Seismic Processing Algorithms Research Articles

3-D Data Interpolation and Denoising by an Adaptive Weighting Rank-Reduction Method Using Multichannel Singular Spectrum Analysis Algorithm

Addressing insufficient and irregular sampling is a difficult challenge in seismic processing and imaging. Recently, rank reduction methods have become popular in seismic processing algorithms for simultaneous denoising and interpolating. These methods are based on rank reduction of the trajectory matrices using truncated singular value decomposition (TSVD). Estimation of the ranks of these trajectory matrices depends on the number of plane waves in the processing window; however, for the more complicated data, the rank reduction method may fail or give poor results. In this paper, we propose an adaptive weighted rank reduction (AWRR) method that selects the optimum rank in each window automatically. The method finds the maximum ratio of the energy between two singular values. The AWRR method selects a large rank for the highly curved complex events, which leads to remaining residual errors. To overcome the residual errors, a weighting operator on the selected singular values minimizes the effect of noise projection on the signal projection. We tested the efficiency of the proposed method by applying it to both synthetic and real seismic data.

Seismic delineation of the gold‐bearing structures in the South Rand goldfield (South Africa): A comparison of pre‐stack time and depth migration approaches on legacy seismic data

ABSTRACTTo better image complex geological structures and explore for the gold‐bearing quartz pebble conglomerate (locally termed Kimberley Reef) near Burnstone mine in the South Rand goldfield (South Africa), we reprocessed legacy 2D reflection seismic data using up‐to‐date seismic processing algorithms. The mining region is dominated by steeply dipping normal and reverse faults, as well as dolerite intrusions that crosscut the tabular gold mineralization and complicate the extraction of the ore. The legacy seismic data were acquired in 1993 in the South Rand goldfield as part of the gold exploration programme by the Gold Division of Anglo‐American Corporation. The pre‐stack data quality was improved by cautiously removing noise and applying static corrections to enhance the continuity of the reflection events. Improved structural imaging was then achieved using pre‐stack time migration and pre‐stack depth migration through careful velocity analysis. In particular, pre‐stack depth migration provided better imaging of near‐surface stratigraphic units and deep‐seated complex structures, relative to older post‐stack migrated images produced in 1993. Other reprocessing improvements included accurate imaging of key seismic reflective interfaces that can be used as proxies to 2D map the gold deposit, its dip variations, and geological structures (faults/dykes) crosscutting it. Synthetic shot gathers data computed using a 2D finite‐difference algorithm provided some insight into the source of seismic reflectivity observed on the reprocessed seismic data. The new structural information from reprocessing is essential for enhancing ore resource evaluation and guiding future exploration projects in the region.

DEEP LEARNING-BASED NUMERICAL DISPERSION MITIGIATION IN SEISMIC MODELLING

Seismic modelling is the most computationally intense and time consuming part of seismic processing and imaging algorithms. Indeed, generation of a typical seismic data-set requires approximately 10 core-hours of a standard CPU-based clusters. Such a high demand in the resources is due to the use of fine spatial discretizations to achieve a low level of numerical dispersion (numerical error). This paper presents an original approach to seismic modelling where the wavefields for all sources (right-hand sides) are simulated inaccurately using coarse meshes. A small number of the wavefields are generated with computationally intense fine-meshes and then used as a training dataset for the Deep Learning algorithm - Numerical Dispersion Mitigation network (NDM-net). Being trained, the NDM-net is applied to suppress the numerical dispersion of the entire seismic dataset.

A high school student's introduction to geophysics through acquisition, processing, and interpretation of GPR data from marked and unmarked grave sites

During the 2019–2020 school year, a high school student engaged in a science fair project that involved acquiring, processing, and interpreting geophysical data. The project used ground-penetrating radar (GPR) to identify response signatures of marked and unmarked grave sites in Fairlawn Cemetery in Stillwater, Oklahoma. During the investigation, the student was introduced to GPR acquisition equipment, seismic processing algorithms, and interpretation techniques. With the help of local university outreach and community mentors, the student was able to complete the science fair project with a positive outcome.

Unsupervised physics-based neural networks for seismic migration

We have developed a novel framework for combining physics-based forward models and neural networks to advance seismic processing and inversion algorithms. Migration is an effective tool in seismic data processing and imaging. Over the years, the scope of these algorithms has broadened; today, migration is a central step in the seismic data processing workflow. However, no single migration technique is suitable for all kinds of data and all styles of acquisition. There is always a compromise on the accuracy, cost, and flexibility of these algorithms. On the other hand, machine-learning algorithms and artificial intelligence methods have been found immensely successful in applications in which big data are available. The applicability of these algorithms is being extensively investigated in scientific disciplines such as exploration geophysics with the goal of reducing exploration and development costs. In this context, we have used a special kind of unsupervised recurrent neural network and its variants, Hopfield neural networks and the Boltzmann machine, to solve the problems of Kirchhoff and reverse time migrations. We use the network to migrate seismic data in a least-squares sense using simulated annealing to globally optimize the cost function of the neural network. The weights and biases of the neural network are derived from the physics-based forward models that are used to generate seismic data. The optimal configuration of the neural network after training corresponds to the minimum energy of the network and thus gives the reflectivity solution of the migration problem. Using synthetic examples, we determine that (1) Hopfield neural networks are fast and efficient and (2) they provide reflectivity images with mitigated migration artifacts and improved spatial resolution. Specifically, the presented approach minimizes the artifacts that arise from limited aperture, low subsurface illumination, coarse sampling, and gaps in the data.

