Practical Implementation of Multiple Attenuation Methods on 2D Deepwater Seismic Data : Seram Sea Case Study

Some deepwater multiple attenuation processing methods have been developed in the past with partial success. The success of surface multiple attenuation relies on good water bottom reflections for most deepwater marine situations. It brings the bigger ability to build an accurate water bottom multiple prediction model. Major challenges on 2D deepwater seismic data processing especially such a geologically complex structure of Seram Sea, West Papua – Indonesia are to attenuate surface related multiple and to preserve the primary data. Many multiple attenuation methods have been developed to remove surface multiple on these seismic data including most common least-squares, prediction-error filtering and more advanced Radon transform.Predictive Deconvolution and Surface Related Multiple Elimination (SRME) method appears to be a proper solution, especially in complex structure where the above methods fail to distinguish interval velocity difference between primaries and multiples. It does not require any subsurface info as long as source signature and surface reflectivity are provided. SRME method consists of 3 major steps: SRME regularization, multiple modeling and least-square adaptive subtraction. Near offset regularization is needed to fill the gaps on near offset due to unrecorded near traces during the acquisition process. Then, isolating primaries from multiples using forward modeling. Inversion method by subtraction of input data with multiple models to a more attenuated multiple seismic section.Results on real 2D deepwater seismic data show that SRME method as the proper solution should be considered as one of the practical implementation steps in geologically complex structure and to give more accurate seismic imaging for the interpretation.Keywords : multiple attenuation, 2D deepwater seismic, Radon transform, Surface Related Multiple Elimination (SRME). Banyak metode atenuasi pengulangan ganda dikembangkan pada pengolahan data seismik dengan tingkat keberhasilan yang rendah pada masa lalu. Keberhasilan dalam atenuasi pengulangan ganda permukaan salah satunya bergantung pada hasil gelombang pantul pada batas dasar laut dan permukaan pada hampir seluruh survei seismik laut. Hal tersebut menentukan keakuratan dalam membuat model prediksi pengulangan ganda dasar laut dan permukaan air. Tantangan utama dalam pemrosesan data seismik 2D laut dalam khususnya struktur geologi kompleks seperti Laut Seram, Papua Barat – Indonesia adalah pada kegiatan menekan pengulangan ganda permukaan sekaligus mempertahankan data primer. Beberapa metode yang dikembangkan untuk menghilangkan pengulangan ganda permukaan pada data seismik seperti least-square, filter prediksi kesalahan dan transformasi Radon

Practical Implementation of Multiple Attenuation Methods on 2D Deepwater Seismic Data : Seram Sea Case Study

Some deepwater multiple attenuation processing methods have been developed in the past with partial success. The success of surface multiple attenuation relies on good water bottom reflections for most deepwater marine situations. It brings the bigger ability to build an accurate water bottom multiple prediction model. Major challenges on 2D deepwater seismic data processing especially such a geologically complex structure of Seram Sea, West Papua – Indonesia are to attenuate surface related multiple and to preserve the primary data. Many multiple attenuation methods have been developed to remove surface multiple on these seismic data including most common least-squares, prediction-error filtering and more advanced Radon transform.Predictive Deconvolution and Surface Related Multiple Elimination (SRME) method appears to be a proper solution, especially in complex structure where the above methods fail to distinguish interval velocity difference between primaries and multiples. It does not require any subsurface info as long as source signature and surface reflectivity are provided. SRME method consists of 3 major steps: SRME regularization, multiple modeling and least-square adaptive subtraction. Near offset regularization is needed to fill the gaps on near offset due to unrecorded near traces during the acquisition process. Then, isolating primaries from multiples using forward modeling. Inversion method by subtraction of input data with multiple models to a more attenuated multiple seismic section.Results on real 2D deepwater seismic data show that SRME method as the proper solution should be considered as one of the practical implementation steps in geologically complex structure and to give more accurate seismic imaging for the interpretation.Keywords : multiple attenuation, 2D deepwater seismic, Radon transform, Surface Related Multiple Elimination (SRME). Banyak metode atenuasi pengulangan ganda dikembangkan pada pengolahan data seismik dengan tingkat keberhasilan yang rendah pada masa lalu. Keberhasilan dalam atenuasi pengulangan ganda permukaan salah satunya bergantung pada hasil gelombang pantul pada batas dasar laut dan permukaan pada hampir seluruh survei seismik laut. Hal tersebut menentukan keakuratan dalam membuat model prediksi pengulangan ganda dasar laut dan permukaan air. Tantangan utama dalam pemrosesan data seismik 2D laut dalam khususnya struktur geologi kompleks seperti Laut Seram, Papua Barat – Indonesia adalah pada kegiatan menekan pengulangan ganda permukaan sekaligus mempertahankan data primer. Beberapa metode yang dikembangkan untuk menghilangkan pengulangan ganda permukaan pada data seismik seperti least-square, filter prediksi kesalahan dan transformasi Radon.Dekonvolusi Prediktif dan Metode Surface Related Multiple Elimination (SRME) digunakan sebagai solusi yang baik pada struktur kompleks dimana metode-metode lain gagal untuk memisahkan perbedaan kecepatan interval data primer dan pengulangan ganda. Metode tersebut tidak membutuhkan informasi bawah permukaan selain parameter sumber dan reflektivitas permukaan. Metode SRME terdiri dari 3 tahapan utama : regularisasi SRME, pemodelan pengulangan ganda dan pengurangan adaktif least-square. Regularisasi near offset diperlukan untuk mengisi kekosongan pada near offset yang disebabkan oleh adanya sejumlah tras terdekat yang tidak terekam selama akuisisi. Pemodelan maju digunakan untuk memisahkan data primer dan pengulangan ganda kemudian inversi dengan pengurangan input data dengan model multiple.Hasil pada data seismik 2D laut dalam menunjukkan bahwa metode SRME layak diterapkan sebagai salah satu pengembangan metode atenuasi multiple permukaan serta untuk meningkatkan akurasi data seismik terutama untuk struktur geologi kompleks.Kata kunci : peredaman pengulangan ganda (multiple), seismik 2D laut dalam, transformasi Radon, Surface Related Multiple Attenuation (SRME)

