Larry Lines

3D reverse-time migration using the acoustic wave equation: An experience with the SEG/EAGE data set

Kirchhoff is the most commonly used 3D prestack migration algorithm because of its speed and other economic advantages, but it uses a high-frequency ray approximation to the wave equation and, therefore, has difficulties in imaging complex geologic structures where multipathing occurs (e.g., beneath rugose horizons such as faulted salt domes where traveltime calculations become difficult).

A recipe for stability of finite‐difference wave‐equation computations

Finite‐difference solutions to the wave equation are pervasive in the modeling of seismic wave propagation (Kelly and Marfurt, 1990) and in seismic imaging (Bording and Lines, 1997). That is, they are useful for the forward problem (modeling) and the inverse problem (migration). In computational solutions to the wave equation, it is necessary to be aware of conditions for numerical stability. In this short note, we examine a convenient recipe for insuring stability in our finite‐difference solutions to the wave equation. The stability analysis for finite‐difference solutions of partial differential equations is handled using a method originally developed by Von Neumann and described by Press et al. (1986, p. 827–830).

Past, present, and future of geophysical inversion—A new millennium analysis

Geophysicists have been working on solutions to the inverse problem since the dawn of our profession. An interpreter infers subsurface properties on the basis of observed data sets, such as seismograms or potential field recordings. A rough model of the process that produces the recorded data resides within the interpreter’s brain; the interpreter then uses this rough mental model to reconstruct subsurface properties from the observed data. In modern parlance, the inference of subsurface properties from observed data is identified with the solution of a so‐called “inverse problem.” In contrast, the “forward problem” consists of the determination of the data that would be recorded for a given subsurface configuration and under the assumption that given laws of physics hold. Until the early 1960s, geophysical inversion was carried out almost exclusively within the geophysicist’s brain. Since then, we have learned to make the geophysical inversion process much more quantitative and versatile by recourse to a...

VP/VS characterization of a heavy-oil reservoir

This article demonstrates a VP/VS application for a heavy oil field near Plover Lake, Saskatchewan, where Nexen has applied both hot and cold production methods. Plover Lake Field is about 8 km east of the Alberta-Saskatchewan border and about 320 km north of the Canada-U.S. border. Oil sands of the Devonian-Mississippian Bakken Formation are found in NE-SW trending shelf-sand tidal ridges that can be up to 30 m thick, 5 km wide, and 50 km long. Overlying Upper Bakken shales are preferentially preserved between sand ridges. The Bakken Formation is disconformably overlain by Lodgepole Formation carbonates (Mississippian) and/or clastics of the Lower Cretaceous Mannville group. Since sandstones have larger S-wave velocities (and hence lower VP/VS ratios) than shales, VP/VS maps should help to identify thickening sand layers within the target zone. We also intend to examine changes within the reservoir due to cold production. Unlike the steam injection processes used in enhanced heavy oil recovery, cold prod...

Seismic pursuit of wormholes

Cold production has become increasingly popular in the extraction of heavy oil, due to the development and widespread use of progressing cavity pumps—essentially powerful augers that suck both oil and sand into the well. At the onset of production, these pumps produce about 60% oil and 40% sand. However, production can improve to 95% oil with only 5% sand after a few months. This increase in oil production and reduction in sand production is attributed to the development of high-porosity tubes termed “wormholes.” Roche (2002) describes wormhole development as the creation of a network of “horizontal wells without using a drilling rig.” Operators who plan infill drilling rely on wormhole distribution information to optimize well spacing. It is accepted that aggressive cold production of oil sands will increase oil recovery, and this has been demonstrated in several pools, both in Alberta and Saskatchewan.nnSo, assuming these induced sand channels can boost cold heavy oil production, can we map them? Thats a good question because wormholes have small dimensions compared to seismic wavelengths, making their seismic detection extremely difficult. This challenge caused us to perform feasibility tests based on a number of models from the literature. The following describes the results of these tests. We also show some real seismic data with promising indications for wormhole imaging.nnMuch heavy oil recovery in Western Canada involves steam injection. Time-lapse seismology plays a major role in monitoring steam fronts and time-lapse or “4D seismology” is now a standard reservoir characterization tool.nnHowever, steam production/injection is costly, and heavy oil production now increasingly uses cold flow techniques. As stated earlier, cold production methods use special pumps, known as progressing cavity pumps (Figure 1). These pumps, similar to an auger or “Archimedes screw” within a flexible sleeve, lift the oil/sand mixtures from the producing formation …

