Machine learning techniques hold significant promise in identifying and delineating heterogeneous 3-D seismic facies, as they allow us to integrate the information content from multiple seismic attribute volumes.
There is a well-established unsupervised ML technique, called self-organizing mapping, which has been applied to a seismic data volume from New Zealand (figure 1). We find that SOM can enhance spatial resolution and, therefore, assist in seismic interpretation. ML algorithms do not replace the interpreter; rather, the interpreter now needs to bias their area of investigation and training data to address their objectives, choose an appropriate suite of attributes, modify the attribute histograms, and weight the attributes to obtain an accurate result.
Self-Organizing Mapping
SOM is a technique used to generate a seismic facies map from multiple seismic attributes in an unsupervised manner. It starts by defining initial cluster centroids in an N-dimensional attribute data space and utilizes the first two eigenvectors of the covariance matrix to least-squares fit the data with a plane. Grid prototype vectors (also called neurons), defined in this plane, are attracted to data points outside the plane, deforming it into a 2-D surface known as a manifold that better fits the data. Upon convergence, the N-dimensional data are projected onto this 2-D surface, which is then mapped onto a 2-D plane or “latent” space, defined by axes SOM-1 and SOM-2. The SOM workflow is shown in figure 2. In this space, the interpreter can either explicitly define clusters by drawing polygons or implicitly define them by plotting the results against a 2-D color bar. For more details see the November 2022, October 2023 and December 2023 installments of Geophysical Corner.
In many software packages, the input attributes used for SOM computation are treated equally, with each attribute assigned the same weight. While this approach may work in some cases, attributes often serve different objectives and may require varied emphasis depending on the geological context. To better reflect geological significance, it is advisable to assign different weights to different attributes in a data-adaptive manner.
We used the Pipeline 3D seismic survey from New Zealand for the application of PCA and SOM workflows and understand the different architectural elements and discriminate seismic facies along the deepwater channel complex identified at close to 2.3 seconds two-way travel time. Figure 1 shows the location of the 3-D survey in the Taranaki Basin offshore western side of the North Island, New Zealand. The survey was acquired in 2013 and covers an area of 515 square kilometers. The data are zero phase, exhibit negative polarity, with a sample increment of 4 milliseconds, a bin size of 25 meters by 12.5 meters and a record length of 6 seconds.
Significant uplift of the New Zealand North Island landmass occurred throughout Miocene, and coupled with climate-driven erosion, led to the development of the Neogene major submarine system that transported large volumes of sediment from onshore areas into the deepwater Taranaki Basin (figure 1). It is well documented that during the Middle Miocene a change from sand-dominated to more mud-dominated deposits took place. We aim to understand the architectural elements as well as delineation of the facies of the main channel system using the available seismic data.
Figure 2 shows the SOM seismic facies analysis workflow. Sixteen input attributes were used for the SOM computation. The SOM-1 and SOM-2 components were generated using the input volumes and assigning equal weights to each of them, and then the computation was repeated by assigning different weights to them for SOM computation. The SOM computations were carried out on stratal volumes of attribute data generated about an interpreted horizon, 400 milliseconds above it, which encompassed the main channel seen in the different displays.
Choice of Attributes
The literature is filled with numerous studies that explore various attribute selections for unsupervised seismic facies classification. We believe, however, that attributes representing the main body of subsurface rocks are a more appropriate choice for seismic facies classification than those focused on edges or discontinuities, which may not align with facies boundaries. If we look at the histograms of different seismic attributes being used for unsupervised seismic facies classification (some of which are shown in figures 3a to 3f) we notice that those for body attributes are rounded and symmetric, whereas those for edge attributes are highly skewed and sharp (figure 3g). Statistical measures such as skewness and kurtosis which measure the symmetry and sharpness of histograms respectively, can be computed, which can help quantify the preference of body over edge attributes. These computed values for the shown attributes can be seen in the inset for each of the displays. Many of unsupervised seismic facies classification algorithms are built on Gaussian statistics. If the target of interest falls towards the middle of the range of the attributes selected, modifying the histogram helps separate the features of interest. In contrast, if the targets are represented by attribute extrema (low coherence salt domes or anomalously high negative amplitude bright spots, for example), exacerbating the non-Gaussian nature of the histogram may help. Figure 3a-3f show histograms with high values of kurtosis, where the histogram in figure 3g shows a high value of skewness.
