Array Of Receivers In Borehole Research Articles

A Method for Estimating the Green's Function of a Near-Surface Layer for SH-Waves by Means of a Borehole Receiver Array

Abstract I herein propose a new method for estimating the true Green’s function of a near-surface layered structure for SH waves at the borehole receiver depth from the apparent Green’s function that contains downgoing waves from the upper layers and the free surface. These Green’s functions are defined using transfer functions in the z -transform domain. The information required for the proposed method is a set of pole frequencies that are the frequencies at which the transfer function (the input and output of which are borehole and surface recordings, respectively) has poles. The real part of the true Green’s function is related to the gain function of this transfer function for a perfectly elastic lossless medium, and the imaginary part is connected to the real part by means of a Kramers–Kronig relation. The results obtained by applying the proposed method to actual borehole receiver array recordings show that convolutions of the impulse response of the estimated reciprocal of the Green’s function and surface recordings successfully output upcoming and downgoing waves at the borehole receiver depth. As a result, the synthesized borehole wave is in good agreement with the recorded borehole wave.

Imaging internal multiples from subsalt VSP data — Examples of target-oriented interferometry

Seismic interferometry has become a technology of growing interest for imaging borehole seismic data. We demonstrate that interferometry of internal multiples can be used to image targets above a borehole receiver array. By internal multiples, we refer to all types of waves that scatter multiple times inside the model. These include, for instance, interbed, intrasalt, and water-bottom multiples as well as conversions among them. We use an interferometry technique that is based on representation theorems for perturbed media and targets the reconstruction of specific primary reflections from multiply reflected waves. In this interferometry approach, we rely on shot-domain wavenumber separation to select the directions of waves arriving at a given receiver. Using a numerical walkaway (WAW) VSP experiment recorded by a subsalt borehole receiver array in the Sigsbee salt model, we use the interference of internal multiples to image the salt structure from below. In this numerical example, the interferometric image that uses internal multiples reconstructs the bottom- and top-of-salt reflectors above the receiver array as well as the subsalt sediment structure between the array and the salt. Because of the limited source summation in this interferometry example, the interferometric images show artifact reflectors within the salt body. We apply this method to a field walkaway VSP from the Gulf of Mexico. With the field data, we demonstrate that the choice of shot-domain wavenumbers in the target-oriented interferometry procedure controls the wavenumbers in the output pseudoshot gathers. Target-oriented interferometric imaging from the 20-receiver array recovers the top-of-salt reflector that is consistent with surface seismic images. We present our results with both correlation-based and deconvolution-based interferometry.

Local Determination of Weak Anisotropy Parameters from Walkaway VSP qP-Wave Data in the Java Sea Region

We apply the inversion scheme of Zheng and Pysenyc´ok (2002) to the walkaway VSP data of Horne and Leaney (2000) collected in the Java Sea region. The goal is a local determination of parameters of the medium surrounding the borehole receiver array. The inversion scheme is based on linearized equations expressing qP-wave slowness and polarization vectors in terms of weak anisotropy (WA) parameters. It thus represents an alternative approach to Horne and Leaney (2000), who based their procedure on inversion of the Christoffel equation using a global optimization method. The presented inversion scheme is independent of structural complexities in the overburden and of the orientation of the borehole. The inverson formula is local, and has therefore potential to separate effects of anisotropy from effects of inhomogeneity. The data used are components of the slowness vector along the receiver array and polarization vectors. The inversion is performed without any assumptions concerning the remaining components of the slowness vector. The inversion is made (a) assuming arbitrary anisotropy, i.e., without any assumptions about symmetry of the medium, (b) assuming transverse isotropy with a vertical axis of symmetry and (c) assuming isotropy of the medium. Inverted are the raw data as well as data, in which weighting is used to reduce the effect of outliers. It is found that the WA parameters ǫz, ǫ15 and ǫ35 are considerably more stable than the parameters ǫx and δx. The latter two parameters are also found to be strongly correlated. Weaker correlation is also found between the mentioned two parameters and ǫz. The results of inversion show clearly that the studied medium is not isotropic. They also seem to indicate that the studied medium does not possess the VTI symmetry.