Abstract:
The present invention provides self-servo writing by which self-propagated servo pattern track shape errors are reduced or eliminated. The method includes providing first servo bursts on a first track, measuring edge errors of the first servo bursts, and self-servo writing second servo bursts to a second track using different combinations of the edge errors to adjust the position error signals for the second servo bursts.

Description:
RELATED APPLICATION 
     This application claims priority from U.S. Provisional Application Ser. No. 60/285,015, filed on Apr. 19, 2001, which is incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to disk drives, and more particularly to correcting compound errors during self-servo writing. 
     BACKGROUND OF THE INVENTION 
     Disk drives are well known in the computer art for providing secondary mass storage with random access. A disk drive includes one or more magnetic data storage disks rotated on a spindle by a spindle motor within an enclosed housing. A magnetic read/write head (transducer or slider) with an air bearing surface is placed on an actuator arm and positioned close to a corresponding disk. 
     The close proximity of the head to the disk enables high-resolution servo patterns and user data to be recorded on the disk. The servo patterns are written in servo sectors which are interleaved between data sectors. The servo patterns provide a servo controller with head position information to enable a head positioner, such as a rotary voice coil motor, to move the head from track-to-track during random access seek operations, and to maintain the head in proper alignment with a track during track following operations when user data is written to or read from the available data sectors on the track. The servo patterns include short servo bursts of constant frequency, precisely located relative to a track centerline. The servo patterns allow the head to follow the track centerline even when the track is non-circular, as can occur with spindle wobble, disk slip and thermal expansion. 
     The servo patterns have been written by an external servo track writer that supports the disk drive on a large granite block to reduce vibration. However, servo track writers are expensive, require a clean room environment and expose the head and the disk to the environment. The servo patterns have also been written by the disk drive during self-servo writing without a servo track writer. Self-servo writing involves the head reading position and timing information from the disk, the head being positioned using the position information and the head writing the servo patterns to the disk using the timing information. 
     Self-servo writing suffers from self-propagation, as described in U.S. Pat. No. 5,907,447 to Yarmchuk et al. During self-propagation, servo bursts in a previous track are used to position the head as the head writes servo bursts to the next track. However, perturbations in the servo bursts in the previous track propagate to the servo bursts in the next track. Compound errors that propagate across the tracks can lead to excessive track non-circularity. 
     There is, therefore, a need to reduce compound errors due to self-propagation during self-servo writing in a disk drive. 
     SUMMARY OF THE INVENTION 
     The present invention provides self-servo writing by which self-propagated servo pattern track shape errors are reduced or eliminated. The method includes providing first servo bursts on a first track, measuring edge errors of the first servo bursts, and self-servo writing second servo bursts to a second track using different combinations of the edge errors to adjust the position error signals for the second servo bursts. 
     The method can include providing A, B, C and D first servo bursts on the first track, measuring top and bottom edge errors of the A, B, C and D first servo bursts, and self-servo writing A, B, C, and D second servo bursts that are radially aligned with the A, B, C and D first servo bursts, respectively, using different combinations of the edge errors during different revolutions of the disk. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and other features, aspects and advantages of the present invention will become understood with reference to the following description and accompanying figures where: 
         FIG. 1  shows a disk drive in which the present can be implemented; 
         FIG. 2  shows servo bursts written on circular tracks; 
         FIG. 3  shows servo busts written on non-circular tracks; 
         FIG. 4  shows servo bursts that contain edge errors; 
         FIG. 5  shows a flowchart of self-servo writing that removes WRO to prevent compound errors; 
         FIG. 6  shows a logic diagram for self-servo writing that removes WRO to prevent compound errors; 
         FIG. 7  shows a head with read and write elements having a single track offset; 
         FIG. 8  shows a head with read and write elements having a multiple track offset; and 
