Wavefield separation using densely deployed three‐component single‐sensor groups in land surface‐seismic recordings

Geophysics ◽  
2002 ◽  
Vol 67 (5) ◽  
pp. 1624-1633 ◽  
Author(s):  
Johan O. A. Robertsson ◽  
Andrew Curtis
Keyword(s):  
Free Surface ◽  
Seismic Data ◽  
Land Surface ◽  
Material Constant ◽  
Normal Incidence ◽  
S Wave ◽  
P Waves ◽  
Wavefield Separation ◽  
Single Sensor ◽  
Spatial Derivatives

Surface seismic data are usually acquired by placing receivers on the earth's free surface. This is exactly the surface at which all up‐coming wave energy is reflecting and converting into down‐going energy, so the wavefield recorded is the sum of up‐coming, down‐going reflected, and down‐going converted waves. In order to anaylze up‐coming (from the reservoir) energy only (e.g., for “true” amplitude analysis), it is necessary to separate and remove all down‐going waves from the recorded data. We present a new approach for wavefield separation of land surface‐seismic data based on receiver groups with densely deployed single‐sensor recordings. By converting vertical spatial derivatives to horizontal derivatives using the free‐surface condition, the methodology only requires locally dense measurements of the wavefield at the free surface to calculate all spatial derivatives of the wavefield. These can in turn be used to compute divergence (giving P‐wave potential) and curl (giving S‐wave potential) of the wavefield at the free surface. The effects of the free surface are removed through an up/down separation step using the elastodynamic representation theorem. This results in infinite spatial‐filter expressions that are appropriate for homogeneous media. The filter for P‐waves depends on both P‐ and S‐velocity at the receivers, whereas the S‐wave filters only depend on the S‐velocity. These velocities can be estimated using the techniques in the companion paper by Curtis and Robertsson in this issue. Spatially compact filters are chosen to approximate the analytical filter expressions. The filters are designed so that they can be applied within a densely deployed, spatially limited group of three‐component (3C) receivers. By assuming that the earth is locally homogeneous (no significant variations within the near‐surface region of the group), wavefield separation can be carried out also in areas with significant statics variations over the survey area. In particular, the simplest approximate expression for P‐waves consists of two terms. The first term corresponds to divergence in the presence of the free surface scaled by a material constant. The second term is a time derivative of the recorded vertical component scaled by a material constant. Hence, the first term is a correction that is added to the “traditional” P‐interpretation—the second term—which improves accuracy for incidence angles other than normal incidence. The proposed methodology is tested on synthetic data. By comparing “traditional” P‐sections to those obtained using the new methodology, we demonstrate that a significant improvement in amplitudes and phases of arrivals is obtained using the new methodology. By using the simplest possible filter which only involves first‐order derivatives in time and space, we obtained sufficiently accurate results up to incidence angles of around 30° away from normal incidence.

Geometrical spreading in a layered transversely isotropic medium with vertical symmetry axis

Geophysics ◽  
2003 ◽  
Vol 68 (6) ◽  
pp. 2082-2091 ◽  
Author(s):  
Bjørn Ursin ◽  
Ketil Hokstad
Keyword(s):  
Ray Tracing ◽  
Seismic Data ◽  
Symmetry Axis ◽  
Transversely Isotropic ◽  
Analytical Approximation ◽  
Geometrical Spreading ◽  
S Wave ◽  
Weak Anisotropy ◽  
P Waves ◽  
Amplitude Versus

Compensation for geometrical spreading is important in prestack Kirchhoff migration and in amplitude versus offset/amplitude versus angle (AVO/AVA) analysis of seismic data. We present equations for the relative geometrical spreading of reflected and transmitted P‐ and S‐wave in horizontally layered transversely isotropic media with vertical symmetry axis (VTI). We show that relatively simple expressions are obtained when the geometrical spreading is expressed in terms of group velocities. In weakly anisotropic media, we obtain simple expressions also in terms of phase velocities. Also, we derive analytical equations for geometrical spreading based on the nonhyperbolic traveltime formula of Tsvankin and Thomsen, such that the geometrical spreading can be expressed in terms of the parameters used in time processing of seismic data. Comparison with numerical ray tracing demonstrates that the weak anisotropy approximation to geometrical spreading is accurate for P‐waves. It is less accurate for SV‐waves, but has qualitatively the correct form. For P waves, the nonhyperbolic equation for geometrical spreading compares favorably with ray‐tracing results for offset‐depth ratios less than five. For SV‐waves, the analytical approximation is accurate only at small offsets, and breaks down at offset‐depth ratios less than unity. The numerical results are in agreement with the range of validity for the nonhyperbolic traveltime equations.

