# US 11,906,683 B2 · Dynamic time warping of signals plus user picks

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- Number: US 11,906,683 B2
- Document ID: US11906683B2
- Status: Granted
- Kind: B2
- Application number: 16/954,874
- Filed: 2019-12-12
- Published: 2021-10-14
- Granted: 2024-02-20
- Earliest claimed: 2019-08-26
- Assignees: Landmark Graphics Corporation
- Applicants: Landmark Graphics Corporation
- Inventors: Marc Paul Servais
- Web page: https://patentgrep.com/patent/US11906683B2

## CPC

- E21B 44/00: Automatic control systems specially adapted for drilling operations, i.e. self-operating systems which function to carry out or modify a drilling operation without intervention of a human operator, e.g. computer-controlled drilling systems; Systems specially adapted for monitoring a plurality of drilling variables or conditions
- G01V 11/002: {Details, e.g. power supply systems for logging instruments, transmitting or recording data, specially adapted for well logging, also if the prospecting method is irrelevant (means for transmitting well survey signals E21B47/12; signal transmission systems in general G08C; transmission in general H04B)}
- E21B 47/12: Means for transmitting measuring-signals or control signals from the well to the surface, or from the surface to the well, e.g. for logging while drilling
- E21B 49/00: Testing the nature of borehole walls; Formation testing; Methods or apparatus for obtaining samples of soil or well fluids, specially adapted to earth drilling or wells
- G01V 1/48: Processing data
- G01V 3/18: specially adapted for well-logging
- G01V 3/38: Processing data, e.g. for analysis, for interpretation, for correction
- E21B: EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- G01V: GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS (means for indicating the location of accidentally buried, e.g. snow-buried, persons A63B29/02)

## Abstract

A method for correlating data comprises acquiring a first sequence signal and a second sequence signal, wherein the first sequence signal comprises at least a first data point including a first set of components and the second sequence signal comprises at least a second data point including a second set of components; acquiring a first set of user picks and a second set of user picks, wherein the first and the second sets of user picks each contain a respective first and second correspondence between a component in the first set of components and a component in the second set of components; combining the first and second sets of user picks with the first and second sequence signals to create a first hyper-complex signal and a second hyper-complex signal; and performing signal alignment on the first and second hyper-complex signals.

## Claims

### Claim 1

A method for correlating well log data, comprising:
acquiring, by a computer processor, a first sequence signal from at least one first logging tool lowered into a first borehole of a first well at a first speed and a second sequence signal from at least one second logging tool lowered into a second borehole of a second well at a second speed, the first sequence signal and the second sequence signal each being an ordered series having a shared ordering, wherein the first sequence signal comprises at least a first data point including a first set of components and a second data point including a second set of components, the first data point representing parameters at a first depth of the first well and the second data point representing parameters at a second depth of the first well, and wherein the second sequence signal comprises at least a third data point including a third set of components and a fourth data point including a fourth set of components, the third data point representing parameters at a first depth of the second well and the fourth data point representing parameters at a second depth of the second well;
acquiring, by the computer processor, a first set of user picks and a second set of user picks, wherein the first set of user picks contains a first correspondence between the first data point and the third data point, and wherein the second set of user picks contains a second correspondence between the second data point and the fourth data point;
combining, by the computer processor, the first set of user picks and the second set of user picks with the first sequence signal and the second sequence signal to create at least a first modified hyper-complex signal and a second modified hyper-complex signal;
performing, by the computer processor, signal alignment on the first modified hyper-complex signal and the second modified hyper-complex signal to correlate well data between the first sequence signal and the second sequence signal, the signal alignment comprising aligning the ordered series of the first modified hyper-complex signal and the ordered series of the second modified hyper-complex signal along the shared ordering, performing the signal alignment further comprising calculating a distance between a point a and a point b according to the following equation:
ɛ
k
⁡
(
a
,
⁢
b
)
=
Σ
i
|
δ
i
⁢
|
k
k
,
wherein εk denotes the distance between data points a and b, wherein a denotes the first data point or the second data point and b denotes the third data point or the fourth data point, wherein k denotes a norm number, wherein i denotes a quantity of signal components in the first, second, third, and fourth sets of components, and wherein δi denotes a delta value for at least one of a signal component or a user pick,
and further wherein the delta value for the user pick is calculated according to the following equation:
δ
i
=
{
a
i
-
b
i
when
⁢
⁢
neither
⁢
⁢
a
i
⁢
⁢
nor
⁢
⁢
b
i
⁢
⁢
is
⁢
⁢
null
C
i
when
⁢
⁢
⁢
exactly
⁢
⁢
one
⁢
⁢
of
⁢
⁢
a
i
⁢
⁢
and
⁢
⁢
⁢
b
i
⁢
⁢
is
⁢
⁢
null
λ
⁢
C
i
when
⁢
⁢
both
⁢
⁢
a
i
⁢
⁢
and
⁢
⁢
b
i
⁢
⁢
are
⁢
⁢
null
,
wherein wu denotes a user weight, and wherein the user weight is selected according to a skill level of a user associated with the user pick; and
storing, based on the signal alignment, at least a first modified and aligned hyper-complex signal and a second modified and aligned hyper-complex signal, wherein at least one of the first data point or the second data point in the first modified and aligned hyper-complex signal aligns with at least one of the third data point or the fourth data point in the second modified and aligned hyper-complex signal.

