IEEE Signal Processing - March 2018 - 73

Necessity of preprocessing
The preprocessing stage of the prediction framework involving normalization, filtering, and feature selection plays a crucial role to obtain acceptable performances in the subsequent
stages. The first step for RC is the integration of data sets from
several sources, e.g., seismic attributes and well logs. Well logs
are acquired at specific boreholes in the study area. The distributions of lithological properties in the subsurface are more
accurate in borehole locations due to the direct high-resolution
measurements along the wells. On the other hand, the seismic
attributes are recorded spatially with a low vertical resolution
in the time domain. Therefore, it is imperative to use densely
available 3-D seismic attributes along with the existing well
logs as a guide to generate pseudologs of the target lithological
properties over the study area. Figure 1 shows the seismic attributes over a study area along all three dimensions, i.e., inlines,
xlines, and time (depth), whereas a few wells (in this article,
five) are marked by the red lines. Depth and time are synonymous in the reservoir study. Depth can be converted to time by
the velocity profiles available at the well locations.

Integration
Figure 2 lists the difference in the properties of the well logs and
seismic attributes, indicating the requirement of the regularization step to match the high-information-carrying well logs to the
low-information-carrying seismic attributes. The integration of
the well logs and seismic attributes to generate pseudologs over
a study area is demonstrated here. To integrate both types of data
sets, it is necessary to convert the well logs into the time domain
by available velocity profiles from the well-seismic tie [3].

Well C
Time (ms)

the area. At times, vital information related to thin layers and
smaller anomalies are subdued in the seismic data. On the other
hand, well logs with high vertical resolution are recorded at
specific well locations over the study area. Various lithological properties such as porosity, permeability, sand fraction, and
shale fraction are either derived from the well logs or determined from core samples in a laboratory environment. The
well logs and the derived lithological properties can be used as
indicators of potential hydrocarbon-enriched zones in the study
area [3]. The distributions of lithological properties are helpful
to categorize the subsurface layers in dry, water-bearing, and
hydrocarbon-containing sections to identify potential hydrocarbon-enriched zones. However, these properties are available
only in the borehole locations and therefore need to be estimated at other regions in the study area [3]. Seismic attributes,
along with existing well logs, can be used to predict the lithological properties. Nevertheless, there is no clear-cut approach
to relate the lithological properties to seismic attributes. The
most challenging task for researchers is to calibrate the relationship between these data. The mapping of the seismic data
to the lithology cannot be generalized. It is mostly field specific
and needs rigorous statistical-learning methods to bring out
the relationship between them. This article aims to provide an
overview of RC by ascertaining the necessity of each and every
stage such as preprocessing, prediction, and postprocessing.

Well A

Well B
Well D

Well E

Xline
Inline

Figure 1. A representative depiction of distributions of seismic attributes
and well logs.

The disparity in resolution, frequency content, and sampling
interval of the seismic and well-log data sets are resolved during
the integration process [4]. Researchers have worked on interpolation schemes based on wavelet transform (WT) to match
the well-log signals and the seismic data set [5]. A detailed
analysis has been carried out with respect to the resolution,
sampling, and frequency content of the seismic data and well
logs in [4]. In general, the sampling interval of a seismic data set
is 2-4 ms, whereas the well logs are sampled at a much higher
rate (around 0.1 ms). The two data sets can be integrated either
by upsampling the seismic data or downsampling the well logs.
The upsampling of the smooth seismic signals will introduce
negligible artifacts to the data set due to its band-limited characteristic. On the other hand, downsampling of the well logs
would result in information loss [4] as well as a decrease in the
number of training samples. Therefore, the integration can be
carried out by extracting the seismic attributes at the borehole
locations from the 3-D seismic volumes, followed by resampling the seismic signals to well-log instants by a sinc interpolator [3]. Thus, the seismic and well-log data can be integrated
without introducing major artifacts to the data sets while ensuring that the number of samples is sufficiently large for training
of the ML algorithms.

Regularization
As indicated in Figure 2, the sparsely available well logs (with
respect to inlines and crosslines) have high resolution along
the depth, whereas the 3-D seismic attributes have low resolution along the depth. The smooth seismic attributes have lower
information content compared to the well logs. The difference
of information content between the lithological properties
and the seismic attributes necessitates an information filtering scheme [3]. In [3], three regularization approaches based
on empirical mode decomposition (EMD), Fourier transform
(FT), and WT have been evaluated. The parameters associated
with these methods have been optimized as per normalized
mutual information (NMI) and level of entropy. A simplified
block diagram as shown in Figure 3 brings out the basic principles of regularization to match the information content of a
predictor seismic attribute and a target lithological property.

IEEE SIgnal ProcESSIng MagazInE

March 2018

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