Thin-Bed Interpretation
Design Objective
The thickness of many reservoirs is only a fraction of the vertical dimension spanned by the
dominant wavelength of the seismic wavelet that illuminates and images those reservoirs. Such
reservoirs are referred to as seismic thin beds.
The seismic reflection process that occurs when two or more interfaces are separated
vertically by less than one-fourth of a wavelength (thin beds) differs from the reflection process
associated with isolated interfaces (thick beds). The purpose of this module is to demonstrate
how seismic reflection amplitude can be used to interpret reservoirs that have thicknesses less
than one-fourth of the dominant wavelength of the illuminating wavefield.
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Basic Concepts
The dominant wavelength associated with a seismic wavelet is defined as the distance
between two identical phase points of an oscillating function.
Insert Figure 1 here.
Typically wavelength is measured between adjacent peaks or troughs by the symbol . This
seismic wavelet contains a wide spectrum of wavelengths, but the wavelength that is most
apparent is the one shown by , thus it is called the dominant wavelength.
A thin bed is a stratigraphic unit that has a thickness much less than the dominant
wavelength of the seismic wavelet that illuminates the bed. It is generally accepted that if  is the
dominant wavelength of the illuminating seismic wavelet, then a bed with a thickness that is onefourth of  or less can be considered a thin bed.
It is important to note that the definition of a thin bed depends on the length of the
investigative wavelength. A bed that is thin relative to a low-frequency (long-wavelength)
wavelet may not be thin when a higher frequency (shorter wavelength) wavelet is considered, as
is illustrated in Figure 2.
Insert Figure 2 here.
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Ask the Expert
There is some confusion in the literature and among seismic interpreters when referring to
the thickness of a reservoir in time units. This confusion results because many people convert
bed thickness from distance units (feet or meters) directly to one-way traveltime across the bed
(Fig. 3), which is a logical and correct way to define bed thickness in terms of seismic time.
Insert Figure 3 here.
However, all time measurements made from seismic reflection data are two-way traveltime
measurements, not one-way traveltime. Thus a bed that is 1.0 ms thick in one-way traveltime has
to be expressed as a 2-ms bed when it is imaged with a seismic wavelet because the reflection
from the base of the bed involves a downward transmission through the bed (one-way traveltime)
and then an up-going reflection return through the bed (two-way traveltime). Bed thickness can
be defined in terms of either one-way or two-way traveltime as long as
1. The time scale is defined so that there is no confusion and
2. Two-way time is always used when bed thickness is being interpreted from seismic
reflection data.
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Wedge Model
Calculating seismic reflection responses across a bed that thins continuously is a useful
modeling technique for developing the principles of thin-bed interpretation that will be
emphasized in this module. Such a wedge model is displayed in Figure 4.
Insert Figure 4 here.
In this model, the media above and below the thin bed have the same acoustic impedance,
which causes the reflection coefficients at the top and bottom of the bed to have the same
magnitudes but opposite algebraic signs. The basic features of the composite reflection generated
by this simple model can be used to illustrate how bed thickness affects seismic reflection
character for most thin-bed depositional systems. The physics of the reflection process is shown
by the animation associated with the display.
Reinsert Figure 4 here with animation.
When the one-way time thickness of the wedge is one-half or more the dominant
wavelength, the amplitude of the reflection event does not change in magnitude. For such thick
beds, the embedded animation shows that the only indication that bed thickness decreases
(increases) as the modeling process moves across the wedge is that the timing difference between
the reflections from the top and base of the bed decreases (increases).
Wedge Model Exercise Here
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Knowledge Base
The thin-bed regime starts when the one-way traveltime thickness of the wedge is onefourth the dominant wavelength of the illuminating wavelet (or when the two-way traveltime is
one-half the dominant wavelength) and then extends across the thinner portion of the wedge. The
wedge-model animation shows that the magnitude of the reflection amplitude decreases and that
the time difference between the reflections from the top and base of the bed stays constant as the
bed thickness continues to decrease to smaller values.
The key distinctions between the seismic reflection process for thick beds and thin beds are
summarized in the following table.
Reflection amplitude
Time thickness
Thick bed
Constant
Decreases as bed thickness
decreases
Thin bed
Decreases as bed thickness
decreases
Constant
Insert xplot figure here.