         FIG. 9  shows a flowchart of self-servo writing that removes WRO to prevent compound errors with the read and write elements having multiple track offset. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 1  shows a disk drive  10  in which the present invention can be implemented. The disk drive  10  includes a data storage disk  12 , a head  14  (having a read element and a write element), an actuator arm assembly  16 , a voice coil motor (VCM)  18 , a read/write channel  20 , an interface  22 , a servo controller  24 , a drive controller  26  and a memory  28 . The disk drive  10  is coupled to an external host computer  30  that uses the disk drive  10  as a mass storage device. 
     The disk drive  10  receives read and write requests from the host computer  30  and carries out the requests by performing data transfers between the disk  12  and the host computer  30 . In a preferred embodiment, the disk drive  10  includes multiple disks  12  in a vertical stack and multiple heads  14  with one head  14  for each operative disk surface. Typically, both surfaces of each disk  12  store user data and therefore the disk drive  10  includes two heads  14  for each disk  12 . Single-sided disk arrangements can also be used. 
     The interface  22  provides an interface between the disk drive  10  and the host computer  30 . During read and write operations, the interface  22  provides a communications path that includes data buffering between the channel  20  and the host computer  30 . In addition, the interface  22  receives commands and requests from the host computer  30  and directs them to the drive controller  26 . The drive controller  26  carries out the commands by appropriately controlling the elements within the disk drive  10 . 
     The VCM  18  positions the head  14  with respect to the disk  12  in response to a control signal generated by the servo controller  24 . The head  14  is coupled to the actuator arm assembly  16  and thus moves under the influence of the VCM  18 . When performing a read or write operation, the drive controller  26  instructs the servo controller  24  to move the head  14  to a target track on the disk  12  so that a data transfer can take place. The servo controller  24  then generates a control signal to move the head  14  from the present track to a target track during a seek operation. 
     Once the head  14  arrives at the target track, the servo controller  24  enters a track following operation during which the head  14  is maintained in a substantially centered position above the target track. The data transfer between the head  14  and the target track occurs during the track following operation. 
     The channel  20  performs data transformations to provide communication between the disk  12  and the host computer  30 . For example, during a write operation, the channel  20  converts digital data received from the host computer  30  into an analog write current for delivery to the head  14 . During a read operation, the channel  20  converts an analog read signal received from the head  14  into a digital representation that can be recognized by the host computer  30 . The channel  20  also separates out servo information read by the head  14  and directs the servo information to the servo controller  24  for positioning the head  14 . 
     The blocks illustrated in  FIG. 1  are functional in nature and do not necessarily represent discrete hardware elements. For example, two or more of the functional blocks within the disk drive  10  can be implemented in software in a common digital processor. 
       FIG. 2  shows servo busts written on circular tracks. The disk  12  includes tracks  32  with track centerlines  34 . The tracks  32  are centered relative to the track centerlines  34 , and therefore are circular. The tracks  32  also include servo sectors  36  arranged in servo wedges that extend radially across the tracks  32 . The servo sectors  36  each include A, B, C and D servo bursts. In a given servo sector  36 , the servo bursts are circumferentially staggered and radially offset. Furthermore, the servo sectors  36  in different tracks  32  are radially aligned, and the servo bursts in the servo sectors  36  in different tracks  32  are radially aligned. For instance, in radially aligned servo sectors  36  in tracks  1  and  2 , the A servo bursts are radially aligned, the B servo bursts are radially aligned, the C servo bursts are radially aligned, and the D servo bursts are radially aligned. 
     The servo bursts each include magnetic flux transitions, and when the head  14  passes over the magnetic flux transitions it generates a read signal with repeating cycle variations. The channel  20  demodulates and decodes the read signal to provide a position error signal (PES) that indicates the position of the head  14  relative to the track centerline. The servo controller  24  positions the head  14  relative to the track centerline in response to the PES during track following operations. Thus, the PES reflects the shape of the track. A distorted (non-circular) track shape changes the servo burst locations, thereby changing the PES. 
