Telemetry coding and surface detection for a mud pulser

1. A method for encoding a non-negative integer, the method comprising:

(a) acquiring a non-negative integer;

(b) encoding at least a portion of the non-negative integer using a first order Fibonacci derived sequence to obtain a first encoded portion;

(c) encoding an uncoded remainder of the integer using a zero-th order Fibonacci sequence to obtain a second encoded portion;

(d) combining the first encoded portion and the second encoded portion to obtain an encoded integer;

(e) transmitting the encoded integer from a downhole location to a surface location; and

(f) receiving the encoded integer at the surface location.

2. The method of claim 1 , wherein the non-negative integer represents an MWD/LWD measurement.

3. The method of claim 1 , wherein (b) comprises encoding at least a portion of the non-negative integer using first through n-th order Fibonacci derived sequences, wherein n is at least 2.

4. The method of claim 3 , wherein the n-th order Fibonacci derived sequence is defined mathematically as follows:

F n ( j )= F n ( j− 1)+ F n-1 ( j )

wherein F n (j) represents the j-th element of the n-th order Fibonacci derived sequence such that j≧2 and n≧1 and F n (1)=1.

5. The method of claim 3 , wherein x represents the non-negative integer and (b) comprises executing the following steps iteratively from F n to F 1 wherein F n represents the n-th order Fibonacci derived sequence and F 1 represents the first order Fibonacci derived sequence:

(i) searching in F k , wherein 1≦k≦n, for the biggest element less than or equal to x, the biggest element being the k i -th element;

(ii) setting the (k i +k+2)-th bit of the first encoded portion to 1; and

(iii) setting x=x−F k (k i ).

6. The method of claim 3 , wherein n is at least 4.

7. The method of claim 3 , wherein n is at least 7.

8. The method of claim 1 , wherein y represents the uncoded remainder of the integer and (c) comprises the following sequence of steps:

(i) searching F 0 for the biggest element smaller than y, the biggest element being the i-th element;

(ii) setting the (i+2)-th bit and the (i+1)-th bit of the second encoded portion to 1 and setting y=y−F 0 (i); and

(iii) repeating the following steps until y=0: (a) searching F 0 for the biggest element smaller than y (the j-th element), (b) setting the (j+1)-th bit of the second encoded portion to 1, and (c) setting y=y−F 0 (j).

9. The method of claim 1 , further comprising:

(e) denormalizing the encoded integer.

10. The method of claim 9 , wherein Q represents a number of idle slots and (e) further comprises:

(i) inserting Q-1 idle slots before each ‘1’ located before a first ‘11’;

(ii) inserting Q-1 idle slots before and after a first ‘1’ in the first ‘11’; and

(iii) inserting Q idle slots before each ‘1’ after the first ‘11’.

11. The method of claim 1 , wherein the encoded integer includes a predefined word tag.

12. The method of claim 1 , wherein the encoded integer comprises an identifier located between the first encoded portion and the second encoded portion.

13. The method of claim 1 , wherein (e) further comprises transmitting the encoded integer with a downhole electromechanical mud pulser.

14. A method for transmitting downhole data to a surface location, the method comprising:

(a) acquiring a non-negative integer representative of the downhole data;

(b) encoding at least a portion of the non-negative integer using a first order Fibonacci derived sequence to obtain a first encoded portion;

(c) encoding an uncoded remainder of the integer using a zero-th order Fibonacci sequence to obtain a second encoded portion;

(d) combining the first encoded portion and the second encoded portion to obtain an encoded integer;

(e) transmitting the encoded integer to the surface;

(f) receiving the encoded integer at the surface location; and

(g) decoding the encoded integer at the surface location to obtain a decoded integer.

15. The method of claim 14 , wherein (g) further comprises:

(i) searching for a first ‘11’ in the encoded integer;

(ii) recording positions of each ‘1’ after the first ‘11’

(iii) decoding a value for each ‘1’ recorded in (ii) using the at least first order Fibonacci derived sequence;

(iv) recording positions of each ‘1’ prior to a second ‘1’ in the first ‘11’;

(v) decoding a value for each ‘1’ recorded in (iv) using the zero-th order Fibonacci sequence; and

(vi) summing the decoded values obtained in (iii) and (v).

16. The method of claim 14 , wherein (e) further comprises transmitting the encoded integer with a downhole electromechanical mud pulser.

17. The method of claim 14 , wherein the non-negative integer represents an MWD/LWD measurement.

18. The method of claim 14 , wherein (b) comprises encoding at least a portion of the non-negative integer using first through n-th order Fibonacci derived sequences, wherein n is at least 2.

19. The method of claim 18 , wherein n is at least 4.

20. The method of claim 18 , wherein n is at least 7.