Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Earth science
Reexamination Certificate
2001-01-23
2003-06-03
McElheny, Jr., Donald E. (Department: 2862)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Earth science
Reexamination Certificate
active
06574567
ABSTRACT:
FIELD OF THE INVENTION
The invention relates to the field of attenuating noise in signals. More particularly, the invention relates to attenuating incoherent, impulsive and coherent noise in seismic data. Even more particularly, the invention relates to using a weighted slant stack to attenuate incoherent, impulsive and coherent noise in seismic data.
BACKGROUND OF THE INVENTION
Geophysicists collect seismic data and analyze it to determine the characteristics of underground and undersea formations. Such information is useful in the search for hydrocarbons and other minerals.
In its raw, unprocessed form, seismic data consists of a large number, typically millions, of “traces.” Each trace is a recording of a signal which represents the seismic energy emitted by a seismic transmitter, reflected off underground formations and received by a receiver. The seismic energy may be transmitted by an underground or undersea explosion or the action of a vibrator truck or through some other means of imparting energy into the earth. The seismic data typically includes signals gathered from receivers arrayed in two dimensions over a geographical region to be analyzed. Typically, a number of traces is gathered from each receiver, with the location of the source of the seismic energy being varied from one trace to the next.
In many cases, analysis of the seismic data is complicated by unwanted noise recorded in the traces along with the signal. The noise may include incoherent noise, impulsive noise or coherent noise or all of those together. Incoherent noise is random noise such that the incoherent noise from two or more traces tends to have a low level of correlation. Impulsive noise tends to appear in the form of spikes or abnormally large amplitudes in isolated portions of a seismic trace or in a whole trace in a number of traces of the seismic data set. Coherent noise tends to correlate among traces and, in many cases, can be grouped early in the processing of the seismic data into sets having identifiable “time dips.”
Incoherent noise is traditionally attenuated by “stacking” or adding a group of traces together. Since incoherent noise is random, it tends to be eliminated by the stacking process. More effective elimination of incoherent noise is accomplished by a technique called f-x-y prediction error filtering (fxy PEF). This technique predicts the signal in the x-y space at each temporal frequency f, thereby reducing the incoherent noise, which is not predictable.
Impulsive noise is usually attenuated using statistical techniques in running windows in which abnormally large amplitudes are edited based on certain types of average measurement. Other techniques use adaptive filtering or neural networks. These algorithms are based on prior training on data containing a typical signal and typical noise. Once the algorithm understands what the signal is and what the noise is, the algorithm is applied to a data set.
Existing techniques for attenuating coherent noise include transforming the traces from the space-time domain into a transform domain, such as the f-k or Radon or slant-stack domain, in which the signal is separated from the noise. The noise is muted in the transform domain and the signal is transformed back into the space-time domain for further processing. Since the noise was muted in the transform domain, it is attenuated in the space-time domain. For example, coherent noise having a particular time dip may be separated from the signal in transforming a trace into the Radon or slant-stack transform domain where it can be muted.
Other existing technologies include combining the diversity stack technique with the slant stack technique. In this technique, incoherent noise is attenuated by a variation on the diversity stack technique and coherent noise is attenuated by transforming the traces to the Radon or slant-stack domain, muting the traces associated with the coherent noise, and transforming the traces back into the space-time domain. The impulsive noise is also attenuated by the diversity technique by suppressing abnormally large amplitudes present in the amplitude array to be stacked.
SUMMARY OF THE INVENTION
In general, in one aspect, the invention features a method of attenuating noise in seismic data including a plurality of input traces. The method includes transforming the seismic data from the space-time domain into the slant-stack domain. Seismic data having a preselected characteristic is excluded when the transforming into the slant-stack domain. The transformed data is inverse transformed from the slant-stack domain into the time space domain.
Implementations of the invention may include one or more of the following. Transforming may include transforming the seismic data from the space-time domain into the &tgr;−p domain. Excluding may include excluding data corresponding to the coordinates: t=&tgr;+px, where t is time, &tgr; is a t-axis intercept, x is a signed distance from an origin and p is a slope. Transforming may include transforming the seismic data from the space-time domain into the &tgr;−p
x
−p
y
domain. Excluding may include excluding data corresponding to the coordinates: t=&tgr;+p
x
x+p
y
y, where t is time, &tgr; is a t-axis intercept, x is a signed distance from an origin in a first direction, y is a signed distance from an origin in a second direction, p
x
is slope in the first direction, and p
y
is slope in the second direction.
In general, in another aspect, the invention features a method of attenuating noise in seismic data. The method includes accepting seismic data comprising a plurality of traces arrayed in two physical dimensions and a time dimension. The method further includes transforming the seismic data into the slant stack domain using a Radon transform.
Implementations of the invention may include one or more of the following. The Radon transform may include a three-dimensional transform using the following equation:
T
(
τ
,
p
x
,
p
y
)
=
N
·
∑
x
=
a
b
∑
y
=
c
d
S
x
,
y
(
τ
+
p
x
x
+
p
y
y
,
x
,
y
)
·
F
x
,
y
(
τ
+
p
x
x
+
p
y
y
,
x
,
y
)
∑
x
=
a
b
∑
y
=
c
d
F
x
,
y
(
τ
+
p
x
x
+
p
y
y
,
x
,
y
)
where:
N is the number of traces in the plurality of traces;
S
x,y
(t) is a subset of the plurality of traces;
F
x,y
(t) is a scaling function;
x is a distance in a first direction;
p
x
is a slope in the first direction;
y is a distance in a second direction;
p
y
is a slope in the second direction;
a and b for the first direction and c and d for the second direction define a volume to be transformed;
t is time in the space-time domain;
&tgr; is intercept time in the &tgr;−p domain; and
T(&tgr;,p
x
, p
y
) is the output data.
The following equation may apply:
F
x
,
y
(
t
)
=
1
S
_
x
,
y
(
t
)
where
{overscore (S)}
x,y
(t) is an average of S
x,y
(t) over predetermined ranges of x, y and t for each x, y and t.
The following equation may apply:
F
x
,
y
(
t
)
=
1
S
_
x
,
y
2
(
t
)
where
{overscore (S)}
2
x,y
(t) is an average of S
2
x,y
(t) over predetermined ranges of x, y and t for each x, y and
a, b, c and d may be such that x and y span S
x,y
(t), a, b, c and d may be such that x and y define a subset of S
x,y
(t). The subset defining S
x,y
(t) may be the full set.
The method may include Fourier transforming T(&tgr;,p
x
, p
y
), multiplying the Fourier-transformed data by &ohgr;
2
; and inverse-Fourier transforming the Fourier-transformed data.
The Radon transform may include a two-dimensional transform using the following equation:
T
(
τ
,
p
)
=
N
·
∑
x
=
a
b
S
x
,
y
(
τ
+
p
x
,
x
)
·
F
x
,
y
(
τ
+
p
x
,
x
)
∑
x
=
a
b
F
x
,
y
(
τ
+
p
x
,
x
)
where:
N is the number of traces in the plurality of traces;
S
x,y
(t) is a subset of the plurality of traces;
F
x,y
(t) is a scaling function;
x is a distance from
McElheny Jr. Donald E.
PGS Americas, Inc.
Thigpen E. Eugene
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