Tieyuan Zhu

Approximating constant-Q seismic propagation in the time domain

Summary In this study, we investigate the accuracy of approximating constant-Q by a series of Zener or standard linear solids (SLS) mechanisms. Modeling of approximately constant-Q in a viscoacoustic medium is implemented in time domain using finite-difference (FD) approach. The accuracy of numerical solutions is evaluated by comparison with the analytical solution of the constant-Q model. We found the FD solutions using three SLS (relaxation mechanisms) as well as a single SLS mechanism are quite accurate for weak and strong attenuation. Although the RMS errors of FD simulations using the single relaxation mechanism become larger with increasing offset, especially for strong attenuation (Q=20), the results are still acceptable. The simulated synthetic data of the complex model further illustrate that the single SLS mechanism to model constantQ is efficient and sufficiently accurate. Moreover, it benefits from less computational costs in time and memory. Therefore, we suggest that the single relaxation is a promising choice to model constant-Q for computational intensive seismic modeling and inversion.

Implementation aspects of attenuation compensation in reverse-time migration

Attenuation compensation in reverse-time migration has been shown to improve the resolution of the seismic image. In this paper, three essential aspects of implementing attenuation compensation in reverse-time migration are studied: the physical justification of attenuation compensation, the choice of imaging condition, and the choice of a low-pass filter. The physical illustration of attenuation compensation supports the mathematical implementation by reversing the sign of the absorption operator and leaving the sign of the dispersion operator unchanged in the decoupled viscoacoustic wave equation. Further theoretical analysis shows that attenuation compensation in reverse-time migration using the two imaging conditions (cross-correlation and source-normalized cross-correlation) is able to effectively mitigate attenuation effects. In numerical experiments using a simple-layered model, the source-normalized cross-correlation imaging condition may be preferable based on the criteria of amplitude corrections. The amplitude and phase recovery to some degree depend on the choice of a low-pass filter. In an application to a realisticMarmousi model with added Q, high-resolution seismic images with correct amplitude and kinematic phase are obtained by compensating for both absorption and dispersion effects. Compensating for absorption only can amplify the image amplitude but with a shifted phase.

Image integration with learned dictionaries and application to seismic monitoring

Sparse coding can be applied to train an overcomplete dictionary on time-lapse seismic data or images. The learned dictionary generally consists of sparse representations of one or more images. We then use such sparse representations, along with L1-regularization techniques, to predict missing values in seismic images by solving an inverse problem. The practical outcome of the proposed methodology can be a significant reduction in field operational costs by requiring only sparse instead of dense surveys, and by integrating in the seismic images the information captured by the learned dictionary from previous time-lapse and baseline images. A synthetic example is presented to test the method.

Iterative Joint Inversion of P-wave And S-wave Crosswell Traveltime Data

Joint inversion of multiple geophysical data-sets is promising to reduce uncertainties in independently inverted models. Here, we present an iterative joint inversion approach for P and S traveltime data using crossgradient function as constraint term. This type of joint inversion scheme links independent inversions through iterations and the cross-gradient function. The primary advantage of this joint inversion strategy is to avoid determining relative weighting of different data-sets. To investigate the performance of this method, we test our algorithm in synthetic examples of P and S traveltime data and field data acquired in west Texas. The results of synthetic example show that the joint inversion significantly reduces the ambiguities of inverted models and improves the identification of boundaries. In results of field data, jointly inverted S velocities have better correlation with P velocities. Moreover, lithologies delineated from Vp/Vs map by joint inversion matches log data very well and also shows clearly a dipping structure below reservoir that was not shown in previous crosswell tomography results.

Strategies for stable attenuation compensation in reverse-time migration: Strategies for stable attenuation compensation in reverse-time migration

Attenuation in seismic wave propagation is a common cause for poor illumination of subsurface structures. Attempts to compensate for amplitude loss in seismic images by amplifying the wavefield may boost high-frequency components, such as noise, and create undesirable imaging artifacts. In this paper, rather than amplifying the wavefield directly, we develop a stable compensation operator using stable division. The operator relies on a constant-Q wave equation with decoupled fractional Laplacians, and compensates for the full attenuation phenomena by performing wave extrapolation twice. This leads to two new imaging conditions to compensate for attenuation in reverse-time migration (RTM). A time-dependent imaging condition is derived by applying Q-compensation in the frequency domain, while a time-independent imaging condition is formed in the image space by calculating image normalization weights. We demonstrate the feasibility and robustness of the proposed methods using three synthetic examples. We found that the proposed methods are capable of properly compensating for attenuation without amplifying high-frequency noise in the data. This article is protected by copyright. All rights reserved

Better Imaging the Hydrocarbon Reservoir Using Q-compensated Reverse-time Migration

I present an application of Q-compensated reverse-time migration to the crosswell seismic field data from west Texas. A key feature of Q-RTM algorithm is the restoration of the high frequencies (in amplitude and phase) in the wavefield, thus resulting in an improved stack of source gathers. I found that the Q-compensated reverse-time migration imaging is able to provide an improved reflection image with many high-resolution details about geological layers and structures. For instance, the lateral and vertical extent and the internal features of the reservoir pay zone can be clearly determined in the Q-RTM image.