## Online Conference

May 5, 2021 Celebration No comments

The first ever worldwide Madagascar conference will take place on June 21-27, 2021. The participation is free of charge.

The conference program will be announced later. Meanwhile, please indicate the level of your interest in participation by filling a form on the website.

## Enhancements to Python interface

April 9, 2021 Systems No comments

Behind the scene, temporary files are created, and Madgascar programs run in the usual way, but, for the user, they appears like native Python functions. This way, the full power of Madagascar becomes available to people who prefer to work on data analysis projects in a Python environment.

• However, there is no good reason to abandon Madagascar’s use of SCons for managing data analysis workflows even when working in a Python framework. Because SConstruct scripts are written in Python, they are easy to adapt for including Python functions in place of command-line instructions. See an example of using Keras with SCons or an example of using PyTorch with SCons.

In deep learning projects, the training data, the neural-network model, and the testing data can be treated as files and handled effectively through SCons workflows while mixing with Madagascar commands and workflows.

• Plotting with Matplotlib may offer some advanced functionality in comparison with Vplot, such as the possibility of using $\LaTeX$ code in figure labels. It is now possible to use Matplotlib plots in papers reproducible with Madagascar through an application of sfmatplotlib. The figures will be saved in the PDF format and included in reproducible papers in the usual way. See an example.

The main advantage of continuing to use Vplot is the availability of sfvplotdiff, a key tool for reproducibility testing and continuous integration.

Madagascar users are invited to try the new functionality and contribute to its further development.

## Diffraction imaging using anisotropic smoothing

February 24, 2021 Documentation No comments

\

We use least-squares migration to emphasize edge diffractions. The inverted forward modeling operator is the chain of three operators: Kirchhoff modeling, azimuthal plane-wave destruction and path-summation integral filter. Azimuthal plane-wave destruction removes reflected energy without damaging edge diffraction signatures. Path-summation integral guides the inversion towards probable diffraction locations. We combine sparsity constraints and anisotropic smoothing in the form of shaping regularization to highlight edge diffractions. Anisotropic smoothing enforces continuity along edges. Sparsity constraints emphasize diffractions perpendicular to edges and have a denoising effect. Synthetic and field data examples illustrate the effectiveness of the proposed approach in denoising and highlighting edge diffractions, such as channel edges and faults.

## Legislating reproducibility

January 23, 2021 Celebration No comments

American Innovation and Competitiveness Act was adopted unanimously by the U.S. Congress and signed into law by president Obama in January 2017.

The law contains a section called Research Reproducibility and Replication, which asked the Director of the National Science Foundation in agreement with the National Research Council to prepare a report on issues related to research reproducibility and “to make recommendations for improving rigor and transparency in scientific research”.

To fulfill this requirement, a consensus report of the National Academies of Sciences, Engineering, and Medicine was published in 2019. The report is summarized in the special issue of Harvard Data Science Review in December 2020.

Among the recommendations:

All researchers should include a clear, specific, and complete description of how the reported results were reached. Reports should include details appropriate for the type of research, including:

• a clear description of all methods, instruments, materials, procedures, measurements, and other variables involved in the study;
• a clear description of the analysis of data and decisions for exclusion of some data or inclusion of other;
• for results that depend on statistical inference, a description of the analytic decisions and when these decisions were made and whether the study is exploratory or confirmatory;
• a discussion of the expected constraints on generality, such as which methodological features the authors think could be varied without affecting the result and which must remain constant;
• reporting of precision or statistical power; and
• discussion of the uncertainty of the measurements, results, and inferences.

Funding agencies and organizations should consider investing in research and development of open-source, usable tools and infrastructure that support reproducibility for a broad range of studies across different domains in a seamless fashion. Concurrently, investments would be helpful in outreach to inform and train researchers on best practices and how to use these tools.

Journals should consider ways to ensure computational reproducibility for publications that make claims based on computations, to the extent ethically and legally possible.

## Full waveform inversion and joint migration inversion with an automatic directional total variation constraint

December 7, 2020 Documentation No comments

As full waveform inversion (FWI) is a non-unique and typically ill-posed inversion problem, it needs proper regularization to avoid cycle-skipping. To reduce the non-linearity of FWI, Joint Migration Inversion (JMI) is proposed as an alternative, explaining the reflection data with decoupled velocity and reflectivity parameters. However, the velocity update may also suffer from being trapped in local minima. To optimally include geologic information, we propose FWI/JMI with directional total variation as an L1-norm regularization on the velocity. We design the directional total variation operator based on the local dip field, instead of ignoring the local structural direction of the subsurface and only using horizontal- and vertical- gradients in the traditional TV. The local dip field is estimated using plane-wave destruction based on a raw reflectivity model, which is usually calculated from the initial velocity model. With two complex synthetic examples, based on the Marmousi model, we demonstrate that the proposed method is much more effective compared to both FWI/JMI without regularization and FWI/JMI with the conventional TV regularization. In the JMI-based example, we also show that L1 directional TV works better than L2 directional Laplacian smoothing. In addition, by comparing these two examples, it can be seen that the impact of regularization is larger for FWI than for JMI, because in JMI the velocity model only explains the propagation effects and, thereby, makes it less sensitive to the details in the velocity model.

