmetry. The main motivation of t his study is to understand the seismic anisotropy of th e overburden shale. Geological formations in the regi on under study are generally experiencing a horizontal stress field. This stress field may cause azimuthal anisot ropy by either tilting the symmetry axis of shale formation s and/or causing the directional planes of weakness. To char a terize the seismic anisotropy, we have used P-wave travelt imes from a spherical shale core sample from the top of a sand reservoir. Unlike others, e.g Delinger (2005) and Vestrum and Brown (1994), we find the symmetry axis first a nd then invert for elasticity parameters to reduce the comp lexity of the inversion. Assuming TI symmetry, we have estima ted the elasticity tensor using the Simulating Annealin g followed by quasi Newton algorithm .