Resolution encompasses a broad topic. To fully grasp its nature and how to enhance it, we must consider various facets, including the challenges of 3-D survey design, acquisition, processing and interpretation. During the last several decades, both academia and industry have made significant advancements in the first two areas. Modern digital seismic data are typically characterized by fairly wide frequency range (from 10 to 100 hertz), a zero-phase wavelet, accurate 3-D positioning and a satisfactory signal-to-noise ratio. Assuming good data quality, the third area is addressed here: interpretation. While this discussion is not exhaustive, it is intended to provide useful concepts and methods for our geologist colleagues.
Definition
To start, how should one define “seismic resolution”?
At least three definitions exist, based on various criteria (figure 1). Using a zero-phase wavelet and a wedge encased in a host with differing impedance (e.g., a sand bed in thick shale), Widess claimed the constant “peak-to-trough” traveltime at λ/8 (λ = dominant wavelength, or 5-150 meters for sedimentary rocks) marks the limit of resolution.
Using a zero-phase wavelet and a stepwise, wedged impedance model (figure 1b), Ricker contended that the “flat spot” of the composite waveform at < λ/٤ should be considered as the resolution limit.
Kallweit and Wood convinced many interpreters that the “peak-to-trough” separation of composite waveform at λ/4 is the most practical resolution limit. For a wedge with a box impedance profile (figure 1a), this is also the “tuning point” at which the maximum composite amplitude is recognized.
For the rest of the discussion, the third concept will be employed. Obviously, the concept of resolution is related to human cognition to the geological target. New concepts are possible in the future to fit new applications; we simply need to be receptive to them. Also, the above-mentioned definitions are from idealized earth models, representing the best possible theoretical resolution. However, the actual (or practical) resolution might not always match the theoretical ideal, partly due to imperfect interpretation. Our objective is to identify more effective techniques and workflows to enhance the practical resolution.
Some Better Practices
For the digital seismic data delivered to interpreters after processing, the key determinants that influence realized resolution include choice of attributes, selection of frequency bandwidth and the wavelet shape. Some strategies are more suitable than others for particular geologic and geophysical formations (stratigraphy, structure, rock physics and fluid content). A comprehensive understanding of those issues requires an extensive literature review. The focus here is on some useful strategies for stratigraphic and sedimentological interpretations.
Strategies to use frequency information: During the last three decades, there have been notable advancements in the analysis and application of seismic frequency information. (1) Partyka and his colleagues pioneered the spectral decomposition method by applying the short window discrete Fourier transform (SWDFT) to compute the spectral energy for time-frequency data volumes. (2) Alternatively, Grossmann and Morlet advanced a procedure called the continuous wavelet transform (CWT) that cross-correlates a group of wavelets against a time series to construct localized frequency representations of a seismic trace in time, which is further improved by matching pursuit decomposition (MPD) for higher vertical resolution in the frequency domain. Moreover, removing interference of low-frequency components, the high-frequency subvolumes from these analyses can effectively increase seismic resolution for thin beds. (3) An even more effective way is RGB color blending of high-, moderate-, and low-frequency spectral components or seismic travel-time traces, which I refer to as “frequency fusion.” In particular, frequency fusion is more useful for stratigraphic and sedimentological reconstruction of a formation in vertical view by creating a geologically realistic display (akin to outcrop photos) that integrate thick and thin beds without significant interferences (figure 2).
Wavelet shape and compactness: Seismic interpreters commonly use zero-phase wavelets as a standard because of their symmetric waveform, which is compact and of the highest temporal resolution. This holds true when dealing with a single reflection surface, such as in structural mapping. However, in the case of a thin bed (figure 1a), the resulting composite waveform is antisymmetric, negating the advantages of the symmetric wavelet. Instead, a 90-degree wavelet can recreate the symmetric waveform, maintaining compactness and achieving optimal resolution. On comparing a stratal slices series from 90-degree data to data from zero-phase volume in the same 3-D survey, an interpreter will see fewer channel images on the 90-degree slice series because there is less vertical mixing of the stacked events, with reduced interferences. This technique is especially useful for interpreting inter-fingered thin-bed formations.
From vertical to horizontal and spatial resolution: When processed properly, a 3-D seismic cube should have a horizontal resolution approximately equal to the vertical resolution. However, the effectiveness of both types of resolutions in interpretation depends on the natural stacking pattern of geological formations. The spatial resolution status of a bed is determined by the ratio of the horizontal versus the vertical dimensions. Field observations reveal that most of the sedimentary thin beds possess a large horizontal dimension (tens to thousands of meters) and a small vertical dimension (meters to tens of meters), resulting in their seismic resolution being one-dimensional horizontally, but merely detectable vertically. Thin beds are volumetrically important in both marine and lacustrine environments. Fortunately, such beds can be effectively interpreted using seismic geomorphology on stratal slices. Apparently, seismic interpretation of thin beds is restricted only to the detectable limit. We observed in a case study that, with wire-line log verification, distributary channel sands as thin as one meter (λ/80) can be spatially resolved on the stratal slice (figure 3), far thinner than λ/25 defined by Sheriff decades ago.
What is Next?
Reflecting on the future of enhancing seismic resolution, we should consider:
- We need to publish more model and case studies to validate useful workflows and thin-bed indicative attributes.
- We should acknowledge that achieving higher resolution isn’t solely a geophysical endeavor; it requires greater geological collaboration.
- We should leverage machine learning, which is currently a hot topic. With a high-quality training datasets, ML can extrapolate high-resolution well data to inter-well regions through a complex nonlinear combination of seismic attributes, as demonstrated in model tests (refer to figure 4). Further research is essential to understand the underlying mechanisms.
- Ultimately, the development of next-generation acquisition and processing technologies is crucial to definitively address the resolution challenge.