# US 8,788,206 B2 · Data compression transforms for use in downhole applications

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- Number: US 8,788,206 B2
- Document ID: US8788206B2
- Status: Granted
- Kind: B2
- Application number: 12/148,890
- Filed: 2008-04-23
- Published: 2009-07-30
- Granted: 2014-07-22
- Earliest claimed: 2008-01-25
- Assignees: Schlumberger Technology Corporation
- Applicants: Caimu Tang
- Inventors: Caimu Tang
- Web page: https://patentgrep.com/patent/US8788206B2

## CPC

- G01V 11/00: Prospecting or detecting by methods combining techniques covered by two or more of main groups G01V1/00 - G01V9/00
- 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

Borehole image data is compressed and transmitted to the surface one or more pixilated traces at a time. The compression methodology typically includes transform, quantization, and entropy encoding steps. The invention advantageously provides an efficient fixed point Karhünen-Loève like transform for compressing sensor data. A significant reduction in latency is achieved as compared to the prior art.

## Claims

### Claim 1

A method for logging a subterranean borehole, the method comprising:
(a) acquiring a pixilated trace of sensor data, the pixilated trace including a plurality of borehole parameter values at a corresponding plurality of discrete tool face angles;
(b) causing a downhole processor to apply a non-orthogonal, KLT-like transform to the pixilated trace to obtain transform coefficients, the transform being selected such that the transform times its transpose equals a diagonal scaling matrix;
(c) causing the downhole processor to quantize the transform coefficients to obtain quantized coefficients; and
(d) transmitting the quantized coefficients uphole.

### Claim 2 (depends on 1)

The method of claim 1, wherein the pixilated trace of sensor data is reorganized to obtain a two-dimensional square matrix of parameter values and (b) comprises causing the downhole processor to apply a two-dimensional transform to the parameter values to obtain a two-dimensional square matrix of transform coefficients.

### Claim 3 (depends on 2)

The method of claim 2, wherein the transform is selected from the group consisting of:
(
a
a
a
b
-
2
⁢
b
b
c
0
-
c
)
;
(
a
a
a
a
b
c
-
c
-
b
a
-
a
-
a
a
c
-
b
b
-
c
)
;
(
a
a
a
a
a
b
-
b
0
-
b
b
c
-
d
0
d
-
c
e
e
-
4
⁢
e
-
e
-
e
d
-
c
0
c
-
d
)
;
and
⁢
(
a
a
a
a
a
a
a
a
b
c
d
e
-
e
-
d
-
c
-
b
f
g
-
g
-
f
-
f
-
g
g
f
c
-
e
-
b
-
d
d
b
e
-
c
a
-
a
-
a
a
a
-
a
-
a
a
d
-
b
e
c
-
c
-
e
b
-
d
g
-
f
f
-
g
-
g
f
-
f
g
e
-
d
c
-
b
b
-
c
d
-
e
)
where a, b, c, d, e, f, and g represent positive rational numbers.

### Claim 4 (depends on 1)

The method of claim 1, wherein (b) comprises causing the downhole processor to apply a one-dimensional transform to the pixilated trace to obtain a one-dimensional matrix of transform coefficients.

### Claim 5 (depends on 1)

The method of claim 1, wherein each matrix element in the transform is selected from the group consisting of rational numbers and integers.

### Claim 6 (depends on 1)

The method of claim 1, wherein scaling factors in the diagonal matrix are bounded rational numbers that are within a factor of two of each another.

### Claim 7 (depends on 1)

The method of claim 1, wherein the scaling factors are applied during quantization in (c).

### Claim 8 (depends on 1)

The method of claim 1, wherein (b) and (c) comprise fixed point operations.

### Claim 9 (depends on 1)

The method of claim 1, wherein:
the pixilated trace of sensor data is separated into first and second blocks;
(b) comprises causing the downhole processor to apply a transform to each of the blocks to obtain first and second blocks of transform coefficients;
(c) comprises causing the downhole processor to quantize the transform coefficients in each block to obtain first and second blocks of quantized coefficients; and
(d) comprises transmitting the first and second blocks of quantized coefficients uphole.

### Claim 10 (depends on 9)

The method of claim 9, wherein each of the first and second blocks of sensor data is a two-dimensional square matrix.

### Claim 11 (depends on 9)

The method of claim 9, wherein the first block of sensor data is a two-dimensional square matrix and the second block of sensor data is a one-dimensional matrix.

