According to the SourceForge statistics, the previous stable distribution has been downloaded about 12,000 times. The top country (with 36% of all downloads) was USA, followed by China, Germany, Brazil, and India.
The total cumulative number of downloads for the stable version of Madagascar has reached 65 thousand. The current development version continues to be available through Github.
Deconvolution mainly improves the resolution of seismic data by compressing seismic wavelets, which is of great significance in high-resolution processing of seismic data. Prediction-error filtering/least-square inverse filtering is widely used in seismic deconvolution and usually assumes that seismic data is stationary. Affected by factors such as earth filtering, actual seismic wavelets are time- and space-varying. Adaptive prediction-error filters are designed to effectively characterize the nonstationarity of seismic data by using iterative methods, however, it leads to problems such as slow calculation speed and high memory cost when dealing with large-scale data. We have proposed an adaptive deconvolution method based on a streaming prediction-error filter. Instead of using slow iterations, mathematical underdetermined problems with the new local smoothness constraints are analytically solved to predict time-varying seismic wavelets. To avoid the discontinuity of deconvolution results along the space axis, both time and space constraints are used to implement multichannel adaptive deconvolution. Meanwhile, we define the parameter of the time-varying prediction step that keeps the relative amplitude relationship among different reflections. The new deconvolution improves the resolution along the time direction while reducing the computational costs by a streaming computation, which is suitable for handling nonstationary large-scale data. Synthetic model and filed data tests show that the proposed method can effectively improve the resolution of nonstationary seismic data, while maintaining the lateral continuity of seismic events. Furthermore, the relative amplitude relationship of different reflections is reasonably preserved.
The Q-factor is an important physical parameter for characterizing the absorption and attenuation of seismic waves propagating in underground media, which is of great significance for improving the resolution of seismic data, oil and gas detection, and reservoir description. In this paper, the local centroid frequency is defined using shaping regularization and used to estimate the Q values of the formation. We propose a continuous time-varying Q-estimation method in the time-frequency domain according to the local centroid frequency, namely, the local centroid frequency shift (LCFS) method. This method can reasonably reduce the calculation error caused by the low accuracy of the time picking of the target formation in the traditional methods. The theoretical and real seismic data processing results show that the time-varying Q values can be accurately estimated using the LCFS method. Compared with the traditional Q-estimation methods, this method does not need to extract the top and bottom interfaces of the target formation; it can also obtain relatively reasonable Q values when there is no effective frequency spectrum information. Simultaneously, a reasonable inverse Q filtering result can be obtained using the continuous time-varying Q values.
We propose a method to efficiently measure time shifts and scaling functions between seismic images using amplitude-adjusted plane-wave destruction filters. Plane-wave destruction can efficiently measure shifts of less than a few samples, making this algorithm particularly effective for detecting small shifts. Separating shifts and scales allows shifting functions to be measured more accurately. When shifts are large, amplitude-adjusted plane-wave destruction can also be used to refine shift estimates obtained by other methods. The effectiveness of this algorithm in predicting shifting and scaling functions is demonstrated by applying it to a synthetic trace and a time-lapse field data example from the Cranfield CO$_2$ sequestration project.
The problem with interpolating insufficient, irregularly sampled data is that there exist infinitely many solutions. When solving ill-posed inverse problems in geophysics, we apply regularization to constrain the model space in some way. We propose to use plane-wave shaping in iterative regularization schemes. By shaping locally planar events to the local slope, we effectively interpolate in the structure-oriented direction and preserve the most geologic dip information. In our experiments, this type of interpolation converges in fewer iterations than alternative techniques. The proposed plane-wave shaping mave have potential applications in seismic tomography and well-log interpolation.
We propose and demonstrate a variational method for determining optimal velocity fields from semblance-like volumes using continuation. The proposed approach finds a minimal-cost surface through a volume, which often corresponds to a velocity field within a semblance scan. This allows picked velocity fields to incorporate information from gathers that are spatially near the midpoint in question. The minimization process amounts to solving a nonlinear elliptic partial differential equation, which is accomplished by changing the elliptic problem to a parabolic one and solving it iteratively until it converges to a critical point which minimizes the cost functional. The continuation approach operates by using a variational framework to iteratively minimize the cost of a velocity surface through successively less-smoothed semblance scans. The method works because a global minimum for the velocity cost functional can only exist when the semblance scan varies smoothly in space and convexly in the parameter being scanned. Using a discretization of the functional with a limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm we illustrate how the continuation approach is able to avoid local minima that would typically capture the iterative solution of an optimal velocity field determined without continuation. Incorporating continuation enables us to find a lower cost final model which is used for seismic processing of a field data set from the Viking Graben. We then utilize a field data set from the Gulf of Mexico to show how the final velocity model determined by the method employing continuation is largely independent of the starting velocity model, producing something resembling a global minimum. Finally, we illustrate the versatility of the variational picking approach by demonstrating how it may be used for automatic interpretation of a seismic horizon from the Heidrun Field.
Time migration, as opposed to depth migration, suffers from two well-known shortcomings: (1) approximate equations are used for computing Green’s functions inside the imaging operator; (2) in case of lateral velocity variations, the transformation between the image ray coordinates and the Cartesian coordinates is undefined in places where the image rays cross. We show that the first limitation can be removed entirely by formulating time migration through wave propagation in image-ray coordinates. The proposed approach constructs a time-migrated image without relying on any kind of traveltime approximation by formulating an appropriate geometrically accurate acoustic wave equation in the time-migration domain. The advantage of this approach is that the propagation velocity in image-ray coordinates does not require expensive model building and can be approximated by quantities that are estimated in conventional time-domain processing. Synthetic and field data examples demonstrate the effectiveness of the proposed approach and show that the proposed imaging workflow leads to a significant uplift in terms of image quality and can bridge the gap between time and depth migrations. The image obtained by the proposed algorithm is correctly focused and mapped to depth coordinates it is comparable to the image obtained by depth migration.