### Claim 2 (depends on 1)

The method of claim 1, wherein performing the signal alignment comprises performing dynamic time warping (DTW) on the first modified hyper-complex signal and the second modified hyper-complex signal, wherein at least one of the first modified hyper-complex signal or the second modified hyper-complex signal includes real-value components and imaginary components, wherein the real-value components correspond to at least one of the first, second, third, or fourth sets of components, and wherein the imaginary components correspond to at least one of the first or second sets of user picks.

### Claim 3 (depends on 1)

The method of claim 1, further comprising generating a first well log and a second well log based on output signals of the at least one first logging tool and the at least one second logging tool, wherein the first sequence signal and the second sequence signal are acquired from the first well log and the second well log, respectively.

### Claim 4 (depends on 3)

The method of claim 3, wherein the first set of components in the first data point and the second set of components in the second data point represent parameters at a first depth and a second depth of the first borehole within the first well, and wherein the third set of components in the third data point and the fourth set of components in the fourth data point represent parameters at a third depth and a fourth depth of the second borehole within the second well.

### Claim 5 (depends on 4)

The method of claim 4, wherein a first signal component in the first set of components represents a same type of parameter represented by a signal component in the second set of components, and wherein a second signal component in the first set of components represents another type of parameter represented by another signal component in the second set of components.

### Claim 6 (depends on 4)

The method of claim 4, wherein the parameters represented by components in the first, second, third, or fourth sets of components comprise at least two or more of density measurements, porosity measurements, permeability measurements, gamma ray measurements, formation resistivity measurements, or velocity measurements.

### Claim 7 (depends on 1)

The method of claim 1, wherein the components in one or more of the first, second, third, or fourth sets of components contain valid data, nulls, or a combination thereof, and wherein the first and second sets of user picks contain valid data, nulls, or a combination thereof.

### Claim 8 (depends on 7)

The method of claim 7, wherein the delta value for the signal component is calculated according to the following equation:
δ
i
=
{
w
u
⁡
(
a
i
-
b
i
)
when
⁢
⁢
neither
⁢
⁢
a
i
⁢
⁢
nor
⁢
⁢
b
i
⁢
⁢
is
⁢
⁢
null
w
u
when
⁢
⁢
⁢
exactly
⁢
⁢
one
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⁢
of
⁢
⁢
a
i
⁢
⁢
and
⁢
⁢
⁢
b
i
⁢
⁢
are
⁢
⁢
null
,
0
when
⁢
⁢
both
⁢
⁢
a
i
⁢
⁢
and
⁢
⁢
b
i
⁢
⁢
are
⁢
⁢
null
wherein Ci denotes a first constant and λ denotes a second constant.