### Claim 12 (depends on 2)

The method of claim 2, further comprising:
(e) de-quantizing the quantized coefficients at the surface to obtain reconstructed de-quantized coefficients; and
(f) inverse transforming the reconstructed de-quantized coefficients at the surface to obtain reconstructed sensor data.

### Claim 13 (depends on 12)

The method of claim 12, further comprising:
(g) re-organizing the reconstructed sensor data to obtain a reconstructed trace.

### Claim 14

A method for logging a subterranean borehole, the method comprising:
(a) acquiring a plurality of pixilated traces of sensor data, each of the pixilated traces including a plurality of borehole parameter values at a corresponding plurality of discrete tool face angles;
(b) causing a downhole processor to re-organize the plurality of borehole parameter values in the plurality of traces to obtain a square matrix of parameter values, the size of the square matrix being greater than the number of pixilated traces acquired in (a);
(c) causing the downhole processor to apply a non-orthogonal, KLT-like transform to the square matrix of parameter values to obtain a square matrix of transform coefficients, the transform being selected such that the transform times its transpose equals a diagonal scaling matrix;
(d) causing the downhole processor to quantize the transform coefficients to obtain quantized coefficients; and
(e) transmitting the quantized coefficients uphole.

### Claim 15 (depends on 14)

The method of claim 14, wherein the number of pixilated traces acquired in (a) is less than or equal to four.

### Claim 16 (depends on 14)

The method of claim 14, further comprising:
(f) de-quantizing the quantized coefficients at the surface to obtain reconstructed de-quantized coefficients;
(g) inverse transforming the reconstructed de-quantized coefficients at the surface to obtain reconstructed sensor data; and
(h) re-organizing the reconstructed sensor data at the surface to obtain a plurality of reconstructed traces.

### Claim 17

A method for logging a subterranean borehole, the method comprising:
(a) acquiring at least one pixilated trace of sensor data, the pixilated trace including a plurality of borehole parameter values at a corresponding plurality of discrete tool face angles;
(b) causing a downhole processor to process the at least one pixilated trace of sensor data to obtain a transform matrix;
(c) causing the downhole processor to apply the transform matrix obtained in (b) to the at least one pixilated trace of sensor data to obtain transform coefficients;
(d) causing the downhole processor to quantize the transform coefficients to obtain quantized coefficients; and
(e) transmitting the transform matrix and the quantized coefficients uphole.

### Claim 18 (depends on 17)

The method of claim 17, wherein:
the transform matrix is defined by first and second parameters; and
(e) comprises transmitting the first and second parameters and the quantized coefficients uphole.

### Claim 19 (depends on 18)

The method of claim 18, wherein the first parameter is a mathematical correlation between nearest neighbor pixels in the at least one pixilated trace of sensor data and the second parameter is a mathematical correlation between second nearest neighbor pixels in the at least one pixilated trace of sensor data.

### Claim 20 (depends on 18)

The method of claim 18, further comprising:
(f) processing the first and second parameters at the surface to obtain the transform matrix and a corresponding inverse transform matrix;
(g) de-quantizing the quantized coefficients at the surface to obtain reconstructed de-quantized coefficients; and
(h) utilizing the inverse transform matrix obtained in (f) to inverse transform the reconstructed de-quantized coefficients to obtain reconstructed sensor data.

### Claim 21 (depends on 17)

The method of claim 17, wherein (b) further comprises:
(i) causing the downhole processor to process the sensor data to obtain a covariance matrix; and
(ii) causing the downhole processor to process the covariance matrix to obtain the transform matrix.

### Claim 22 (depends on 21)

The method of claim 21, wherein the covariance matrix is selected from the group consisting of:
M
3
=
(
1
e
1
e
2
e
1
1
e
1
e
2
e
1
1
)
;
M
4
=
(
1
e
1
e
2
e
3
e
1
1
e
1
e
2
e
2
e
1
1
e
1
e
3
e
2
e
1
1
)
;
and
M
5
=
(
1
e
1
e
2
e
3
e
4
e
1
1
e
1
e
2
e
3
e
2
e
1
1
e
1
e
2
e
3
e
2
e
1
1
e
1
e
4
e
3
e
2
e
1
1
)
;
wherein M3, M4, and M5 represent 3×3, 4×4, and 5×5 covariance matrices, e1=α+β, e2=α+βe1, e3=αe1+βe2, e4=αe2+βe3, α represents a mathematical correlation between nearest neighbor pixels in the at least one pixilated trace of sensor data, and β represents a mathematical correlation between second nearest neighbor pixels in the at least one trace of pixilated sensor data.

