Compensation for absorption and dispersion in prestack depth migration: An offset-related effective Q approach

In prestack depth migration using explicit extrapolators, the attenuation and dispersion of the seismic wave has been neglected so far. We present a method for accommodating absorption and dispersion effects in depth migration schemes. Extrapolation operators that compensate for absorption and dispersion are designed using an optimization algorithm. The design criterion is that the wavenumber response of the operator should equal the true extrapolator. Both phase velocity and absorption macro models are used in the wavefield extrapolation. In a model with medium to high absorption, the images obtained are superior to those obtained using extrapolators without compensation for absorption.

In prestack finite-difference depth migration the attenuation and dispersion of the seismic wave has so far been neglected. The authors present and test a method for accommodating absorption effects in depth migration schemes. Extrapolator coefficients that compensate for absorption are constructed, and the velocity and absorption factor of the medium are used to label them. The method is straightforward to incorporate into an already existing finite-difference migration scheme. A numerical data example in a model with medium to high absorption, shows that the images obtained are superior to those obtained using extrapolators without compensation for absorption. Even when migrating in a Q model that deviates with 10% from the correct model, the authors find that the images are better focused and of a higher quality than when no compensation is performed.

The propagation of seismic waves in real media is in many respects different from propagation in an ideal solid. The anelasticity of the medium will cause dissipation of seismic energy, thus decreasing the amplitude and modifying the frequency content of the propagating wavelet. We present a method for including absorption effects into prestack finite-difference migration schemes. We will outline the theoretical foundation for the method, describe the design of the extrapolation filter, and thereafter test the method on synthetic data. The aim of this work is to show that a prestack depth migration scheme that compensates for absorption is both feasible and gives improved images.

The main challenges of prestack seismic imaging and migration velocity analysis(MVA) in the piedmont areas are the severe variations of the move-out among traces and the low signal to noise ratio (SNR). Both of them are caused by rugged topography and strong near-surface lateral velocity variations. Traditional poststack/prestack migration procedures fail to work well in those regions. We generalize a 3D travltime calculation method to the rugged topography and propose a new Kirchhoff prestack depth migration (PSDM) scheme from rugged topography. We found that choosing a suitable and smooth datum can remove the high wavenumber variation of the move-out among traces. The remaining move-out part can be controlled by the PSDM and MVA from the choosed datum. Both synthetic and field data examples demonstrate that the procedure is quite effective.

Accurate subsurface velocity estimation is crucial in seismic exploration, especially for prestack depth migration, depth conversion, geopressure prediction and AVO attribute computation. 3D reflection tomography is the most accurate method available for velocity estimation. The challenge that we face is in designing an accurate tomographic system capable of efficiently handling large volumes of seismic data acquired over increasingly complex targets. To address this need we have developed a 3D reflection tomography system using a tetrahedra‐based model parameterization. Tetrahedra are capable of accurately representing complex velocity models with far fewer control points compared with other methods. The input for our tomography comes from automatically scanned migration residuals and structural dips generated from Kirchhoff prestack depth migration. An adaptive layer‐based method is employed with flexible geological constraints, which enables global tomographic inversion of both compaction and competent geological environments. Application of global tomography to synthetic data demonstrates its ability to resolve strong and rapid velocity variations. Examples from 3D field data are shown to illustrate the benefits of this global tomographic system in estimating velocity models for large‐scale prestack depth migration projects.

The real geological medium is close to viscoelastic media in which seismic wave propagate with dispersion and attenuation. It is important to compensate the unwanted viscous effects in seismic processing. It is more accurate and physically more consistent to mitigate these effects in a wave-equation-based prestack depth migration. Historically, reverse time migration (RTM) based on directly solving the two-way wave equation has provided a superior way to image complex geologic regions. However, instability usually arises when considering compensation for absorption. Most researchers conduct high frequency filtering in wavenumber domain before or during wavefield extrapolate in RTM to ensure stability. In this paper, we use viscoacoustic wave equation derived by Bai et al. (2013) to do Q-RTM and stabilize extrapolate by adding a regularization term. Compared with direct filtering, the regularization parameter can be space-varying. So this is suitable for severely variational regions. And we also find that source normalized cross-correlation imaging condition is more suitable in Q-RTM.

Prestack depth migration with compensation for absorption

Reflectivity images obtained by prestack depth migration are often distorted by uneven subsurface illumination, especially in areas with complex geology, such as subsalt regions. We address the problem of uneven illumination in subsalt imaging by posing the reflectivity-imaging problem as a linear inverse problem and solving it in the image domain in a target-oriented fashion. The most computationally intensive part of the image-domain inversion is the explicit computation of the so-called Hessian operator. The Hessian is defined to be the normal operator of the associated modeling/imaging operator, which is a direct measure of the illumination deficiency of the imaging system. We can overcome the cost issue by using the phase-encoding technique in the 3D conical-wave domain for marine streamer acquisitions. We apply the inversion-based imaging methodology to a 3D field data set acquired from the Gulf of Mexico, and we precondition the inversion with nonstationary dip filters, which naturally incorporate interpreted geologic information. Numerical examples demonstrate that imaging by regularized inversion successfully recovers the reflectivities from the effects of uneven illumination, yielding images with more balanced amplitudes and higher spatial resolution.