### Claim 9

A non-transitory storage medium comprising computer-readable instructions executable by a processor to implement a method for correlating well log data, the method comprising:
acquiring a first sequence signal from at least one first logging tool lowered into a first borehole of a first well at a first speed and a second sequence signal from at least one second logging tool lowered into a second borehole of a second well at a second speed, the first sequence signal and the second sequence signal each being an ordered series having a shared ordering, wherein the first sequence signal comprises at least a first data point including a first set of components and a second data point including a second set of components, the first data point representing parameters at a first depth of the first well and the second data point representing parameters at a second depth of the first well, and wherein the second sequence signal comprises at least a third data point including a third set of components and a fourth data point including a fourth set of components, the third data point representing parameters at a first depth of the second well and the fourth data point representing parameters at a second depth of the second well;
acquiring a first set of user picks and a second set of user picks, wherein the first set of user picks contains a first correspondence between the first data point and the third data point, and wherein the second set of user picks contains a second correspondence between the second data point and the fourth data point;
combining, by the computer processor, the first set of user picks and the second set of user picks with the first sequence signal and the second sequence signal to create at least a first modified hyper-complex signal and a second modified hyper-complex signal;
performing signal alignment on the first modified hyper-complex signal and the second modified hyper-complex signal to correlate well data between the first sequence signal and the second sequence signal, the signal alignment comprising aligning the ordered series of the first modified hyper-complex signal and the ordered series of the second modified hyper-complex signal along the shared ordering, performing the signal alignment further comprising calculating a distance between a point a and a point b according to the following equation:
ɛ
k
⁡
(
a
,
⁢
b
)
=
Σ
i
|
δ
i
⁢
|
k
k
,
wherein εk denotes the distance between data points a and b, wherein a denotes the first data point or the second data point and b denotes the third data point or the fourth data point, wherein k denotes a norm number, wherein i denotes a quantity of signal components in the first, second, third, and fourth sets of components, and wherein δi denotes a delta value for at least one of a signal component or a user pick,
and further wherein the delta value for the user pick is calculated according to the following equation:
δ
i
=
{
a
i
-
b
i
when
⁢
⁢
neither
⁢
⁢
a
i
⁢
⁢
nor
⁢
⁢
b
i
⁢
⁢
is
⁢
⁢
null
C
i
when
⁢
⁢
⁢
exactly
⁢
⁢
one
⁢
⁢
of
⁢
⁢
a
i
⁢
⁢
and
⁢
⁢
⁢
b
i
⁢
⁢
is
⁢
⁢
null
λ
⁢
C
i
when
⁢
⁢
both
⁢
⁢
a
i
⁢
⁢
and
⁢
⁢
b
i
⁢
⁢
are
⁢
⁢
null
,
wherein wu denotes a user weight, and wherein the user weight is selected according to a skill level of a user associated with the user pick; and
storing, based on the signal alignment, at least a first modified and aligned hyper-complex signal and a second modified and aligned hyper-complex signal, wherein at least one of the first data point or the second data point in the first modified and aligned hyper-complex signal aligns with at least one of the third data point or the fourth data point in the second modified and aligned hyper-complex signal.

### Claim 10 (depends on 9)

The non-transitory storage medium of claim 9, wherein performing the signal alignment comprises performing dynamic time warping (DTW) on the first modified hyper-complex signal and the second modified hyper-complex signal.

### Claim 11 (depends on 9)

The non-transitory storage medium of claim 9, wherein the method further comprises generating a first well log and a second well log based on output signals of the at least one first logging tool and the at least one second logging tool, and wherein the first sequence signal and the second sequence signal are acquired from the first well log and the second well log, respectively.

### Claim 12 (depends on 11)

The non-transitory storage medium of claim 11, wherein the first set of components in the first data point and the second set of components in the second data point represent parameters at a first depth and a second depth of the first borehole within the first well, and wherein the third set of components in the second data point and the fourth set of components in the fourth data point represent parameters at a third depth and a fourth depth of the second borehole within the second well.

### Claim 13 (depends on 12)

The non-transitory storage medium of claim 12, wherein a first signal component in the first set of components represents a same type of parameter represented by a signal component in the third set of components, and wherein a second signal component in the first set of components represents another type of parameter represented by another signal component in the third set of components.

### Claim 14 (depends on 12)

The non-transitory storage medium of claim 12, wherein the parameters represented by at least one of the first, second, third, or fourth sets of components comprise at least two or more of density measurements, porosity measurements, permeability measurements, gamma ray measurements, formation resistivity measurements, or velocity measurements.

### Claim 15 (depends on 9)

The non-transitory storage medium of claim 9, wherein the components in one or more of the first, second, third, or fourth sets of components contain valid data, nulls, or a combination thereof, and wherein the first and second sets of user picks contain valid data, nulls, or a combination thereof.

