Decomposition of multicomponent sea‐floor data into upgoing and downgoing P‐ and S‐waves

Geophysics ◽  
1995 ◽  
Vol 60 (2) ◽  
pp. 563-572 ◽  
Author(s):  
Lasse Amundsen ◽  
Arne Reitan
Keyword(s):  
Particle Velocity ◽  
Layered Medium ◽  
Synthetic Data ◽  
Water Layer ◽  
S Wave ◽  
Sea Floor ◽  
S Waves ◽  
Sea Bottom ◽  
Marine Source ◽  
Horizontal Particle

A method for decomposing multicomponent sea‐floor measurements into upgoing and downgoing P‐ and S‐waves is presented. We assume that a marine survey employing a marine source in the water layer is conducted over a plane‐layered medium. From recordings of the pressure just above the sea floor and the particle velocity vector just below the sea floor, decomposition filters can be determined by plane‐wave analysis. The decomposition filter coefficients depend on the P‐ and S‐wave velocities and the density at the sea bottom. We show how to decompose the multicomponent measurements into upgoing and downgoing P‐ and S‐vertical traction components, vertical‐particle velocity components, and horizontal particle velocity components. The decomposition filters are applied with good results to synthetic data modeled in a plane‐layered medium.

Extraction of P‐ and S‐waves from the vertical component of the particle velocity at the sea floor

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 231-240 ◽  
Author(s):  
Lasse Amundsen ◽  
Arne Reitan
Keyword(s):  
Particle Velocity ◽  
Synthetic Data ◽  
Vertical Component ◽  
Transversely Isotropic ◽  
Vertical Axis ◽  
Elastic Stiffness ◽  
P Wave ◽  
S Wave ◽  
Sea Floor ◽  
S Waves

At the boundary between two solid media in welded contact, all three components of particle velocity and vertical traction are continuous through the boundary. Across the boundary between a fluid and a solid, however, only the vertical component of particle velocity is continuous while the horizontal components can be discontinuous. Furthermore, the pressure in the fluid is the negative of the vertical component of traction in the solid, while the horizontal components of traction vanish at the interface. Taking advantage of this latter fact, we show that total P‐ and S‐waves can be computed from the vertical component of the particle velocity recorded by single component geophones planted on the sea floor. In the case when the sea floor is transversely isotropic with a vertical axis of symmetry, the computation requires the five independent elastic stiffness components and the density. However, when the sea floor material is fully isotropic, the only material parameter needed is the local shear wave velocity. The analysis of the extraction problem is done in the slowness domain. We show, however, that the S‐wave section can be obtained by a filtering operation in the space‐frequency domain. The P‐wave section is then the difference between the vertical component of the particle velocity and the S‐wave component. A synthetic data example demonstrates the performance of the algorithm.

Removal of water‐layer multiples from multicomponent sea‐bottom data

Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 838-851 ◽  
Author(s):  
Are Osen ◽  
Lasse Amundsen ◽  
Arne Reitan
Keyword(s):  
Vertical Velocity ◽  
Water Layer ◽  
Real Data ◽  
Physical Principle ◽  
Sea Floor ◽  
Numerical Tests ◽  
Sea Bottom ◽  
Marine Source ◽  
Suppression Technique ◽  
Fundamental Physical

A method for suppressing water‐layer multiples in multicomponent sea‐floor measurements is presented. The multiple suppression technique utilizes the concept of wavefield separation into upgoing and downgoing modes just below the sea floor for eliminating the sea‐floor ghost, the sea‐surface ghost, and the accompanying water‐layer reverberations. The theory applies to each of the recorded components: pressure, vertical velocity, and horizontal velocities. The fundamental physical principle for the multiple suppression technique rests on identifying these multiples as downgoing waves just below the sea floor, while the primaries of interest arriving from the subsurface are upgoing waves. White presented this realization for the pressure component three decades ago; hence, the theory for the velocity field is an extension of the theory. In this paper, the theory is derived for an experiment with a marine source in the water layer above a locally flat, elastic sea floor with known elastic parameters. The method is otherwise multidimensional and operates on a shot‐to‐shot basis; hence, it is computationally fast. Aside from this, we show that this demultiple method removes the strongest multiples in sea‐floor data without knowledge of the source wavelet. Synthetic and real data examples are provided to illustrate the application of the algorithms to the pressure, in‐line velocity, and vertical velocity components. The numerical tests show that strong multiples have been attenuated on the pressure and the velocity recordings, producing promising results.