Viscosity and Q in heavy-oil reservoir characterization

In heavy oil reservoirs, viscosity of fluids is very high and the mobility of the fluids in the reservoir is very low. Different production scenarios are used, depending on oil and reservoir properties, such as cold heavy oil production with sand (CHOPS) or steam-assisted gravity drainage (SAGD). In the former method, a progressive cavity pump is used to extract oil, water, gas, and sand simultaneously from the reservoir; in the latter, the viscosity of the fluid is lowered by injecting steam into the reservoir.

Reverse-time Migration For Tilted TI Media

Seismic anisotropy in dipping shales results in imaging and positioning problems for underlying structures. We develop a reverse-time anisotropic depth migration approach for Pwave and SV-wave seismic data in transversely isotropic (TI) media with a tilted axis of symmetry normal to bedding. Based on an accurate phase velocity formula, the wave equation of weak anisotropy for P-wave and SVwave in tilted transversely isotropic (TTI) media is derived from a P and SV dispersion relationship. The accuracy of the P-wave equation and the SV-wave equation are analyzed and compared with other acoustic wave equations for TTI media. The pseudo-spectral method is used to solve these equations implementing reverse-time migration. The resulting anisotropic depth-migration algorithm is applied to numerical seismic data and physical-model seismic data. According to the comparison between the isotropic and anisotropic migration results, the reverse-time anisotropic depth migration offers significant improvements in positioning and reflector continuity over those obtained using isotropic algorithms.

Research Note: Experimental measurements of Q-contrast reflections

While seismic reflection amplitudes are generally determined by real acoustical nimpedance contrasts, there has been recent interest in reflections due to contrasts in seismic-Q. Herein we compare theoretical and modelled seismic reflection amplitudes for two different cases of material contrasts. In case A, we examine reflections from material interfaces that have a large contrast in real-valued impedance (ρv) with virtually no contrast in seismic-Q. In case B, we examine reflections from material interfaces that have virtually no contrast in ρv but that have very large seismic-Q contrasts. The complex-valued reflection coefficient formula predicts non-zero seismic reflection amplitudes for both cases.We choose physical materials that typify the physics of both case A and case B. Physical modelling experiments show significantly nlarge reflections for both cases – with the reflections in the two cases being phase shifted with respect to each other, as predicted theoretically. While these modelling experiments show the existence of reflections that are predicted by theory, there are still intriguing questions regarding the size of the Q-contrast reflections, the existence of large Q-contrast reflections in reservoir rocks and the possible application of Q-reflection analysis to viscosity estimation in heavy oilfields.

Influence of seismic anisotropy on prestack depth migration

The structural geology of the Alberta Rocky Mountain Foothills is dominated by thrust faults and complex folds, often resulting in steeply dipping formations. In these fold and thrust belt areas, hydrocarbon reservoirs are frequently overlain by thick, dipping clastic sequences including shales and thinly interbedded sandstones and shales. Shalles exhibit intrinsic seismic velocity anisotropy, which refers to the variation of velocity with direction, with the main symmetry axis perpendicular to bedding. The main physical reasons for seismic anisotropy are due to aligned mineral grains, aligned cracks, aligned crystals, and periodic thin layering.

Neural networks and AVO

In this tutorial we will discuss how a neural network can solve a simple AVO problem. In doing so, we will shed light on two important questions: Why are some neural networks only able to solve linear problems (but others can solve nonlinear problems) and how can neural networks be trained to do these tasks? The type of neural network that we will use is the multilayer perceptron (MLP), sometimes called the multilayer feed-forward network (MLFN). The AVO problem that we will train the network to address is the recognition of a class 3 anomaly on an AVO attribute plot. As we shall see, training a computer to perform tasks that are simple for a human being (that is, an interpreter) can often be quite difficult. However, if we can train a computer to systematically and objectively interpret an AVO plot, it will be worth the effort.