### Claim 16 (depends on 15)

The non-transitory storage medium of claim 15, wherein the delta value for the signal component is calculated according to the following equation:
δ
i
=
{
w
u
⁡
(
a
i
-
b
i
)
when
⁢
⁢
neither
⁢
⁢
a
i
⁢
⁢
nor
⁢
⁢
b
i
⁢
⁢
is
⁢
⁢
null
w
u
when
⁢
⁢
⁢
exactly
⁢
⁢
one
⁢
⁢
of
⁢
⁢
a
i
⁢
⁢
and
⁢
⁢
⁢
b
i
⁢
⁢
are
⁢
⁢
null
,
0
when
⁢
⁢
both
⁢
⁢
a
i
⁢
⁢
and
⁢
⁢
b
i
⁢
⁢
are
⁢
⁢
null
wherein Ci denotes a first constant and λ denotes a second constant.

### Claim 17

A dynamic time warping system comprising:
a drilling system comprising logging and measurement elements communicatively coupled to a logging a facility having a system controller;
the system controller comprising a processor, a non-transitory memory, secondary storage and instructions executing in the non-transitory memory, the instructions configured to:
acquire a first sequence signal from at least one first logging tool lowered into a first borehole of a first well at a first speed and a second sequence signal from at least one second logging tool lowered into a second borehole of a second well at a second speed, the first sequence signal and the second sequence signal each being an ordered series having a shared ordering, wherein the first sequence signal comprises at least a first data point including a first set of components and a second data point including a second set of components, the first data point representing parameters at a first depth of the first well and the second data point representing parameters at a second depth of the first well, and wherein the second sequence signal comprises at least a third data point including a third set of components and a fourth data point including a fourth set of components, the third data point representing parameters at a first depth of the second well and the fourth data point representing parameters at a second depth of the second well;
acquire a first set of user picks and a second set of user picks, wherein the first set of user picks contains a first correspondence between the first data point and the third data point, and wherein the second set of user picks contains a second correspondence between the second data point and the fourth data point;
combine, by the processor, the first set of user picks and the second set of user picks with the first sequence signal and the second sequence signal to create at least a first modified hyper-complex signal and a second modified hyper-complex signal;
perform signal alignment on the first modified hyper-complex signal and the second modified hyper-complex signal to correlate well data between the first sequence signal and the second sequence signal, the signal alignment comprising aligning the ordered series of the first modified hyper-complex signal and the ordered series of the second modified hyper-complex signal along the shared ordering, performing the signal alignment further comprising calculating a distance between a point a and a point b according to the following equation:
ε
k
(
a
,
b
)
=
∑
i
❘
"\[LeftBracketingBar]"
δ
i
❘
"\[RightBracketingBar]"
k
k
wherein εk denotes the distance between data points a and b, wherein a denotes the first data point or the second data point and b denotes the third data point or the fourth data point, wherein k denotes a norm number, wherein i denotes a quantity of signal components in the first, second, third, and fourth sets of components, and wherein δi denotes a delta value for at least one of a signal component or a user pick,
and further wherein the delta value for the user pick is calculated according to the following equation:
δ
i
=
{
w
u
(
a
i
-
b
i
)
when
⁢
neither
⁢
a
i
⁢
nor
⁢
b
i
⁢
is
⁢
null
w
u
when
⁢
exactly
⁢
one
⁢
of
⁢
a
i
⁢
and
⁢
b
i
⁢
are
⁢
null
0
when
⁢
both
⁢
⁢
a
i
⁢
and
⁢
b
i
⁢
are
⁢
null
wherein wu denotes a user weight, and wherein the user weight is selected according to a skill level of a user associated with the user pick; and
store, based on the signal alignment, at least a first modified and aligned hyper-complex signal and a second modified and aligned hyper-complex signal, wherein at least one of the first data point or the second data point in the first modified and aligned hyper-complex signal aligns with at least one of the third data point or the fourth data point in the second modified and aligned hyper-complex signal.

### Claim 18 (depends on 17)

The system of claim 17, wherein performing the signal alignment comprises performing dynamic time warping (DTW) on the first modified hyper-complex signal and the second modified hyper-complex signal.

### Claim 19 (depends on 17)

The system of claim 17, the instructions further configured to:
generate a first well log and a second well log based on output signals of the at least one first logging tool and the at least one second logging tool; and
wherein the first sequence signal and the second sequence signal are acquired from the first well log and the second well log, respectively.

### Claim 20 (depends on 17)

The system of claim 17, wherein the components in one or more of the first, second, third, or fourth sets of components contain valid data, nulls, or a combination thereof, and wherein the first and second sets of user picks contain valid data, nulls, or a combination thereof.