Data‐driven adaptive decomposition of multicomponent seabed recordings

Geophysics ◽  
2004 ◽  
Vol 69 (5) ◽  
pp. 1329-1337 ◽  
Author(s):  
Remco Muijs ◽  
Johan O. A. Robertsson ◽  
Klaus Holliger
Keyword(s):  
Water Layer ◽  
P Wave ◽  
Data Driven ◽  
Minimal Amount ◽  
S Wave ◽  
Sea Floor ◽  
Decomposition Scheme ◽  
Wave Potential ◽  
Dual Sensor ◽  
Adaptive Decomposition

Dual‐sensor (hydrophone and three‐component geophone) data recorded on the sea floor allow the elastic wavefield to be decomposed into its upgoing and downgoing P‐ and S‐wave components. Most decomposition algorithms require accurate knowledge of the elastic properties of the sea floor in the vicinity of the receivers and properly calibrated sensors, in order for the data to be a faithful vector representation of the ground motion. We present a multistep adaptive decomposition scheme that provides the necessary information directly from the data by imposing constraints on intermediate decomposition results. The proposed scheme requires no a priori information and only a minimal amount of user‐defined input, thus allowing multicomponent data to be decomposed in an automated data‐driven fashion. The performance of the technique is illustrated using seabed data acquired in the North Sea with prototype single sensors (multicomponent geophones individually sampled). Realistic sea floor properties and sensor calibration operators are obtained, and elastic decomposition of the calibrated data generally yields good results. Dominant water‐layer reverberations are successfully attenuated and primary reflections are substantially enhanced in the computed upgoing P‐wave potential just below the sea floor. In contrast, the result for the upgoing S‐wave potential is somewhat less convincing; although the energy of water‐layer multiples is substantially reduced, notable amounts of undesired multiple energy remain in this section after decomposition, particularly at high offsets. These imperfections may point to inaccuracies in the parametrization of the sea floor or remaining inaccuracies in the vector fidelity of the horizontal geophone recordings. Nevertheless, the results obtained with the extended data‐driven decomposition scheme are at least comparable to previously published results.

A two‐layer stacking procedure to enhance converted waves

Geophysics ◽  
1993 ◽  
Vol 58 (7) ◽  
pp. 997-1001 ◽  
Author(s):  
B. L. N. Kennett
Keyword(s):  
Lower Layer ◽  
Effective Means ◽  
Water Layer ◽  
Physical Models ◽  
S Wave ◽  
P Waves ◽  
S Waves ◽  
Receiver Array ◽  
Sea Bed ◽  
Layer Stacking

For marine seismic sources quite efficient conversion of P‐waves to S‐waves can occur at hard seafloors, e.g., carbonate horizons in tropical waters. The S‐waves are reflected back from structures at depth and are reconverted to P‐waves in the water before detection by the receiver array. Such PSSP reflections can carry useful information on the structure beneath the sea bed but are most significant at large offsets and so are not easily stacked with a conventional normal moveout (NMO) procedure based on a hyperbolic time trajectory. A two‐layer stacking procedure that separates the water layer from the region below the seafloor provides a very effective means of extracting the PSSP arrivals, but also works well for P‐waves. There is no direct analytic form for the stacking trajectories but they can be calculated quite efficiently numerically. A further advantage is that the stacking velocity for S‐waves in the lower layer can be interpreted directly in terms of S‐wave propagation, so that S‐wave interval velocities can be found. Stacking procedures based on such simple physical models are likely to be useful in other cases where attention needs to be focused on a particular aspect of the wavefield.

Estimation of sea‐floor wave velocities and density from pressure and particle velocity by AVO analysis

Geophysics ◽  
1995 ◽  
Vol 60 (5) ◽  
pp. 1575-1578 ◽  
Author(s):  
Lasse Amundsen ◽  
Arne Reitan
Keyword(s):  
Numerical Study ◽  
Offshore Structures ◽  
P Wave ◽  
Rock Properties ◽  
Sea Floor ◽  
S Waves ◽  
Interface Waves ◽  
Wave Velocities ◽  
Sea Bottom ◽  
Sea Bed

Sea‐bottom properties play an important role in fields as diverse as underwater acoustics, earthquake and geotechnical engineering, and marine geophysics. Water‐column acousticians study shear and interface waves in the nearbottom sediments with the aim of inferring sea‐bed geoacoustic parameters for predicting reflection and absorption of waves at the sea floor. On the other hand, geotechnical engineers working on design and siting of offshore structures focus on these waves to characterize soil and rock properties. In the field of geophysics, sea‐bottom parameters are of interest for several reasons. In conventional marine acquisition, these parameters determine the partitioning of the incident P‐wave energy from the source into transmitted P‐waves and mode‐converted S‐waves (Tatham and Goolsbee, 1984; Kim and Seriff, 1992). The sea‐floor P‐ and S‐wave velocities and density are also necessary inputs for decomposing multicomponent sea‐floor data into P‐ and S‐waves (Amundsen and Reitan, 1995a and b), as well as in the numerical study of wave propagation phenomena.