### Claim 23 (depends on 21)

The method of claim 21 wherein (b) (ii) further comprises causing the downhole processor to process the covariance matrix to obtain its eigenvalues and eigenvectors and further processing the eigenvectors to obtain the transform matrix.

### Claim 24 (depends on 23)

The method of claim 23 wherein:
(b) (ii) further comprises causing the downhole processor to truncate the transform matrix to obtain a fixed point transform matrix; and
(c) comprises causing the downhole processor to apply the fixed point transform matrix obtained in (b) (ii) to the at least one pixilated trace of sensor data to obtain transform coefficients.

### Claim 25

A method for logging a subterranean borehole, the method comprising:
(a) acquiring at least one pixilated trace of sensor data, the pixilated trace including a plurality of borehole parameter values at a corresponding plurality of discrete tool face angles;
(b) causing a downhole processor to quantize the at least one pixilated trace of sensor data to obtain quantized sensor data;
(c) causing the downhole processor to apply a non-orthogonal, KLT-like transform to the quantized sensor data to obtain transform coefficients;
(d) causing the downhole processor to quantize the transform coefficients to obtain quantized coefficients; and
(e) transmitting the quantized coefficients uphole.

### Claim 26 (depends on 25)

The method of claim 25, wherein (b) further comprises causing the downhole processor to apply a Lloyd-Max Quantizer to the at least one pixilated trace of sensor data to obtain the quantized sensor data.

### Claim 27 (depends on 25)

The method of claim 25, further comprising:
(f) de-quantizing the quantized coefficients at the surface to obtain reconstructed de-quantized coefficients;
(g) inverse transforming the reconstructed de-quantized coefficients to obtain reconstructed sensor data; and
(h) de-quantizing the reconstructed sensor data to obtain floating point sensor data.

### Claim 28

A method for logging a subterranean borehole, the method comprising:
(a) acquiring at least one pixilated trace of sensor data, the pixilated trace including a plurality of borehole parameter values at a corresponding plurality of discrete tool face angles;
(b) causing a downhole processor to azimuthally partition the sensor data to obtain a plurality of blocks of sensor data, the plurality of blocks including a first block and at least one other block;
(c) causing the downhole processor to compute differences between each of the at least one other blocks and the first block to obtain at least one block of residuals;
(d) causing the downhole processor to apply a transform to the first block to obtain a first block of transform coefficients and to each of the at least one block of residuals to obtain at least one block of residual transform coefficients;
(e) causing the downhole processor to quantize the first block of transform coefficients and the at least one block of residual transform coefficients to obtain a first block of quantized coefficients and at least one block of residual quantized coefficients; and
(f) transmitting the first block of quantized coefficients and the at least one block of residual quantized coefficients uphole.

### Claim 29 (depends on 28)

The method of claim 28, wherein:
steps (d), and (e) are applied to the first block prior to performing step (c);
obtaining a first reconstructed block of sensor data by using a downhole decoder to reconstruct the first block of quantized coefficients obtained in (e); and
(c) further comprises causing the downhole processor to compute differences between each of the at least one other block and the first reconstructed block to obtain at least one block of residuals.

### Claim 30 (depends on 28)

The method of claim 28, further comprising:
(g) de-quantizing the quantized coefficients at the surface to obtain a first block of reconstructed de-quantized coefficients and at least one block of reconstructed de-quantized residuals;
(h) inverse transforming the first block of reconstructed de-quantized coefficients and the at least one block of reconstructed de-quantized residuals to obtain a first block of reconstructed sensor data and at least one block of reconstructed residuals;
(i) computing a sum of each of the at least one block of reconstructed residuals and the first block of reconstructed sensor data to obtain at least one other block of reconstructed sensor data.

### Claim 31 (depends on 30)

The method of claim 30, further comprising:
(j) de-partitioning the first block of reconstructed sensor data and the at least one other block of reconstructed sensor data to obtain at least one pixilated trace of reconstructed sensor data.

### Claim 32 (depends on 28)

The method of claim 28, wherein the transform applied in (d) comprises a non-orthogonal, fixed point, KL-like transform.