## Five-dimensional seismic data reconstruction using the optimally damped rank-reduction method

December 7, 2020 Documentation No comments

It is difficult to separate additive random noise from spatially coherent signal using a rank-reduction method that is based on the truncated singular value decomposition (TSVD) operation. This problem is due to the mixture of the signal and the noise subspaces after the TSVD operation. This drawback can be partially conquered using a damped rank reduction method, where the singular values corresponding to effective signals are adjusted via a carefully designed damping operator. The damping operator works most powerfully in the case of a small rank and a small damping factor. However, for complicated seismic data, e.g., multi-channel reflection seismic data containing highly curved events, the rank should be large enough to preserve the details in the data, which makes the damped rank reduction method less effective. In this paper, we develop an optimal damping strategy for adjusting the singular values when a large rank parameter is selected so that the estimated signal can best approximate the exact signal. We first weight the singular values using optimally calculated weights. The weights are theoretically derived by solving an optimization problem that minimizes the Frobenius-norm difference between the approximated signal components and the exact signal components. The damping operator is then derived based on the initial weighting operator to further reduce the residual noise after the optimal weighting. The resulted optimally damped rank reduction method is nearly an adaptive method, i.e., insensitive to the rank parameter. We demonstrate the performance of the proposed method on a group of synthetic and real five-dimensional seismic data.

## Seismic signal enhancement based on the lowrank methods

December 6, 2020 Documentation No comments

A new paper is added to the collection of reproducible documents: Seismic signal enhancement based on the lowrank methods

Based on the fact that the Hankel matrix constructed by noise-free seismic data is lowrank (LR), LR approximation (or rank-reduction) methods have been widely used for removing noise from seismic data. Due to the linear-event assumption of the traditional LR approximation method, it is difficult to define a rank that optimally separates the data subspace into signal and noise subspaces. For preserving the most useful signal energy, a relatively large rank threshold is often chosen, which inevitably leaves residual noise. To reduce the energy of residual noise, we propose an optimally damped rank-reduction method. The optimal damping is applied via two steps. In the first step, a set of optimal damping weights is derived. In the second step, we derive an optimal singular-value damping operator. We review several traditional lowrank methods and compare their performance with the new one. We also compare these lowrank methods with two sparsity-promoting transform methods. Examples demonstrate that the proposed optimally damped rank-reduction method could get significantly cleaner denoised images compared with the state-of-the-art methods.

## Simultaneous denoising and reconstruction of 5D seismic data via damped rank-reduction method

December 6, 2020 Documentation No comments

The Cadzow rank-reduction method can be effectively utilized in simultaneously denoising and reconstructing 5D seismic data that depends on four spatial dimensions. The classic version of Cadzow rank-reduction method arranges the 4D spatial data into a level-four block Hankel/Toeplitz matrix and then applies truncated singular value decomposition (TSVD) for rank-reduction. When the observed data is extremely noisy, which is often the feature of real seismic data, traditional TSVD cannot be adequate for attenuating the noise and reconstructing the signals. The reconstructed data tends to contain a significant amount of residual noise using the traditional TSVD method, which can be explained by the fact that the reconstructed data space is a mixture of both signal subspace and noise subspace. In order to better decompose the block Hankel matrix into signal and noise components, we introduced a damping operator into the traditional TSVD formula, which we call the damped rank-reduction method. The damped rank-reduction method can obtain a perfect reconstruction performance even when the observed data has extremely low signal-to-noise ratio (SNR). The feasibility of the improved 5D seismic data reconstruction method was validated via both 5D synthetic and field data examples. We presented comprehensive analysis of the data examples and obtained valuable experience and guidelines in better utilizing the proposed method in practice. Since the proposed method is convenient to implement and can achieve immediate improvement, we suggest its wide application in the industry.

## Separation and imaging of seismic diffractions

December 5, 2020 Documentation No comments

Seismic diffractions are some weak seismic events hidden within the more dominant reflection events in a seismic profile. Separating diffraction energy from the post-stack seismic profiles can help infer the subsurface discontinuities that generate the diffraction events. The separated seismic diffractions can be migrated with a traditional seismic imaging method or a specifically designed migration method to highlight the diffractors, i.e., the diffraction image. Traditional diffraction separation methods based on the the underlying plane-wave assumption are limited by either the inaccurate slope estimation or the plane-wave assumption of the PWD filter, and thus will cause reflection leakage into the separated diffraction profile. The leaked reflection energy will deteriorate the resolution of the subsequent diffraction imaging result. Here, we propose a new diffraction separation method based on a localized rank-reduction method. The localized rank-reduction method assumes the reflection events to be locally low-rank and the diffraction energy can be separated by a rank-reduction operation. Compared with the global rank-reduction method, the localized rank-reduction method is more constrained in selecting the rank and is free of separation artifacts. We use a carefully designed synthetic example to demonstrate that the localized rank-reduction method can help separate the diffraction energy from a post-stack seismic profile with both kinematically and dynamically accurate performance.

## Time-frequency analysis of seismic data using non-stationary Prony method

July 18, 2020 Documentation No comments

The empirical mode decomposition aims to decompose the input signal into a small number of components named intrinsic mode functions with slowly varying amplitudes and frequencies. In spite of its simplicity and usefulness, however, the empirical mode decomposition lack solid mathematical foundation. In this paper, we describe a method to extract the intrinsic mode functions of the input signal using non-stationary Prony method. The proposed method captures the philosophy of the empirical mode decomposition, but use a different method to compute the intrinsic mode functions. Having the intrinsic mode functions obtained, we then compute the spectrum of the input signal using Hilbert transform. Synthetic and field data validate the proposed method can correctly compute the spectrum of the input signal, and could be used in seismic data analysis to facilitate interpretation.