This paper describes the implementation and results of portable, production-scale 3D Pre-stack Kirchhoff depth migration software. Full volume pre-stack imaging was applied to a six million trace (46.9 Gigabyte) data set horn a subsalt play in the Garden Banks area in the Gulf of Mexico. The velocity model building and updating, were derived using image depth gathers and an image-driven strategy. After three velocity iterations, depth migrated sections revealed drilling targets that were not visible in the conventional 3D post-stack time migrated data set. As expected from the implementation of the migrationalgorithm, it was found that amplitudes are well preserved and anomalies associated with known reservoirs, conform to petrophysical predictions. Image gathers for velocity analysis and the final depth migrated volume, were generated on an 1824 node Intel Paragon at Sandia National Laboratories. The code has been successfullyported to a CRAY (T3D) and Unix workstation Parallel Virtual Machine environments (PVM). Introduction This project is the result of a unique partnership between Oryx Energy Company, Sandia National Laboratories, and theUniversity of Texas at Dallas, through a Cooperative Research And Development Agreement program from the federal government (CRADA). The project developed out of a need identified at Oryx Energy Company in 1992 for a cost effective, yet high quality 3D Pre-Stack Depth Migration (PreSDM) program for imaging seismic data underneath salt structures in the Gulf of Mexico. Lacking resources for internal development of a PreSDM system, the CRADA program provided Oryx with parallel programming expertise and access to one of the fastest computers in the world at Sandia, and a prototype parallel code, geophysical and programming expertise from the University of Texas at Dallas. The entire project took 13 months from preliminary code porting, through the generation of a 3D synthetic data set for testing purposes, velocity field updating and, the final migration run generating the PreSDM volume. Migration Algorithm 3D pre-stack depth migration has been conceptually available for decades (Schneider, 1978), it only required the advent of super computers to become viable (French, 1992). lmplementations of3D Pre-Stack Kirchhoff Depth Migration now exist for both vector and parallel computers (Charrette, 1991; Highnam andPieprzalG 1991; Kao, 1992; Liu, 1993) along with numerous field data examples (Cabrera et al, 1992; Wyatt et al, 1992; Lewis et al, 1994; Ratcliff et al, 1994 and 1995; Schleicher et al, 1995; Epili and McMechan, 1996). The prototype 3D PreSDM algorithm used in this project was described in detail by Epili and McMechan (1996), so only a brief summary is given in this paper. The algorithm consist of three main steps. The first step is ray tracing to compute arrays of travel times flom each source and receiver location, to each point in a grid that corresponds spatially to the desired migrated image. For efficiency, the source and receiver locations are assigned to a grid defined by the binned line and receiver spacing.

Summary The presence of seismic absorption distorts seismic record and reduces seismogram resolution, which can be partially compensated by application of absorption compensation algorithms. Conventional absorption compensation techniques are based on 1D forward model with each seismic trace being compensated independently. Therefore, the 2D results combined by each compensation trace may be noisy and discontinuity. To eliminate this issue, we extend the 1D forward model to the 2D forward system and further add an additional lateral constraint to the compensation algorithm for enforcing the lateral continuity of the compensated section. By solving the proposed laterally constrained absorption compensation (LCAC) algorithm, we simultaneously obtain the multiple compensated traces with lateral smoother transition and higher signal-to-noise ratio (S/N). We testify the effectiveness of the proposed method by applying both synthetic and field data. Synthetic data examples demonstrate the superior performance of the LCAC algorithm in terms of improving algorithmic stability and protecting lateral continuity. The field data tests further indicate its ability to not only improve seismic resolution, but also maintain the S/N of compensated data.

The presence of seismic absorption distorts seismic record and reduces seismogram resolution, which can be partially compensated by application of absorption compensation algorithms. Conventional absorption compensation techniques are based on 1D forward model with each seismic trace being compensated independently. Therefore, the 2D results combined by each compensation trace may be noisy and discontinuity. To eliminate this issue, we extend the 1D forward model to the 2D forward system and further add an additional lateral constraint to the compensation algorithm for enforcing the lateral continuity of the compensated section. Solving the proposed laterally constrained absorption compensation (LCAC) problem, we simultaneously obtain the multiple compensated traces with lateral smoother transition and higher signal-to-noise ratio (S/N). We testify the effectiveness of the proposed method by applying both synthetic and field data. Synthetic data examples demonstrate the superior performance of the LCAC algorithm in terms of improving algorithmic stability and protecting lateral continuity. The field data tests further indicate its ability to not only improve seismic resolution, but also inhibit the amplification of high-frequency noise.