Real data results of Kirchhoff elastic wave migration

Geophysics ◽  
1986 ◽  
Vol 51 (4) ◽  
pp. 1006-1011 ◽  
Author(s):  
Ting‐Fan Dai ◽  
John T. Kuo
Keyword(s):  
Seismic Data ◽  
Real Data ◽  
Horizontal Layer ◽  
S Wave ◽  
P Waves ◽  
S Waves ◽  
Surface Data ◽  
And Migration ◽  
Wave Migration ◽  
Kirchhoff Integral

Although Kirchhoff integral migration has attracted considerable attention for seismic data processing since the early 1970s, it, like all other seismic migration methods, is only applicable to compressional (P) waves. Because of a recent surge of interest in shear (S) waves, Kuo and Dai (1984) developed the Kirchhoff elastic (P and S) wave migration (KEWM) formulation and migration principle for the case of source and receiver noncoincidence. They obtained encouraging results using two‐dimensional (2-D) synthetic surface data from various geometric elastic models, including a dipping layer, a composite dipping and horizontal layer, and two layers over a half‐space.

A case study showing the value of multioffset synthetic seismograms in seismic data interpretation

2016 ◽  
Vol 4 (4) ◽  
pp. T455-T459 ◽  
Author(s):  
J. Helen Isaac ◽  
Don C. Lawton
Keyword(s):  
Seismic Data ◽  
Upper Cretaceous ◽  
Normal Incidence ◽  
High Amplitude ◽  
Synthetic Seismogram ◽  
Synthetic Seismograms ◽  
Seismic Survey ◽  
Research Station ◽  
S Wave ◽  
Low Amplitude

A baseline 3D3C seismic survey was acquired in May 2014 at a Field Research Station in Southern Alberta, Canada, which is the site of experimental [Formula: see text] injection into an Upper Cretaceous sandstone at approximately 300 m depth. We have created synthetic seismograms from sonic and density logs to identify reflectors seen on the processed seismic data. The high-amplitude positive response (peak) at the top of the Upper Cretaceous Milk River Formation sandstone on the normal incidence PP synthetic seismogram does not match the response seen on the migrated PP seismic data, which is a very low amplitude peak. For such a high impedance, low Poisson’s ratio sandstone, the Zoeppritz equations predict a high-amplitude reflection coefficient at zero offset, then a decrease in amplitude, and even a change in polarity with increasing source-receiver offset. To match the stacked seismic data better, we have created offset synthetic seismograms using P- and S-wave sonic logs and density logs. The character of the top Milk River reflection on the seismic data stacked using all offset traces resembles that observed on the stacked offset synthetic seismogram, which is a similar low-amplitude peak. The character of the top Milk River reflection on the seismic data stacked using only near-offset traces to 250 m looks like that seen on the normal incidence synthetic seismogram.

Attenuating primaries and free‐surface multiples of vertical cable (VC) data while preserving receiver ghosts of primaries

Geophysics ◽  
2001 ◽  
Vol 66 (3) ◽  
pp. 953-963 ◽  
Author(s):  
Luc T. Ikelle
Keyword(s):  
Free Surface ◽  
Seismic Data ◽  
Ocean Bottom ◽  
Direct Wave ◽  
Sea Floor ◽  
Multiple Attenuation ◽  
Wavefield Separation ◽  
Internal Multiples ◽  
Streamer Data ◽  
Imaging Algorithms

