John Etgen

Seismic migration problems and solutions

Historically, seismic migration has been the practice (science, technology, and craft) of collapsing diffraction events on unmigrated records to points, thereby moving (“migrating”) reflection events to their proper locations, creating a true image of structures within the earth. Over the years, the scope of migration has broadened. What began as a structural imaging tool is evolving into a tool for velocity estimation and attribute analysis, making detailed use of the amplitude and phase information in the migrated image. With its expanded scope, migration has moved from the final step of the seismic acquisition and processing flow to a more central one, with links to both the processes preceding and following it. In this paper, we describe the mechanics of migration (the algorithms) as well as some of the problems related to it, such as algorithmic accuracy and efficiency, and velocity estimation. We also describe its relationship with other processes, such as seismic modeling. Our approach is tutorial; we avoid presenting the finest details of either the migration algorithms themselves or the problems to which migration is applied. Rather, we focus on presenting the problems themselves, in the hope that most geophysicists will be able to gain an appreciation of where this imaging method fits in the larger problem of searching for hydrocarbons.

An overview of depth imaging in exploration geophysics

Prestack depth migration is the most glamorous step of seismic processing because it transforms mere data into an image, and that image is considered to be an accurate structuraldescriptionoftheearth.Thus,ourexpectationsofitsaccuracy, robustness, and reliability are high.Amazingly, seismic migration usually delivers. The past few decades have seen migration move from its heuristic roots to mathematically sound techniques that, using relatively few assumptions, render accurate pictures of the interior of the earth. Interestingly,theearthandthesubjectswewanttoimageinside itarevariedenoughthat,sofar,nosinglemigrationtechnique has dominated practical application.All techniques continually improve and borrow from each other, so one technique mayneverdominate.Despitetheprogressinstructuralimaging,wehavenotreachedthepointwhereseismicimagesprovide quantitatively accurate descriptions of rocks and fluids. Nor have we attained the goal of using migration as part of a purelycomputationalprocesstodeterminesubsurfacevelocity. In areas where images have the highest quality, we might be nearing those goals, collectively called inversion. Where data are more challenging, the goals seem elusive. We describe the progress made in depth migration to the present and the most significant barriers to attaining its inversion goalsinthefuture.Wealsoconjectureonprogresslikelytobe made in the years ahead and on challenges that migration mightnotbeabletomeet.

Computational methods for large-scale 3D acoustic finite-difference modeling: A tutorial

We present a set of methods for modeling wavefields in three dimensions with the acoustic-wave equation. The primary applications of these modeling methods are the study of acquisition design, multiple suppression, and subsalt imaging for surface-streamer and ocean-bottom recording geometries. We show how to model the acoustic wave equation in three dimensions using limited computer memory, typically using a single workstation, leading to run times on the order of a few CPU hours to a CPU day. The structure of the out-of-core method presented is also used to improve the efficiency of in-core modeling, where memory-to-cache-to-memory data flow is essentially the same as the data flow for an out-of-core method. Starting from the elastic-wave equation, we develop a vector-acoustic algorithm capable of efficiently modeling multicomponent data in an acoustic medium. We show that data from this vector-acoustic algorithm can be used to test upgoing/downgoing separation of P-waves recorded by ocean-bottom seismic...

Efficient 2.5-D true‐amplitude migration

Kirchhoff depth migration is a widely used algorithm for imaging seismic data in both two and three dimensions. To perform the summation at the heart of the algorithm, standard Kirchhoff migration requires a traveltime map for each source and receiver. True‐amplitude Kirchhoff migration in 2.5-D υ(x, z) media additionally requires maps of amplitudes, out‐of‐plane spreading factors, and takeoff angles; these quantities are necessary for calculating the true‐amplitude weight term in the summation. The increased input/output (I/O) and computational expense of including the true‐amplitude weight term is often not justified by significant improvement in the final muted and stacked image. For this reason, some authors advocate neglecting the weight term in the Kirchhoff summation entirely for most everyday imaging purposes. We demonstrate that for nearly the same expense as ignoring the weight term, a much better solution is possible. We first approximate the true‐amplitude weight term by the weight term for co...

Alford rotation, ray theory, and crossed‐dipole geometry

Two generalizations of Alford rotation have been proposed for processing 2 × 2-component data containing nonorthogonal split shear waves: singular value decomposition (SVD) and eigenvector‐eigenvalue decomposition (EED). Using a simple crossed‐dipole synthetic model, we demonstrate that the physical model behind the EED method is invalid. It incorrectly assumes that a vector source aligned with the particle motion of an anisotropic pure mode will excite only that one mode. Ray theory shows that a vector point‐force source embedded in a homogeneous anisotropic medium instead excites all those modes with particle motions that are not perpendicular to the direction of the applied force, just as a vector point receiver detects all modes with polarizations that are not perpendicular to the receiver. Correctly generalized Alford rotation synthesizes vector sources and receivers such that each component is perpendicular to all but one of the pure modes of the medium. Although this ray‐theory result does not allo...

Pre-stack Depth Imaging In Southern Caspian; A Step-wise Approach For Complex Imaging

The prospective Southern Caspian Basin is an active area for hydrocarbon exploration and development. The large anticlinal structures typical of the area have varying degrees of dip and an overburden with generally smoothly varying velocity gradients. Target depths are between 3-7 km and optimum imaging and positioning of the structures in depth is necessary for reserve estimation and well prognosis. Cost effective and timely depth migration is required for imaging. We have taken a two-step approach to 3D depth imaging in this structurally complex basin. In the first step, we depth migrated the common offset data with a single V(z) velocity function. The residual errors computed from the migrated common image gathers were used as input to 3D tomography to build a spatially varying velocity model in depth. These residual corrections were also used to obtain an optimized stack of the V(z) migrated gathers. The optimized stack was later demigrated with the same V(z) velocity function and subsequently re-migrated poststack using the spatially varying V(x,y,z) velocity model derived from 3D tomography. At the second step, using the newly constructed V(x,y,z) model, we migrated the same offset data using a prestack Kirchhoff algorithm. This integrated methodology yields a cost effective, stepwise approach to provide optimum depth imaging in this complex region where a priori information on subsurface features is limited. Results show that the prestack Kirchhoff migration based on spatially varying velocity has better focusing in complex areas; however, the overall difference between images from the two methods is minimal.

Multicomponent Imaging With Reciprocal Shot Records

Summary Multicomponent recording has been identified as a tool that can be used to obtain improved seismic data quality where traditional P-wave recording has thus far failed. Specifically, converted-wave images, those where down going P-waves are converted to S-waves at every reflection point, have been shown to offer improved seismic continuity in the presence of a gascharged overburden (Thomsen et al, 1997). Converted-waves (C-waves) have also been studied for their potential to improve subsalt images (Kendall et al, 1998). In this paper, we show that C-wave imaging with point-r eceiver (reciprocal-shot) gathers raises issues related to survey design. We find that reciprocal-shot C-wave imaging will cost more than reciprocal-shot P-wave imaging of the same structures.