Chapter 13: Wavefield Decomposition into P- and S-waves, and Upgoing and Downgoing Waves

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. S57-S79 ◽  
Author(s):  
Chen Tang ◽  
George A. McMechan

Elastic reverse time migration (E-RTM) has limitations when the migration velocities contain strong contrasts. First, the traditional scheme of P/S-wave mode separation is based on Helmholtz’s equations, which ignore the conversion between P- and S-waves at the current separation time. Thus, it contains an implicit assumption of the constant shear modulus and requires smoothing the heterogeneous model to approximately satisfy a locally constant condition. Second, the vector-based imaging condition needs to use the reflection-image normal, and it also cannot give the correct polarity of the PP image in all possible conditions. Third, the angle-domain common-image gathers (ADCIGs) calculated using the Poynting vectors (PVs) do not consider the wave interferences that happen at each reflector. Therefore, smooth models are often used for E-RTM. We relax this condition by proposing an improved data flow that involves three new contributions. The first contribution is an improved system of P/S-wave mode separation that considers the converted wave generated at the current time, and thus it does not require the constant-shear-modulus assumption. The second contribution is the new elastic imaging conditions based on multidirectional vectors; they can give the correct image polarity in all possible conditions without knowledge of the reflection-image normal. The third contribution is two methods to calculate multidirectional propagation vectors (PRVs) for RTM images and ADCIGs: One is the elastic multidirectional PV, and the other uses the sign of wavenumber-over-frequency ([Formula: see text]) ratio obtained from an amplitude-preserved approximate-propagation-angle-based wavefield decomposition to convert the particle velocities into multidirectional PRVs. The robustness of the improved data flow is determined by several 2D numerical examples. Extension of the schemes into 3D and amplitude-preserved imaging conditions is also possible.


Geophysics ◽  
2003 ◽  
Vol 68 (3) ◽  
pp. 1091-1102 ◽  
Author(s):  
K. M. Schalkwijk ◽  
C. P. A. Wapenaar ◽  
D. J. Verschuur

With wavefield decomposition, the recorded wavefield at a certain depth level can be separated into upgoing and downgoing wavefields as well as into P‐ and S‐waves. The medium parameters at the considered depth level (e.g., just below the ocean‐bottom) need to be known in order to be able to do a decomposition. In general, these parameters are unknown and, in addition, measurement‐related issues, such as geophone coupling and crosstalk between the different components, need to be dealt with. In order to apply decomposition to field data, an adaptive five‐stage decomposition scheme was developed in which these issues are addressed. In this study, the adaptive decomposition scheme is tested on a data example with a relatively shallow water depth (∼120 m), consisting recordings from of a full line of ocean‐bottom receivers. Although some of the individual stages in the decomposition scheme are more difficult to apply because of stronger interference between events compared to data acquired over deeper water, the end result is satisfying. Also, a good decomposition result is obtained for the S‐waves. The extension of the decomposition scheme to a complete line of ocean‐bottom cable data consists of a repeated application of the procedure for each receiver. The resulting decomposed upgoing P‐ and S‐wavefields are processed, yielding poststack time migrated images of the subsurface. Comparison with the images obtained from the original (i.e., not decomposed) measurements shows that wavefield decomposition just below the ocean bottom leads to a strong attenuation of multiply reflected events at the sea surface and better event definition in both P‐ and S‐wave sections. Other decomposition effects like improved angle‐dependent amplitudes cannot be evaluated in this way.


Geophysics ◽  
2002 ◽  
Vol 67 (6) ◽  
pp. 1972-1982 ◽  
Author(s):  
Remco Muijs ◽  
Klaus Holliger ◽  
Johan O. A. Robertsson

Dense spatial recording patterns of three‐component (3C) receivers allow for direct wavefield decomposition through explicit calculation of divergence and curl of the recorded elastic wavefield. Since this approach is based upon the observation of small phase shifts, it requires highly accurate deployment of the receiver configurations. To study the feasibility of a recently proposed P/S‐wave separation scheme, we systematically assess the effects of position and orientation errors of one or several geophones within the recording pattern on technique performance. We find that realistic deployment errors can significantly affect estimates of the divergence and curl of particle velocity. The errors induced by mispositioned or misoriented geophones differ for each of the geophones that make up a pattern. Moreover, the inaccuracies vary with the angle of incidence, potentially affecting analysis procedures applied to the data at a later stage, such as amplitude variation with offset (AVO). Based on a relative L1‐criterion, the position of each receiver needs to be accurate within 10% of the length of the sides of the configuration to obtain meaningful divergence and curl estimates. Furthermore, the output is particularly sensitive to misorientations of geophones, requiring that the orientations of all geophones be accurate within 2°. These observations point to significant difficulties when applying this technique. To alleviate this problem, we present an approach to detect and compensate for such deployment‐related inaccuracies prior to explicit P/S‐wave separation. This strategy is based on a pyramid‐shaped receiver configuration and relies on minimizing the differences between the divergence and curl estimates calculated over the pyramid and each of the four subtetrahedra that comprise the pyramid.


Author(s):  
I. A. Shibaev ◽  
V. A. Vinnikov ◽  
G. D. Stepanov

Geological engineering often uses geomechanical modeling aimed to enhance efficiency of mining or performance of structures. One of the input parameters for such models are the static elastic moduli of rocks. This article presents the studies into the physical and mechanical properties of rocks-limestone of non-metamorphic diagenesis. The precision measurements of Pand S-waves are carried out to an accuracy of 0.2% by laser ultrasonics. The static moduli of elasticity and the deformation characteristics of rocks are determined in the uniaxial compression tests by the standards of GOST 21153.2-84 and GOST 28985-91, respectively. The correlation dependence is found between the static and dynamic elasticity moduli in limestone samples. The found correlation allows drawing the conclusion that the static modulus of elasticity can be estimated in non-destructive tests, which largely simplifies preliminary diagnostics of samples in case of limited number of test core.


Author(s):  
Hao Wang ◽  
Ning Li ◽  
Caizhi Wang ◽  
Hongliang Wu ◽  
Peng Liu ◽  
...  

Abstract In the process of dipole-source acoustic far-detection logging, the azimuth of the fracture outside the borehole can be determined with the assumption that the SH–SH wave is stronger than the SV–SV wave. However, in slow formations, the considerable borehole modulation highly complicates the dipole-source radiation of SH and SV waves. A 3D finite-difference time-domain method is used to investigate the responses of the dipole-source reflected shear wave (S–S) in slow formations and explain the relationships between the azimuth characteristics of the S–S wave and the source–receiver offset and the dip angle of the fracture outside the borehole. Results indicate that the SH–SH and SV–SV waves cannot be effectively distinguished by amplitude at some offset ranges under low- and high-fracture dip angle conditions, and the offset ranges are related to formation properties and fracture dip angle. In these cases, the fracture azimuth determined by the amplitude of the S–S wave not only has a $180^\circ $ uncertainty but may also have a $90^\circ $ difference from the actual value. Under these situations, the P–P, S–P and S–S waves can be combined to solve the problem of the $90^\circ $ difference in the azimuth determination of fractures outside the borehole, especially for a low-dip-angle fracture.


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