How rough sea affects marine seismic data and deghosting procedures

ABSTRACTMost seismic processing algorithms generally consider the sea surface as a flat reflector. However, acquisition of marine seismic data often takes place in weather conditions where this approximation is inaccurate. The distortion in the seismic wavelet introduced by the rough sea may influence (for example) deghosting results, as deghosting operators are typically recursive and sensitive to the changes in the seismic signal. In this paper, we study the effect of sea surface roughness on conventional (5–160 Hz) and ultra‐high‐resolution (200–3500 Hz) single‐component towed‐streamer data. To this end, we numerically simulate reflections from a rough sea surface using the Kirchhoff approximation. Our modelling demonstrates that for conventional seismic frequency band sea roughness can distort results of standard one‐dimensional and two‐dimensional deterministic deghosting. To mitigate this effect, we introduce regularisation and optimisation based on the minimum‐energy criterion and show that this improves the processing output significantly. Analysis of ultra‐high‐resolution field data in conjunction with modelling shows that even relatively calm sea state (i.e., 15 cm wave height) introduces significant changes in the seismic signal for ultra‐high‐frequency band. These changes in amplitude and arrival time may degrade the results of deghosting. Using the field dataset, we show how the minimum‐energy optimisation of deghosting parameters improves the processing result.

A fast joint seismic data reconstruction by sparsity‐promoting inversion

ABSTRACTSeismic field data are often irregularly or coarsely sampled in space due to acquisition limits. However, complete and regular data need to be acquired in most conventional seismic processing and imaging algorithms. We have developed a fast joint curvelet‐domain seismic data reconstruction method by sparsity‐promoting inversion based on compressive sensing. We have made an attempt to seek a sparse representation of incomplete seismic data by curvelet coefficients and solve sparsity‐promoting problems through an iterative thresholding process to reconstruct the missing data. In conventional iterative thresholding algorithms, the updated reconstruction result of each iteration is obtained by adding the gradient to the previous result and thresholding it. The algorithm is stable and accurate but always requires sufficient iterations. The linearised Bregman method can accelerate the convergence by replacing the previous result with that before thresholding, thus promoting the effective coefficients added to the result. The method is faster than conventional one, but it can cause artefacts near the missing traces while reconstructing small‐amplitude coefficients because some coefficients in the unthresholded results wrongly represent the residual of the data. The key process in the joint curvelet‐domain reconstruction method is that we use both the previous results of the conventional method and the linearised Bregman method to stabilise the reconstruction quality and accelerate the recovery for a while. The acceleration rate is controlled through weighting to adjust the contribution of the acceleration term and the stable term. A fierce acceleration could be performed for the recovery of comparatively small gaps, whereas a mild acceleration is more appropriate when the incomplete data has a large gap of high‐amplitude events. Finally, we carry out a fast and stable recovery using the trade‐off algorithm. Synthetic and field data tests verified that the joint curvelet‐domain reconstruction method can effectively and quickly reconstruct seismic data with missing traces.

Calibration of attribute anomalies through prestack seismic modeling

Seismic modeling is commonly used in determining subsurface illumination of alternative seismic survey designs, in the calibration of seismic processing and imaging algorithms, and in the design of effective processing workflows. Seismic modeling also forms the mathematical kernel of impedance inversion and is routinely used to predict the amplitude-variation-with-offset response as a function of rock and fluid properties. However, the use of seismic modeling in seismic attribute studies is less common. We have evaluated four case studies in which 2D synthetic common shot gathers were computed (acoustic or elastic) and processed (including migration) to evaluate possible interpretation hypotheses. The modeling we used in our study shows that the lack of continuous coherence anomalies in a faulted Chicontepec Basin survey was due to overprinting by coherent interbed multiples. Attributes computed from the resulting processed model data revealed that subtle curvature anomalies in a Mississippi Lime survey were due to karst collapse rather than to velocity pushdown related to vertical gas migration. Impedance attributes computed from a Woodford Shale model favored the hypothesis of increased porosity correlated with the occurrence of subtle faults rather than amplitude dimming due to poor fault imaging. Finally, modeling of a fractured basement survey in the Texas Panhandle survey indicated that headwave suppression preserved the basement fracture response while increasing the signal-to-noise ratio. Seismic attribute study on seismic modeling results helped significantly in testing possible interpretation hypotheses in all of our case studies.