     The PES is based various difference signals from the servo bursts. The null (N) signal is the A−B signal (the read signal amplitude from the A servo burst minus the read signal amplitude from the B servo burst), and the quadrature (Q) signal is the C−D signal (the read signal amplitude from the C servo burst minus the read signal amplitude from the D servo burst). The PES is based on the N signal when the head  14  is within about 0.25 track width from the track centerline  34 , and the Q signal when the head is within about 0.25 to 0.75 track width from the track centerline  34 . The PES is based on the N−Q and N+Q signals to obtain a larger linear range. 
     The N and Q signals are cyclic as the head  14  moves circumferentially across the disk  12  and are 90 degrees out of phase. When the head  14  is tracking along the track centerline, the N signal should be zero because the head  14  receives the same magnetic flux from the A and B servo bursts. When the head  14  is tracking ½ track width from the track centerline, the Q signal should be zero because the head  14  receives the same magnetic flux from the C and D servo bursts. 
       FIG. 3  shows servo busts written on non-circular tracks. The tracks  32  contain perturbations relative to the track centerlines  34 , and therefore are non-circular. These track perturbations (distortions) are written-in run-out (WRO) that occur as edge errors in the servo bursts. 
     A first band of tracks  32  that includes track  1  are written to the disk  12  by a servo track writer (STW). The first band of tracks  32  include WRO as repeatable run-out (RRO). Thereafter, a second band of tracks  32  that includes tracks  2 ,  3  and  4  are written to the disk  12  by self-servo writing (SSW). Unfortunately, the perturbations self-propagate from track-to-track during the self-servo writing. For instance, the perturbations in track  1  propagate to track  2  as the head  14  is positioned using a PES from track  1  and writes servo bursts to track  2 , the perturbations in track  2  propagate to track  3  as the head  14  is positioned using a PES from track  2  and writes servo bursts to track  3 , and the perturbations in track  3  propagate to track  4  as the head  14  is positioned using a PES from track  3  and writes servo bursts to track  4 . As a result, the perturbations in track  1  create a compoundable error that propagates across the tracks. That is, each track compounds the errors from the previous tracks. Furthermore, the tracks contain WRO that compounds not only RRO from the previous tracks, but also non-repeatable run-out (NRRO) (such as random mechanical disturbance and electronic noise) from the previous tracks. As a result, the compound errors can lead to excessive track non-circularity that cause the disk drive  10  to fail. 
       FIG. 4  shows servo bursts that contain edge errors. The servo bursts each contain top and bottom edge errors as WRO. In particular, the A servo burst contains a top edge error ΔA t  and a bottom edge error ΔA b , the B servo burst contains a top edge error ΔB t  and a bottom edge error ΔB b , the C servo burst contains a top edge error ΔC t  and a bottom edge error ΔC b , and the D servo burst contains a top edge error ΔD t  and a bottom edge error ΔD b . 
     The head  14  writes the A, B, C and D servo bursts to the track N at six radial positions during eight revolutions of the disk  12  during self-servo writing. In addition, the head  14  is positioned using a PES from a previously written track N−1 (not shown). The head  14  is moved to a first radial position and writes the A servo burst with top edge error ΔA t  during a first revolution of the disk  12 . The head  14  is then moved down to a second radial position and writes the D servo burst with top edge error ΔD t  during a second revolution of the disk  12 . The head  14  is then moved down to a third radial position and trims the bottom edge of the A servo burst with bottom edge error ΔA b  during a third revolution of the disk  12 . The head  14  is then maintained at the third radial position and writes the B servo burst with top edge error ΔB t  during a fourth revolution of the disk  12 . The head  14  is then moved down to a fourth radial position and trims the bottom edge of the D servo burst during a fifth revolution of the disk  12 . The head  14  is then maintained at the fourth radial position and writes the C servo burst with top edge error ΔC t  during a sixth revolution of the disk  12 . The head  14  is then moved down to a fifth radial position and trims the bottom edge of the B servo burst with bottom edge error ΔB b  during a sixth revolution of the disk  12 . The head  14  is then maintained at the fifth radial position and writes another A servo burst with top edge error ΔA t  during a seventh revolution of the disk  12 . The head  14  is then moved down to a sixth radial position and trims the bottom edge of the C servo burst with bottom edge error ΔC b  during an eighth revolution of the disk  12 . The head  14  is then maintained at the sixth radial position and writes another D servo burst with top edge error ΔD t  during a ninth revolution of the disk  12 . And so on. Furthermore, the servo bursts are written in this manner in each servo sector on the track. 
     The PES contains compound errors that propagate from track-to-track as follows:
 