Three essential points about the seismic reflection process can be concluded from the wedge
model results.
1. The timing difference between the first and last troughs of the composite reflection is
directly proportional to bed thickness when the one-way traveltime bed thickness
exceeds one-fourth the dominant wavelength (that is, when the two-way traveltime
thickness exceeds one-half the dominant wavelength). Two-way traveltime bed
thicknesses greater than one-half the dominant wavelength can be determined by
measuring the time differences between the onset of the R1 (top interface) and R2
(bottom interface) reflection events that combine to make the composite waveform.
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2. The shape of the reflected waveform changes very little when the one-way traveltime
bed thickness is less than one-fourth the dominant wavelength (or when the two-way
traveltime is less than one-half the dominant wavelength). In this thickness range, it is
the amplitude of the composite reflection, not a phase change or a timing difference
between phase points of that waveform, that is proportional to bed thickness.
3. A constructive interference occurs when the one-way traveltime bed thickness is onefourth the dominant wavelength (which is a two-way traveltime bed thickness of onehalf the dominant wavelength). The composite reflection acquires its largest amplitude
for this value of bed thickness. This phenomenon is called thin-bed tuning.
Insert xplot figure here that identifys thin-bed tuning (resonance).
Because timing differences between phase points (peak extrema, trough extrema, or zero
crossing) of the reflected waveform do not indicate bed thickness when the vertical dimension of
the bed is less than one-fourth the dominant wavelength in one-way time, interpreters define this
one-way traveltime bed-thickness value (i.e., one-fourth the dominant seismic wavelength) as the
onset of the thin-bed regime. The calculated waveshapes in Figure 4 are noise free. In real data,
when noise is added and wavelet interpretation is more difficult, the thin-bed regime is more
difficult to define because noise alters reflection waveshapes and amplitudes in addtion to bed
thickness effects.
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Resolved versus Detected Thin Beds
Two terms used to describe the quality of a thin-bed image say that the bed is either
resolved or detected. If a bed is resolved in zero-phase seismic data, then both the top and bottom
boundaries of the bed can be identified as a peak and/or trough in the seismic response, and the
bed thickness can be measured in terms of the two-way seismic traveltime across the bed. If the
bed creates a seismic reflection event, but the top and bottom boundaries of the bed are so close
together that they cannot both be positioned at a peak and/or a trough in zero-phase data, then the
bed is said to be detected, not resolved. The thickness of a detected bed must be inferred from the
amplitude behavior of its reflection waveshape because its thickness cannot be measured directly
in terms of a two-way traveltime difference between a peak and a trough.
Resolved Vs. Detected Exercise Here.
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Amplitude and Time-Thickness Crossplots
A common procedure used to interpret and calibrate the thickness of thin beds from seismic
data is to construct an amplitude versus time-thickness crossplot from synthetic reflection
waveforms that are constructed in the manner shown in the wedge-model exercise. In such
crossplots, the amplitude axis is some arbitrary measurement of the amplitude of the reflection
waveform associated with the thin bed (such as a peak amplitude, a trough amplitude, or a peakto-trough amplitude), and the time-thickness axis refers to the time difference between the
extrema of the peak and trough that mark the top and bottom reflections of the thin bed.
An example of the construction of such a calibration graph is shown in Figure 5.
Insert Figure 5 here. Note: As you read through this section, the items in red should be
highlighted on the figure as you place your cursor on the red words.
The model responses (top) are the same data created in the wedge model exercise.
Insert figure 5 and the xplot that goes under it here.
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Knowledge Base
The bed thickness at which the amplitude of the reflected composite waveform is a
maximum in an amplitude-versus-time thickness crossplot is referred to as the tuning thickness.
The actual time thickness of the layer that was used when calculating each synthetic reflection
waveform is plotted on the horizontal axis of this plot and is labeled two-way true thickness.
The principal features of such calibration charts are
1. There is a linear relationship between the apparent (measured) two-way time thickness
of a bed and its actual two-way time thickness when the bed thickness is more than
tuning thickness, which in this model is 16 ms. This relationship is shown by the quasilinear, heavier dashed line that slopes up to the right from a thickness value of 16 ms. In
this thickness range above one-half the dominant wavelength (in two-way time), a bed is
said to be time resolved, and its actual thickness can be determined from its apparent
(measured) two-way time thickness.