Reverse time migrations in transversely isotropic media: A comparison between acoustic and elastic wave equations with two wave mode separation algorithms

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. C95-C105 ◽  
Author(s):  
Wenlong Wang ◽  
Biaolong Hua ◽  
George A. McMechan ◽  
Paul Williamson
Keyword(s):  
Elastic Wave ◽  
Wave Equations ◽  
Synthetic Data ◽  
Low Rank ◽  
Reverse Time ◽  
S Wave ◽  
Data Set ◽  
S Waves ◽  
Elastic Wave Equations ◽  
Anisotropic Elastic

Anisotropic reverse time migrations (RTMs) using pseudoacoustic or elastic wave equations are tested, and the migrated PP images, obtained using the same data set as input, are compared. In anisotropic elastic RTMs, both divergence operators, and localized low-rank approximations (LLA), are tested and compared for P/S separation. Tests with synthetic data indicate that elastic RTMs have better illumination apertures than pseudoacoustic RTMs in subsalt areas because of the involvement of converted S-waves in the former. Pseudoacoustic RTMs have diamond-shaped S-wave artifacts, which do not exist in elastic RTM images, provided that the P- and S-waves are separated in the elastic wavefields. LLAs provide affordable, accurate P/S separations in anisotropic media, and the separation results are better than those obtained using divergence operators. Anisotropic elastic RTMs with LLA give the best quality images.

Separation and enhancement of split S‐waves on multicomponent shot records from the BIRPS WISPA experiment

Geophysics ◽  
1994 ◽  
Vol 59 (1) ◽  
pp. 131-139 ◽  
Author(s):  
M. Boulfoul ◽  
D. R. Watts
Keyword(s):  
Synthetic Data ◽  
P Wave ◽  
Moving Window ◽  
Wave Analysis ◽  
S Wave ◽  
Near Surface ◽  
S Waves ◽  
Wave Velocities ◽  
Wave Splitting ◽  
Explosive Source

Instantaneous rotations are combined with f-k filtering to extract coherent S‐wave events from multicomponent shot records recorded by British Institutions Reflection Profiling Syndicate (BIRPS) Weardale Integrated S‐wave and P‐wave analysis (WISPA) experiment. This experiment was an attempt to measure the Poisson’s ratio of the lower crest by measuring P‐wave and S‐wave velocities. The multihole explosive source technique did generate S‐waves although not of opposite polarization. Attempts to produce stacks of the S‐wave data are unsuccessful because S‐wave splitting in the near surface produced random polarizations from receiver group to receiver group. The delay between the split wavelets varies but is commonly between 20 to 40 ms for 10 Hz wavelets. Dix hyperbola are produced on shot records after instantaneous rotations are followed by f-k filtering. To extract the instantaneous polarization, the traces are shifted back by the length of a moving window over which the calculation is performed. The instantaneous polarization direction is computed from the shifted data using the maximum eigenvector of the covariance matrix over the computation window. Split S‐waves are separated by the instantaneous rotation of the unshifted traces to the directions of the maximum eigenvectors determined for each position of the moving window. F-K filtering is required because of the presence of mode converted S‐waves and S‐waves produced by the explosive source near the time of detonation. Examples from synthetic data show that the method of instantaneous rotations will completely separate split S‐waves if the length of the moving window over which the calculation is performed is the length of the combined split wavelets. Separation may be achieved on synthetic data for wavelet delays as small as two sample intervals.

A wavefield-separation-based elastic least-squares reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. S279-S297 ◽  
Author(s):  
Bingluo Gu ◽  
Zhenchun Li ◽  
Jianguang Han
Keyword(s):  
Least Squares ◽  
Synthetic Data ◽  
P Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
S Waves ◽  
Numerical Tests ◽  
Time Migration

Elastic least-squares reverse time migration (ELSRTM) has the potential to provide improved subsurface reflectivity estimation. Compared with elastic RTM (ERTM), ELSRTM can produce images with higher spatial resolution, more balanced amplitudes, and fewer artifacts. However, the crosstalk between P- and S-waves can significantly degrade the imaging quality of ELSRTM. We have developed an ELSRTM method to suppress the crosstalk artifacts. This method includes three crucial points. The first is that the forward and backward wavefields are extrapolated based on the separated elastic velocity-stress equation of P- and S-waves. The second is that the separated vector P- and S-wave residuals are migrated to form reflectivity images of Lamé constants [Formula: see text] and [Formula: see text] independently. The third is that the reflectivity images of [Formula: see text] and [Formula: see text] are obtained by the vector P-wave wavefields achieved in the backward extrapolation of the separated vector P-wave residuals and the vector S-wave wavefields achieved in the backward extrapolation of the separated vector S-wave residuals, respectively. Numerical tests with synthetic data demonstrate that our ELSRTM method can produce images free of crosstalk artifacts. Compared with ELSRTM based on the coupled wavefields, our ELSRTM method has better convergence and higher accuracy.