Marine vertical cable (VC) data contain primaries, receiver ghosts, free‐surface multiples, and internal multiples just like towed‐streamer data. However, the imaging of towed‐streamer data is based on primary reflections, while the emerging imaging algorithms of VC data tend to use the receiver ghosts of primary reflections instead of the primaries themselves. I present an algorithm for attenuating primaries, free‐surface multiples, and the receiver ghosts of free‐surface multiples while preserving the receiver ghosts of primaries. My multiple attenuation algorithm of VC data is based on an inverse scattering approach known, which is a predict‐then‐subtract method. It assumes that surface seismic data are available or that they can be computed from VC data after an up/down wavefield separation at the receiver locations (streamer data add to VC data some of the wave paths needed for multiple attenuation). The combination of surface seismic data with VC data allows one to predict free‐surface multiples and receiver ghosts as well as the receiver ghosts of primary reflections. However, if the direct wave arrivals are removed from the VC data, this combination will not predict the receiver ghosts of primary reflections. I use this property to attenuate primaries, free‐surface multiples, and receiver ghosts from VC data, preserving only the receiver ghosts of primaries. This method can be used for multicomponent ocean bottom cable data (i.e., arrays of sea‐floor geophones and hydrophones) without any modification to attenuate primaries, free‐surface multiples, and the receiver ghosts of free‐surface multiples while preserving the receiver ghosts of primaries.

scholarly journals New acoustic approximation for transversely isotropic media with a vertical symmetry axis

Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. C1-C12 ◽  
Author(s):  
Shibo Xu ◽  
Alexey Stovas ◽  
Tariq Alkhalifah ◽  
Hitoshi Mikada
Keyword(s):  
Wave Propagation ◽  
Seismic Data ◽  
Eikonal Equation ◽  
Symmetry Axis ◽  
Transversely Isotropic ◽  
P Wave ◽  
Seismic Data Processing ◽  
S Wave ◽  
P Waves ◽  
Acoustic Approximation

Seismic data processing in the elastic anisotropic model is complicated due to multiparameter dependency. Approximations to the P-wave kinematics are necessary for practical purposes. The acoustic approximation for P-waves in a transversely isotropic medium with a vertical symmetry axis (VTI) simplifies the description of wave propagation in elastic media, and as a result, it is widely adopted in seismic data processing and analysis. However, finite-difference implementations of that approximation are plagued with S-wave artifacts. Specifically, the resulting wavefield also includes artificial diamond-shaped S-waves resulting in a redundant signal for many applications that require pure P-wave data. To derive a totally S-wave-free acoustic approximation, we have developed a new acoustic approximation for pure P-waves that is totally free of S-wave artifacts in the homogeneous VTI model. To keep the S-wave velocity equal to zero, we formulate the vertical S-wave velocity to be a function of the model parameters, rather than setting it to zero. Then, the corresponding P-wave phase and group velocities for the new acoustic approximation are derived. For this new acoustic approximation, the kinematics is described by a new eikonal equation for pure P-wave propagation, which defines the new vertical slowness for the P-waves. The corresponding perturbation-based approximation for our new eikonal equation is used to compare the new equation with the original acoustic eikonal. The accuracy of our new P-wave acoustic approximation is tested on numerical examples for homogeneous and multilayered VTI models. We find that the accuracy of our new acoustic approximation is as good as the original one for the phase velocity, group velocity, and the kinematic parameters such as vertical slowness, traveltime, and relative geometric spreading. Therefore, the S-wave-free acoustic approximation could be further applied in seismic processing that requires pure P-wave data.

scholarly journals Three-component amplitude versus offset analysis

1989 ◽  
Vol 20 (2) ◽  
pp. 257
Author(s):  
D.R. Miles ◽  
G. Gassaway ◽  
L. Bennett ◽  
R. Brown
Keyword(s):  
Seismic Data ◽  
P Wave ◽  
S Wave ◽  
Converted Wave ◽  
P Waves ◽  
S Waves ◽  
Avo Analysis ◽  
Avo Inversion ◽  
Amplitude Versus Offset ◽  
Converted Waves

