Amplitude preserving AMO from true amplitude DMO and inverse DMO

SEG Technical Program Expanded Abstracts 1995, 1995

Azimuth moveout (AMO) transforms 3-D prestack seismic data from one common azimuth and offset to different azimuths and offsets. AMO in the time-space domain is represented by a three-dimensional integral operator. The operator components are the summation path, the weighting function, and the aperture. To determine the summation path and the weighting function, we derive the AMO operator by cascading dip moveout (DMO) and inverse DMO for different azimuths in the time-space domain. To evaluate the aperture, we apply a geometric approach, defining AMO as the result of cascading prestack migration (inversion) and modeling. The aperture limitations provide a consistent description of AMO for small azimuth rotations (including zero) and justify the economic efficiency of the method.

Geophysical Prospecting, 2010

We present preserved-amplitude downward continuation migration formulas in the aperture angle domain. Our approach is based on shot-receiver wavefield continuation. Since source and receiver points are close to the image point, a local homogeneous reference velocity can be approximated after redatuming. We analyse this approach in the framework of linearized inversion of Kirchhoff and Born approximations. From our analysis, preserved-amplitude Kirchhoff and Born inverse formulas can be derived for the 2D case. They involve slant stacks of filtered subsurface offset domain common image gathers followed by the application of the appropriate weighting factors. For the numerical implementation of these formulas, we develop an algorithm based on the true amplitude version of the one-way paraxial approximation. Finally, we demonstrate the relevance of our approach with a set of applications on synthetic datasets and compare our results with those obtained on the Marmousi model by multi-arrival ray-based preserved-amplitude migration. While results are similar, we observe that our results are less affected by artefacts.

2015

Moveout analysis of wide-azimuth reflection data is usually performed for smoothly varying velocity fields. However, ve-locity lenses in the overburden can cause significant laterally-varying errors in the moveout parameters. Here, we derive an analytic expression for the NMO ellipse in stratified media with lateral velocity variation and show that the correction for lateral heterogeneity is controlled by the second derivatives of the interval vertical traveltime. This equation provides a quick estimate of the contribution of velocity lenses and substantially mitigates the lens-induced distortions in the effective and inter-val NMO ellipses. To remove the influence of velocity lenses on nonhyper-bolic moveout inversion of wide-azimuth data, we propose a prestack correction algorithm that involves computation of the lens-induced traveltime distortion for each recorded trace. The method is designed for a horizontally-layered overburden but can handle laterally heterogeneous target lay...

SEG Technical Program Expanded Abstracts 2015, 2015

A great deal of effort has been expended to improve the amplitude reliability of migration. The similarity of reverse time migration (RTM) to the gradient of full waveform inversion (FWI) indicates that preserved amplitude RTM can help improve FWI. We develop the theoretical derivation of an improved gradient for FWI based on common shot preserved amplitude RTM. We validate our approach on the Marmousi II model and the Chevron SEG 2014 dataset, showing that it significantly improves the convergence rate of FWI.

2010

Recently prestack Reverse time migration (RTM) algorithm for depth imaging has become feasible due to advances in computational power and clever programming techniques. RTM uses full acoustic two-way wave propagation algorithm for both forward and reverse time extrapolation. Amplitude preservation is based upon the assumption that acoustic wave equation approximates the wave propagation in real elastic earth. In this paper, first the amplitude characteristics of both the acoustic and elastic wave propagation are compared by looking at the reflection coefficients for a simple flat layered model. Then the input gathers generated by both acoustic and elastic forward modeling algorithm are migrated with RTM method. The amplitude behavior of the RTM algorithm is studied by looking at the amplitudes of migrated gathers. The study shows that even for a simple flat layered earth model the assumption of acoustic wave propagation in RTM may not be valid. Therefore special care must be taken while interpreting amplitude information on migrated gathers.

GEOPHYSICS, 2005

Reflection seismic data continuation is the computation of data at source and receiver locations that differ from those in the original data, using whatever data are available. We develop a general theory of data continuation in the presence of caustics and illustrate it with three examples: dip moveout (DMO), azimuth moveout (AMO), and offset continuation. This theory does not require knowledge of the reflector positions. We construct the output data set from the input through the composition of three operators: an imaging operator, a modeling operator, and a restriction operator. This results in a single operator that maps directly from the input data to the desired output data. We use the calculus of Fourier integral operators to develop this theory in the presence of caustics. For both DMO and AMO, we compute impulse responses in a constant-velocity model and in a more complicated model in which caustics arise. This analysis reveals errors that can be introduced by assuming, for example, a model with a constant vertical velocity gradient when the true model is laterally heterogeneous. Data continuation uses as input a subset (common offset, common angle) of the available data, which may introduce artifacts in the continued data. One could suppress these artifacts by stacking over a neighborhood of input data (using a small range of offsets or angles, for example). We test data continuation on synthetic data from a model known to generate imaging artifacts. We show that stacking over input scattering angles suppresses artifacts in the continued data.

2020

The true-amplitude (TA) imaging condition for reverse-time migration (RTM) is based on a combination of temporal and spatial derivatives of the upand downgoing wavefields. By means of partial integrations (or redistribution of the frequency factors in the frequency domain, we derive several alternative expressions for this imaging condition. Interestingly, the temporal derivatives can be completely replaced by spatial derivatives and temporal integrations. In this way, one version of the TA imaging condition makes use of the Laplacian operator, in this way relating to a common way of removing backscattering artifacts in RTM. We demonstrate by means of numerical examples using the Marmousi and Sigsbee2A data that the quality of the migrated image strongly depends on the version chosen for implementation. The best quality is achieved with a version that combines second derivatives of the source wavefield with the Laplacian operator. INTRODUCTION Reverse-time migration (RTM) is a seism...

Journal of Seismic Exploration, 2001

2001

We analyze the amplitude variation as a function of reflection angle (AVA) for angle-domain common image gathers (ADCIG) produced via wave-equation migration. Straightforward implementations of the two main ADCIG methods lead to contradictory, thus inaccurate, amplitude responses. The amplitude inaccuracy is related to the fact that downward-continuation migration is the adjoint of upward-continuation modeling, but it is only a poor approximation of its inverse. We derive the frequency-wavenumber domain diagonal weighting operators that make migration a good approximation to the inverse of modeling. With these weights, both ADCIG methods produce consistent results. The main applications that follow from this paper are true-amplitude migration and pseudounitary modeling/migration, usable for iterative inversion. The two most important factors that degrade the accuracy of wave-equation ADCIGs are the limited sampling and offset range, combined with the band-limited nature of seismic data.

SEP-89: Stanford Exploration Project, 1995

A practical implementation of azimuth moveout (AMO) must be both computationally efficient and accurate. We achieve computational efficiency by parameterizing the AMO operator with the help of a transformed midpoint coordinate system. To achieve accuracy, the AMO operator needs to be carefully designed for antialiasing. We propose a modified version of Hale's antialiasing algorithm, which switches between interpolation in time and interpolation in space depending on the operator dips. The ...