For the delineation of channel or sandstone facies, several attribute volumes were used in the present study, including relative acoustic impedance, GLCM (gray-level co-occurrence matrix) homogeneity, sweetness, peak magnitude, average frequency, and spectral magnitudes at frequencies between 20 and 70 hertz, with 5-hertz increments:
- Relative acoustic impedance is computed by continuously integrating the original seismic trace, followed by the application of a low-cut filter. The impedance transformation of seismic amplitudes allows for the transition from reflection interfaces to interval properties of the data, without requiring a low-frequency model.
- Sweetness is a “meta-attribute” derived from others and is calculated as the ratio of the envelope to the square root of the instantaneous frequency. A clean sand embedded in shale will exhibit a high envelope and lower instantaneous frequency, resulting in a higher sweetness value compared to the surrounding shale-on-shale reflections.
- GLCM homogeneity: The Gray-Level Co-occurrence Matrix homogeneity measures the lateral smoothness of the seismic amplitude along structural dip. For examples, point bars commonly exhibit a high value of GLCM homogeneity.
- Peak magnitude represents the spectral magnitude of the seismic data at the peak frequency.
- Average frequency is the average Fourier spectral frequency, weighted by the amplitude or power spectrum. Alternatively, it can be defined as the average instantaneous frequency, weighted by the instantaneous amplitude or power. This attribute captures the frequency characteristics of the seismic signal across the available dataset.
- Spectral magnitude is the magnitude of each spectral component ranging within the seismic bandwidth, calculated at specific frequency increments.
Application
Figure 4 shows a comparison of horizon slices 208 milliseconds above a tracked marker extracted from a SOM-1 versus SOM-2 crossplot volumes generated for the case of equal weights to the attributes (figure 4a) and then when different weights were used (figure 4b). The geologic features seen on the display shown in figure 4b generated with different weights exhibit better spatial resolution than the equivalent display where equal weights were used. Figure 4c shows the same slice through the corendered SOM with different weights shown in figure 4b and multispectral energy ratio coherence. With the SOM colors defining the stratigraphic “fill” and coherence defining the stratigraphic edges, we can readily interpret the different geological features such as the main channel, scroll bars, and the crevasse splays, as indicated. What coherence maps as “channel edges” (indicated by the white dashed curves) is more accurately defined to be the edges of a meander valley. Inside this meander valley the SOM bluish, greenish and shades of purple colors (and to a lesser extent) coherence delineate individual architectural elements, including thinner channels, some of which may be sand- and others shale filled, preserved point bars and other features. Outside the main meander valley we see scroll bars, indicating the edges of previously deposited point bars. The crevasse splays are shown interpreted and are probably changing facies from the sandy facies in greenish color to mud-like facies away from the channel indicated in bright purple and red colors.
Potential Pitfalls
There are some pitfalls common to both unsupervised and supervised facies classification.
First, the choice of attributes needs to be able to differentiate the target features of interest. Although understanding of what physical properties that each attribute measures and the seismic expression of the target geologic feature is key, the seismic bandwidth, focussing, signal-to-noise ratio, and the effects of the overburden also play a role. This choice of attributes becomes more vexing in unsupervised classification where the goal is to examine the seismic data volume for features that we may not have anticipated as being in the data.
Second, the domain of analysis should be temporally limited to differentiate geologic features with a target geologic package, allowing the attribute analysis technique (in this article, SOM) to “span” the attribute variability and provide maximum resolution. Using large analysis windows (in the extreme, using the entire seismic volume) run the risk of mixing carbonates and volcanics, shale diapirs and carbonate buildups, or dissolution features and pockmarks and other geologic features having an overlapping seismic response into the analysis, leading to potentially ambiguous results. In addition, because of the loss of vertical and lateral resolution with depth, the same geologic feature in the shallow section may have a different attribute response to one in the deeper section resulting in them being mapped as different (rather than the same) seismic facies.
Conclusions
We find that assigning different weights to the input attributes during SOM computation improves the spatial resolution of the resulting displays, compared to when equal weights are applied. This observation significantly enhances the discrimination of different seismic facies on SOM displays, aiding the interpreter in more accurately identifying and distinguishing geological features.
Acknowledgements
The first author would also like to thank the Attribute-Assisted Seismic Processing and Interpretation Consortium, University of Oklahoma, for access to their software, which has been used for all attribute computation.