Three-component (3-C) amplitude versus offset (AVO) inversion is the AVO analysis of the three major energies in the seismic data, P-waves, S-waves and converted waves. For each type of energy the reflection coefficients at the boundary are a function of the contrast across the boundary in velocity, density and Poisson's ratio, and of the angle of incidence of the incoming wave. 3-C AVO analysis exploits these relationships to analyse the AVO changes in the P, S, and converted waves. 3-C AVO analysis is generally done on P, S, and converted wave data collected from a single source on 3-C geophones. Since most seismic sources generate both P and S-waves, it follows that most 3-C seismic data may be used in 3-C AVO inversion. Processing of the P-wave, S-wave and converted wave gathers is nearly the same as for single-component P-wave gathers. In split-spread shooting, the P-wave and S-wave energy on the radial component is one polarity on the forward shot and the opposite polarity on the back shot. Therefore to use both sides of the shot, the back shot must be rotated 180 degrees before it can be stacked with the forward shot. The amplitude of the returning energy is a function of all three components, not just the vertical or radial, so all three components must be stacked for P-waves, then for S-waves, and finally for converted waves. After the gathers are processed, reflectors are picked and the amplitudes are corrected for free-surface effects, spherical divergence and the shot and geophone array geometries. Next the P and S-wave interval velocities are calculated from the P and S-wave moveouts. Then the amplitude response of the P and S-wave reflections are analysed to give Poisson's ratio. The two solutions are then compared and adjusted until they match each other and the data. Three-component AVO inversion not only yields information about the lithologies and pore-fluids at a specific location; it also provides the interpreter with good correlations between the P-waves and the S-waves, and between the P and converted waves, thus greatly expanding the value of 3-C seismic data.

Vector-based elastic reverse time migration based on scalar imaging condition

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. S111-S127 ◽  
Author(s):  
Qizhen Du ◽  
ChengFeng Guo ◽  
Qiang Zhao ◽  
Xufei Gong ◽  
Chengxiang Wang ◽  
...  
Keyword(s):  
Alternative Methods ◽  
Polarity Reversal ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Converted Wave ◽  
Imaging Condition ◽  
Time Migration ◽  
Wavefield Separation ◽  
Wave Modes

The scalar images (PP, PS, SP, and SS) of elastic reverse time migration (ERTM) can be generated by applying an imaging condition as crosscorrelation of pure wave modes. In conventional ERTM, Helmholtz decomposition is commonly applied in wavefield separation, which leads to a polarity reversal problem in converted-wave images because of the opposite polarity distributions of the S-wavefields. Polarity reversal of the converted-wave image will cause destructive interference when stacking over multiple shots. Besides, in the 3D case, the curl calculation generates a vector S-wave, which makes it impossible to produce scalar PS, SP, and SS images with the crosscorrelation imaging condition. We evaluate a vector-based ERTM (VB-ERTM) method to address these problems. In VB-ERTM, an amplitude-preserved wavefield separation method based on decoupled elastic wave equation is exploited to obtain the pure wave modes. The output separated wavefields are both vectorial. To obtain the scalar images, the scalar imaging condition in which the scalar product of two vector wavefields with source-normalized illumination is exploited to produce scalar images instead of correlating Cartesian components or magnitude of the vector P- and S-wave modes. Compared with alternative methods for correcting the polarity reversal of PS and SP images, our ERTM solution is more stable and simple. Besides these four scalar images, the VB-ERTM method generates another PP-mode image by using the auxiliary stress wavefields. Several 2D and 3D numerical examples are evaluated to demonstrate the potential of our ERTM method.

Automatic phase identification of earthquake based on the UBDN deep network

2021 ◽  
pp. 1-10
Author(s):  
Jianxian Cai ◽  
Xun Dai ◽  
Zhitao Gao ◽  
Yan Shi
Keyword(s):  
Seismic Data ◽  
Short Term Memory ◽  
Long Term Memory ◽  
Phase Identification ◽  
S Wave ◽  
Traditional Methods ◽  
Term Memory ◽  
Seismic Stations ◽  
2008 Wenchuan Earthquake ◽  
Deep Network

Seismic data obtained from seismic stations are the major source of the information used to forecast earthquakes. With the growth in the number of seismic stations, the size of the dataset has also increased. Traditionally, STA/LTA and AIC method have been applied to process seismic data. However, the enormous size of the dataset reduces accuracy and increases the rate of missed detection of the P and S wave phase when using these traditional methods. To tackle these issues, we introduce the novel U-net-Bidirectional Long-Term Memory Deep Network (UBDN) which can automatically and accurately identify the P and S wave phases from seismic data. The U-net based UBDN strongly maintains the U-net’s high accuracy in edge detection for extracting seismic phase features. Meanwhile, it also reduces the missed detection rate by applying the Bidirectional Long Short-Term Memory (Bi-LSTM) mode that processes timing signals to establish the relationship between seismic phase features. Experimental results using the Stanford University seismic dataset and data from the 2008 Wenchuan earthquake aftershock confirm that the proposed UBDN method is very accurate and has a lower rate of missed phase detection, outperforming solutions that adapt traditional methods by an order of magnitude in terms of error percentage.

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