Propagation of seismic waves in real media is in many respects different from propagation in an ideal solid. Presented here is a method for accommodating absorption and dispersion effects in a migration scheme, in which extrapolation operators that compensate for absorption and dispersion are designed. The algorithm is developed in the frequency–wavenumber domain, and is characterized by simplicity, speed, less dependence on stratum obliquity, and good stabilization. To demonstrate absorption and dispersion in the viscoacoustic medium, we first perform forward modelling, which shows that the amplitude of the wave is decreased, frequency is lower and the phase is influenced when a wave propagates in the viscoacoustic medium. We then perform viscoacoustic and elastic 2D pre-stack depth migrations on the synthetic data. Without consideration of the absorption and dispersion in the elastic pre-stack migration scheme, a geological model cannot be imaged properly. For the viscoacoustic pre-stack depth migration scheme, extrapolation operators could compensate for absorption and dispersion, and a proper image be obtained.

The exploiting of High Resolution (HR) Pre Stack Depth Migration (PSDM) 3D seismic volumes, normally used for Oil & Gas exploration, has been pushed forward in geomorphological and geohazard risk evaluation. The novel approach proposed here allows to carry out such activities very early in respect of the standard work flow. Early awareness of critical areas turns out to be crucial in fast-tracking projects and allows a design to cost optimization. The 3D HR PSDM outputs are processed in order to generate a detailed imaging of the shallower portion of the seismic volumes. The volumes are processed at a 2 meters depth interval and converted in time (DTT). Finally, a dedicated post migration time processing sequence, followed by time-to-depth conversion, is applied to generate a Higher Resolution Volume (HRV) in depth domain. The resulting 3D volume is then analyzed to study the seabed and the sub-bottom from a geomorphological standpoint. The analyses focus on the identification and mapping of the distribution of the "areas of instability" eventually classified according to a specific KPI (Safety Factor Index in static conditions), providing a quantitative slope stability assessment of the area. The new approach has been validated comparing the DTM (Digital Topographic Model) derived from the 3D HR PSDM volume and the available MBES (Multi Beam Echo Sounder) bathymetry. The proposed approach leads to a dramatic improvement in the detection capability, highlighting the major critical structures such as: canyon flanks, buried slides, creeps and tension cracks on the shelf break, boulders and compacted sediments, sediment banks and sediment waves reshaped by bottom currents, pockmark areas and fluid escapes, turbidity mass movements and furrows due to tectonic activities. The approach matches perfectly the detection capability of a traditional MBES approach. The described workflow is potentially highly beneficial for early de-risking assets and operations, especially for facilities installation. The proposed innovative approach allows a detailed planning of dedicated data acquisition campaigns, restricted to the most critical areas, with a tangible reduction in the turnaround times and cost savings crucial for project economics.

3D realistic sea surface imaging from 3D dual-sensor towed streamer data is presented. The technique is based on separating data acquired by collocated dual-sensors into up-going and down-going wavefields. Subsequently, these wavefields are extrapolated upwards in order to image the sea surface. This approach has previously been demonstrated using 2D data examples. Here, the focus is on 3D data. Controlled 3D data based on the Kirchhoff-Helmholtz algorithm is generated, and the 3D sea surface imaging technique is applied. For coarsely spaced streamers from 3D field data, the technique is applied streamerwise (i.e., 2D wavefield separation, extrapolation, and imaging). In the latter case, the resulting sea surface profiles corresponding to each time frame are interpolated to demonstrate that the main sea surface characteristics are preserved, and artefacts due to 2D processing of 3D data are mainly limited to areas corresponding to large angles of incidence. Time-varying sea surfaces from two different 3D field data are imaged. The data examples were acquired under different weather conditions. The imaged sea surfaces show realistic wave heights, and their spectra suggest plausible speeds and directions.

ABSTRACTWavefield depth extrapolation and prestack depth migration in complex anelastic media are studied. Kjartansson's frequency‐independent Q law is used to describe the absorption of seismic energy. The macromodel used is analogous to the macromodel used for current migration schemes except that an additional frequency‐independent Q macromodel needs to be provided. Absorption in the forward one‐way propagator is introduced by assuming a complex phase velocity, and the inverse one‐way propagator is obtained using the reciprocity theorem for one‐way wavefields in dissipative media. The stability of the inverse propagator is achieved by limiting the angle of propagation of wavefields. A table‐driven explicit operator scheme for imaging complex 2D anelastic media is presented. High‐accuracy, short convolution operators are designed by the weighted least‐squares method, and two kinds of imaging conditions are proposed. Numerical examples of depth extrapolation in laterally varying media, the migration of a spatial impulse with dispersion as well as shot record depth migration demonstrate the potential of the proposed explicit forward operator, the explicit inverse operator and the prestack depth migration scheme, respectively.