2. There is a quasi-linear relationship between the peak-to-trough amplitude curve and the
actual bed thickness when the two-way bed thickness is less than tuning thickness. Beds
in this thickness range exhibit the same apparent (measured) time thickness, regardless
of their actual thickness. This effect is shown by the flat, horizontal portion of the
measured time-thickness curve. If reflection events from such beds can be seen in
seismic data, the beds are said to be detected not resolved, and their actual thicknesses
must be estimated from the linear relationship between the actual bed thickness and the
peak-to-trough amplitude of the reflection composite.
The particular calibration chart shown in Figure 5 is correct only if the basic wavelet that is
contained in the seismic data that are being interpreted can be represented by a 20-Hz Ricker
wavelet. A different calibration chart must be constructed for any other type of wavelet.
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Net-Pay Estimates in Heterogeneous Thin Beds
The preceding models assume that the thin bed is a homogeneous unit composed of a single,
uniform rock type. In many situations, a thin sand may contain one or more shale stringers that
subdivide the gross thin-sand unit into several thinner net sands. A question that needs to be
considered is “What effect do shale stringers within a thin bed have on the thin-bed reflection
response?” A model that provides insight into this problem is shown in Figure 6.
Insert Figure 6 here.
The spatial distribution of sand and shale within the thin bed (red arrow in figure) is shown
at the top of the model, and the calculated reflection responses are plotted below this lithological
cross section (red arrow in figure). The apparent (measured) time thickness (red arrow in figure)
and the peak-to-trough amplitude of the calculated reflection waveforms (red arrow in figure) are
shown in graphical form at the bottom of the illustration. The apparent time thickness is
essentially constant, (red arrow in figure) which it should be in a thin-bed regime. However, the
peak-to-trough amplitude increases and decreases in phase with the net-sand curve (red arrow in
figure). The model shows that reflection amplitude is a reliable indicator of net pay within a
thin-bed when the thin-bed is heterogeneous.
The model in Figure 7 carries the investigation a little farther in that it keeps the total
amount of contaminating shale constant but distributes the shale through the thin sand as one,
two, or four stringers.
Insert Figure 7 here.
The peak-to-trough amplitude of the responses at positions 2, 3, and 4 are the same, (red
arrow in figure) which leads again to the conclusion that reflection amplitude is a measure of
the net pay within a thin-bed regardless of how that pay is distributed within the bed. One
must be cautious and not apply this interpretational guideline (i.e., that reflection amplitude is
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directly proportional to net sand), when the gross sand interval that is being studied is thicker
than one-fourth the dominant wavelength of the seismic wavelet.
Net Pay/Amplitude Exercise Here.
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Ask the Expert
Wavelet Considerations
Thin-bed calibration charts must be constructed with a wavelet that accurately represents the
real wavelet contained in the seismic data that are being interpreted. Otherwise, the calibration
curves will not contain the correct number of resonance peaks and oscillations. An interpreter
should be cautious when using many published thin-bed calibration charts because the wavelet
that was used to construct these charts may not be representative of the wavelet contained in the
real data that need to be analyzed.
Depending on the specific processing steps that are followed, most seismic images are
constructed of either a nonsymmetrical basic wavelet or a long symmetrical wavelet that has
several side lobes. The compact Ricker wavelet used in the wedge-model exercise is the type of
wavelet that is usually used to construct many published thin-bed calibration charts. It has only
one side lobe, and the calibration chart made with this wavelet exhibits only one resonance peak
in the amplitude curve and only one oscillation in the apparent time-thickness curve. On the other
hand, the two-side-lobe wavelet in Figure 8 is more representative of the type of zero-phase
wavelet that is created when processing real seismic data.
Insert Figure 8 here.
The calibration chart made with this wavelet exhibits two resonance peaks in the amplitude
curve and two oscillations in the apparent time-thickness curve. A conclusion that can be drawn
is that the number of resonance peaks in the amplitude calibration curve and the number of
oscillations in the apparent time-thickness calibration curve is the same as the number of side
lobes in the wavelet that is used to construct these curves.
Links, Glossary terms, revisions
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