Laterally constrained low-rank seismic data completion via cyclic-shear transform

A crucial step in seismic data processing consists in reconstructing the wavefields at spatial locations where faulty or absent sources and/or receivers result in missing data. Several developments in seismic acquisition and interpolation strive to restore signals fragmented by sampling limitations; still, seismic data frequently remain poorly sampled in the source, receiver, or both coordinates. An intrinsic limitation of real-life dense acquisition systems, which are often exceedingly expensive, is that they remain unable to circumvent various physical and environmental obstacles, ultimately hindering a proper recording scheme. In many situations, when the preferred reconstruction method fails to render the actual continuous signals, subsequent imaging studies are negatively affected by sampling artefacts. A recent alternative builds on low-rank completion techniques to deliver superior restoration results on seismic data, paving the way for data kernel compression that can potentially unlock multiple modern processing methods so far prohibited in 3D field scenarios. In this work, we propose a novel transform domain revealing the low-rank character of seismic data that prevents the inherent matrix enlargement introduced when the data are sorted in the midpoint-offset domain and develop a robust extension of the current matrix completion framework to account for lateral physical constraints that ensure a degree of proximity similarity among neighbouring points. Our strategy successfully interpolates missing sources and receivers simultaneously in synthetic and field data

Sparse Signal Representation in Digital and Biological Systems

Theories of sparse signal representation, wherein a signal is decomposed as the sum of a small number of constituent elements, play increasing roles in both mathematical signal processing and neuroscience. This happens despite the differences between signal models in the two domains. After reviewing preliminary material on sparse signal models, I use work on compressed sensing for the electron tomography of biological structures as a target for exploring the efficacy of sparse signal reconstruction in a challenging application domain. My research in this area addresses a topic of keen interest to the biological microscopy community, and has resulted in the development of tomographic reconstruction software which is competitive with the state of the art in its field. Moving from the linear signal domain into the nonlinear dynamics of neural encoding, I explain the sparse coding hypothesis in neuroscience and its relationship with olfaction in locusts. I implement a numerical ODE model of the activity of neural populations responsible for sparse odor coding in locusts as part of a project involving offset spiking in the Kenyon cells. I also explain the validation procedures we have devised to help assess the model's similarity to the biology. The thesis concludes with the development of a new, simplified model of locust olfactory network activity, which seeks with some success to explain statistical properties of the sparse coding processes carried out in the network

ИНТЕЛЛЕКТУАЛЬНЫЙ числовым программным ДЛЯ MIMD-компьютер

For most scientific and engineering problems simulated on computers the solving of problems of the computational mathematics with approximately given initial data constitutes an intermediate or a final stage. Basic problems of the computational mathematics include the investigating and solving of linear algebraic systems, evaluating of eigenvalues and eigenvectors of matrices, the solving of systems of non-linear equations, numerical integration of initial- value problems for systems of ordinary differential equations.Для більшості наукових та інженерних задач моделювання на ЕОМ рішення задач обчислювальної математики з наближено заданими вихідними даними складає проміжний або остаточний етап. Основні проблеми обчислювальної математики відносяться дослідження і рішення лінійних алгебраїчних систем оцінки власних значень і власних векторів матриць, рішення систем нелінійних рівнянь, чисельного інтегрування початково задач для систем звичайних диференціальних рівнянь.Для большинства научных и инженерных задач моделирования на ЭВМ решение задач вычислительной математики с приближенно заданным исходным данным составляет промежуточный или окончательный этап. Основные проблемы вычислительной математики относятся исследования и решения линейных алгебраических систем оценки собственных значений и собственных векторов матриц, решение систем нелинейных уравнений, численного интегрирования начально задач для систем обыкновенных дифференциальных уравнений