Empirical studies of some of the seismic phenomena of Hawaii*

1938 ◽  
Vol 28 (4) ◽  
pp. 313-337
Author(s):  
Austin E. Jones
Keyword(s):  
P Wave ◽  
Secondary Peak ◽  
S Wave ◽  
S Waves ◽  
Mauna Loa ◽  
Earthquake Records ◽  
Type K ◽  
Sea Bottom ◽  
The Difference ◽  
The Waves

Summary and Conclusions A comparison was made of all the periods of local earthquakes entered in the record books, and this showed that the P wave of 0.3-sec. period occurred a maximum of 156 times, and a secondary peak for the period of 0.5 sec. occurred 89 times. The S wave of 0.5-sec. period had a maximum of 129 occurrences, and a secondary peak for 0.8-sec. period had 100. This suggested that in any earthquake the ratio of the period of the S to the P wave was inversely as their velocities, or as the square root of three. The maxima just given appear to hold for such waves from all depths of origin. It had been noted previously that large amplitudes and periods occur together. The upper limits of the amplitudes of the P and S waves of local shocks were found to vary with the cube of the periods. Different results were found for the variation of epicentral shocks in California and Japan. The difference may be caused by the difference in physical characteristics of the underlying crustal rock. While these studies in Hawaii were made on shocks of intensities I to IV, Rossi-Forel, they show promise of giving information about the waves to be expected in destructive earthquakes. The sectorial lines may be raised by new data, but in each region should approach some unknown lines as a limit. Formulas were used to correct the observed waves to those of standard displacement and consequent period. These periods were plotted with respect to distance and depth, with no reliable result. A tendency was shown for the period of P waves to increase with distance more rapidly than the period of S waves, whereas observations of more distant earthquakes would suggest the opposite. Study of the ratios of the amplitudes of the P to the S wave (AP/SS) showed no distance effect. The formulas from the previous amplitude-period study suggest that this ratio should not vary with the local distance. For Hawaii the ratio averages about 15 per cent. About 60 per cent of the foci are less than 5 km. deep, 70 per cent less than 10 km. deep. Very few appear to have originated at 60 or more km. depth. The decline in numbers of earthquakes with depth is a rapidly decreasing exponential function. Most of the deep earthquakes are under Mauna Loa and the Kilauea southeast rift zone. A large number of the located shallow foci are in and near the Kilauea crater. Possibly this is an increase that should be expected near any active volcanic crater, but it may be due to the close network of stations about Kilauea crater. The magnitude of the shock is not a function of the location either areally or in depth; that is, large earthquakes may be expected in any part of the island and near-by sea bottom and at all depths to at least 60 km. A method of classifying the earthquake records is based on the number of P or S waves shown on the seismogram, which indicate the key number from one to seven. A map of Hawaii was constructed showing the areas in which the different types of shock had originated. The first type, K-1, occurs either central to Mauna Loa or within 50 to 60 km. radius of the seismograph. Type K-2 is not recorded from northwest Hawaii. Type K-3 does not occur close to the instruments. Types K-4 to K-7 are noted to occur at somewhat greater distances, and to date have been observed only from small outlying areas. Earthquake records of simple character are generally near the area of deep-focus shocks and near the seismographs, so that the waves come in at a steep angle. Earthquakes under Kilauea crater are generally simple. As the foci become more distant and shallow they also become more complicated in type. These criteria should help in designating phases and consequent locations, but they are not final, and may be of no help beyond 100 km. The number of phases in some of the records of outlying earthquakes suggest a complexity of structure in the island mass and the near-by sea bottom. The locations near and on the extension of rifts and in pronounced lines and zones suggest a larger and more numerous system of rifts than has previously been mapped. The resulting pattern of rifts about Mauna Loa is roughly an asterisk. The main accent is on the visible active rifts to the southwest and the east-northeast of Mokuaweoweo. These rifts have apparently controlled most of the island's seismicity in the immediate past.

scholarly journals Responses of dipole-source reflected shear waves in acoustically slow formations

2019 ◽  
Author(s):  
Hao Wang ◽  
Ning Li ◽  
Caizhi Wang ◽  
Hongliang Wu ◽  
Peng Liu ◽  
...  
Keyword(s):  
Finite Difference Time Domain ◽  
Dipole Source ◽  
Sh Wave ◽  
S Wave ◽  
High Fracture ◽  
S Waves ◽  
Angle Fracture ◽  
Dip Angle ◽  
Difference Time

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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