The numerical simulation and imaging of seismic scattered wave applied to base metal exploration

The seismic data collected during base metal exploration are often degraded by a variety of non-reflecting signals due to the heterogeneity of ore bodies and host rocks. It is then difficult to generate a high-quality seismic section when conventional reflection seismic processing algorithms are applied to the data. Two seismic records have been simulated from constructed typical ore geological models using the Kirchhoff integration principle. One geological model is the Tongling copper mine in eastern China, and another is the Gejiu (also known as Gegeo) tin mine in the Yunnan Province of south-western China. The simulated seismic data has then been processed using reflection seismic and seismic scatter imaging methods, respectively. The seismic scatter imaging method, which stacked all kinds of reflected/diffracted waves, seems more powerful to image the complexity of the subsurface.

VSP: Beyond time-to-depth

VSP or vertical seismic profile was originally designed and is currently primarily used to give us time-to-depth for seismic-well ties. Beyond time-to-depth a number of possibilities exist. Recently, there has been considerable interest in VSP imaging (Ray et al., 2003; Paulsson et al., 2004; Hornby et al., 2004; Hornby et al., 2005a), with extensive surveys being acquired both on land and offshore. Modeling studies using full-waveform finite-difference method (FDM) (Payne et al., 1994; Van Gestel et al., 2003) show us what we can image for a particular acquisition geometry and geology, with best image results seen with 3D VSP surveys incorporating a large VSP array in the well and a 2D source pattern acquired using a surface seismic shooting vessel. Traditionally, VSP imaging has been implemented using surface seismic processing algorithms. However, the VSP geometry poses its own challenges and unique opportunities. In this article we explore some imaging methods to attempt to take advantage of the VSP g...

The MIT Geophysical Analysis Group (GAG): 1954 and beyond

The MIT Geophysical Analysis Group (GAG) laid the groundwork for the so-called “digital revolution” in exploration seismology. Enders Robinson traces in this issue GAG's history from its earliest days till 1954; here, the story continues with GAG's subsequent evolution until its end in 1957. But that was just the beginning — during the 1960s and 1970s, the new digital technology spread throughout the oil and service industries worldwide, making it possible to develop progressively more sophisticated seismic processing and imaging algorithms that permanently changed the landscape of geophysical exploration.

Parallel geophysical processing

The use of massively parallel processors (MPP) systems is becoming more widespread in the seismic industry as it begins to take advantage of their strength in solving data processing problems. Today it is common for 3-D prestack depth migration and other computer or I/O intensive processes to be run on such platforms. This paper outlines how we have adapted to MPP in order to run our seismic processing algorithms as efficiently as possible.

Transformation from 2-D to 3-D wave propagation for horizontally layered media

The relationship between 2-D and 3-D wave propagation in horizontally layered media was first investigated by Dampney (1971). In the last few years the usefulness and feasibility of transforming point‐source responses with 3-D geometric spreading to equivalent line‐source responses with 2-D geometric spreading have been thoroughly discussed (see Helgesen, 1990; Wapenaar et al., 1990, 1992; Herrmann, 1992; Helgesen and Kolb, 1993; Amundsen, 1993). In the case of cylindrical symmetry this transformation constitutes a required preprocessing step for several seismic processing algorithms based on 2-D wave propagation. The work of Dampney (1971) has apparently been missed by the authors discussing the 3-D to 2-D geometric spreading transform.

Estimation of source array signatures

The signature generated by an array of marine seismic sources is an important input to many seismic processing algorithms. Several methods have been proposed for determining the source signature from a single source or a source array (see e.g., Ziolkowski et al., 1982; Hargreaves, 1984; Loewenthal and Shtivelman, 1989; Carrion et al., 1990; Weglein and Secrest, 1990; Tygel et al., 1991; Landrø and Sollie, 1992, and Amundsen, 1993).

Rapid convergence of some seismic processing algorithms

The rate of convergence of many numerical algorithms can be greatly improved by repeated application of the method of summation by parts. Cases of interest in seismology arise when we need to resample the spectrum of a function at unevenly spaced frequency values. Related examples include the time‐domain evaluation of the Hilbert transform and the extrapolation to the real axis of spectra evaluated in the complex domain. A formula of this type was first presented by Lanczos (1956). The validity of the algorithms depends upon the fact that summation by parts of the cardinal‐series representation is justified as long as a function is somewhat oversampled.

Using complex trace analysis for 4D matching and 4D noise reduction

Over the last 10 years or so, advances in seismic acquisition techniques and in seismic processing algorithms have led to a steady improvement in the quality of time-lapse data and to an adoption of the technique in more varied settings. The fundamental approach to 4D remains unchanged: close repetition of the acquisition geometry, followed by processing techniques to remove residual differences. But, even with sophisticated 4D processing sequences, all 4D datasets display some level of residual 4D noise when the final data is handed to the asset teams for interpretation. Subtraction of two 3D datasets removes the unchanged, underlying ‘geology’ and provides a key product for interpreting changes due to production.