Applications of Wavelet Transforms to the Suppression of Coherent Noise from Seismic Data in the Pre-Stack Domain

The wavelet transform, a relatively new mathematical technique, allows the analysis of non-stationary signals by using basis functions which are compact in time and frequency. The variables in the wavelet domain, scale (a frequency range), and translation (a temporal increment) can be associated with time-frequency, and so in the wavelet transform we have the potential to filter seismic signals in a pseudo time-frequency sense. The one dimensional discrete multiresolution form of the wavelet transform can be effectively used to suppress low frequency coherent noise on seismic shot records. This process, achieved by the muting or weighting of coefficients in the wavelet transform domain, is demonstrated by suppressing low velocity, low frequency ground roll from land- based seismic data, the benefits of which are visible at both the shot and stack stages of the seismic processing stream. The extension of this technique to the suppression of higher frequency coherent noise is limited by the octave band splitting of frequency space by the transform. The wavelet packet transform, an extension of the wavelet transform, allows a more adaptable tiling of the time frequency domain which in turn allows the suppression of noise containing high frequencies whilst minimising signal distortion. This technique is demonstrated to be effective in suppressing airblast from land based common receiver gathers, whilst minimising the distortion of reflected signals. These filtering techniques can be extended to two dimensions, filtering data in the two dimensional wavelet and wavelet packet domains. This technique involves muting the transform coefficients in the wavelet/wavelet packet transform space which has four variables: temporal translation, offset translation, frequency scale and wavenumber scale. As for the one-dimensional case the two dimensional wavelet transform suffers from poor resolution due to the octave splitting of f-k space, but when used in combination with a velocity based shift such as normal moveout, can be used to filter data with minimal distortion to the residual signal. Extending the process to using the two-dimensional wavelet packet transform eliminates the shift requirement and leads to more effective filtering in the four variable transform space. The wavelet packet filtering technique is effective in suppressing low velocity noise from land based seismic records showing visible improvement in both the common shot records and resultant stack. The non-stationary properties of the wavelet transform allows the filtering across geophone arrays (that is, the common shot record) by the application of the transform in the offset domain. Filtering of the wavelet coefficients, in combination with a linear or hyperbolic shift applied before and removed after filtering, allows discrimination against linear noise on common shot records associated with first breaks and hyperbolic events on common midpoint records such as multiples. The use of a simple muting technique in the wavelet domain effectively suppresses these forms of coherent noise. Where the velocity contrast between signal and noise is high, noise suppression is possible whilst preserving reflector amplitudes. Where the velocity contrast is smaller, weighting of the wavelet coefficients (based on transforms of the input signal after translation) allows noise suppression whilst preserving the amplitude versus offset relationships of the primary signal. This is shown to be effective on synthetic, marine and land based data, with improvements observed on common shot records and resultant stacks. The results of all these wavelet transform based filtering techniques are sensitive to the choice of wavelet transform kernel wavelet. The suitability of a kernel wavelet for filtering can be related to the frequency spectra of the kernel wavelet. A fast rate of frequency amplitude fall-off at the edge of a given scale of basis wavelet minimises frequency overlap between neighbouring kernel wavelet scales and so minimises contamination by noise associated with aliasing in the filtered signal, a process that is inherent in the transform process. A flat amplitude response across the frequency range of a given scale also leads to improved filtering results

Embracing Off-the-Grid Samples

Many empirical studies suggest that samples of continuous-time signals taken at locations randomly deviated from an equispaced grid (i.e., off-the-grid) can benefit signal acquisition, e.g., undersampling and anti-aliasing. However, explicit statements of such advantages and their respective conditions are scarce in the literature. This paper provides some insight on this topic when the sampling positions are known, with grid deviations generated i.i.d. from a variety of distributions. By solving the basis pursuit problem with an interpolation kernel we demonstrate the capabilities of nonuniform samples for compressive sampling, an effective paradigm for undersampling and anti-aliasing. For functions in the Wiener algebra that admit a discrete $s$-sparse representation in some transform domain, we show that $\mathcal{O}(s\log N)$ random off-the-grid samples are sufficient to recover an accurate $\frac{N}{2}$-bandlimited approximation of the signal. For sparse signals (i.e., $s \ll N$), this sampling complexity is a great reduction in comparison to equispaced sampling where $\mathcal{O}(N)$ measurements are needed for the same quality of reconstruction (Nyquist-Shannon sampling theorem). We further consider noise attenuation via oversampling (relative to a desired bandwidth), a standard technique with limited theoretical understanding when the sampling positions are non-equispaced. By solving a least squares problem, we show that $\mathcal{O}(N\log N)$ i.i.d. randomly deviated samples provide an accurate $\frac{N}{2}$-bandlimited approximation of the signal with suppression of the noise energy by a factor $\sim\frac{1}{\sqrt{\log N}}$