 PES ( N )= E×NRRO ( N− 1)+ NRRO ( N )
 
 PES ( N+ 1)= E×[E×NRRO ( N− 1)+ NRRO ( N )]+ NRRO ( N+ 1)
 
 PES ( N+ 2)= E×{E×[E×NRRO ( N− 1)+ NRRO ( N )]+ NRRO ( N+ 1)}+ NRRO ( N+ 2)
 
     where E represents a control loop error transfer function and track N−1 has zero WRO. 
     The present invention prevents self-propagation of compound errors by removing WRO at different radial positions in a track based on different combinations of servo burst edge errors in a previous track. For example, the A, B, C and D servo bursts have eight edge errors, and the PES is based on a selected combination of the edge errors as the head  14  steps through different radial positions in the next track during self-servo writing. The edge errors are selected based on the track following mode (the N signal, the Q signal and combinations thereof) and the WRO is a linear combination of the edge errors. The PES is the target head position plus the WRO. Therefore, the PES is adjusted to remove the WRO by subtracting the edge errors. 
     Table I illustrates eight track following modes that use eight combinations of the top and bottom edge errors for the A, B, C and D servo bursts written during eight revolutions of the disk. 
     
       
         
               
               
               
               
               
               
               
             
           
               
                 TABLE I 
               
               
                   
               
               
                 Mode 
                 A 
                 B 
                 C 
                 D 
                 PES 
                 WRO 
               
               
                   
               
             
             
               
                 N 
                 A + ΔA b   
                 B + ΔB t   
                   
                   
                 (A + ΔA b ) − (B + ΔB t ) 
                 ΔA b  − ΔB t   
               
               
                 N − Q 
                 A + ΔA b   
                 B + ΔB t   
                 C + ΔC t   
                 D + ΔD b   
                 (A + ΔA b ) − (B + ΔB t ) − 
                 ΔA b  − ΔB t  − ΔC t  + 
               
               
                   
                   
                   
                   
                   
                 (C + ΔC b ) + (D + ΔD t ) 
                 ΔD b   
               
               
                 −Q 
                   
                   
                 C + ΔC t   
                 D + ΔD b   
                 −(C + ΔC b ) + (D + ΔD t ) 
                 −ΔC t  + ΔD b   
               
               
                 −(N + 
                 A + ΔA t   
                 B + ΔB b   
                 C + ΔC t   
                 D + ΔD b   
                 −(A + ΔA t ) + (B + ΔB b ) − 
                 −ΔA t  + ΔB b  − ΔC t  + 
               
               
                 Q) 
                   
                   
                   
                   
                 (C + ΔC t ) + (D + ΔD b ) 
                 ΔD b   
               
               
                 −N 
                 A + ΔA t   
                 B + ΔB b   
                   
                   
                 −(A + ΔA t ) + (B + ΔB b ) 
                 −ΔA t   + ΔB b   
               
               
                 −(N − Q) 
                 A + ΔA t   
                 B + ΔB b   
                 C + ΔC b   
                 D + ΔD t   
                 −(A + ΔA t ) + (B + ΔB b ) + 
                 −ΔA t   + ΔB b  + ΔC b  − 
               
               
                   
                   
                   
                   
                   
                 (C + ΔC t ) − (D + ΔD b ) 
                 ΔD t   
               
               
                 Q 
                   
                   
                 C + ΔC b   
                 D + ΔD t   
                 (C + ΔC b ) − (D + ΔD t ) 
                 ΔC b  − ΔD t   
               
               
                 N + Q 
                 A + ΔA b   
                 B + ΔB t   
                 C + ΔC b   
                 D + ΔD t   
                 (A + ΔA b ) − (B + ΔB t ) + 
                 ΔA b  − ΔB t   + ΔC b  − 
               
               
                   
                   
                   
                   
                   
                 (C + ΔC b ) − (D + ΔD t ) 
                 ΔD t   
               
               
                   
               
             
          
         
       
     
     In another embodiment, the A, B, C and D servo bursts are written during six revolutions of the disk. The bottom edge of the A servo burst is trimmed during the same disk revolution that the top edge of the B servo burst is written, and the top edge of the C servo burst is written during the same disk revolution that the bottom edge of the D servo burst is trimmed. As a result, the bottom edge of the A servo burst and the top edge of the B servo burst have the same error with opposite sign, and the top edge of the C servo burst and the bottom edge of the D servo burst have the same error with opposite sign. 
     Table II illustrates eight track following modes that use eight combinations of the top and bottom edge errors for the A, B, C and D servo bursts written during six revolutions of the disk. 
     
       
         
               
               
               
               
               
               
               
             
           
               
                 TABLE II 
               
               
                   
               
               
                 Mode 
                 A 
                 B 
                 C 
                 D 
                 PES 
                 WRO 
               
               
                   
               
             
             
               
                 N 
                 A + ΔA b   
                 B − ΔB t   
                   
                   
                 (A + ΔA b ) − (B − ΔB t ) 
                 2ΔA b  = 2ΔB t   
               
               
                 −N 
                 A + ΔA t   
                 B − ΔB b   
                   
                   
                 −(A + ΔA t ) + (B − ΔB b ) 
                 −2ΔA t  = −2ΔB b   
               
               
                 Q 
                   
                   
                 C + ΔC b   
                 D − ΔD t   
                 (C + ΔC b ) − (D − ΔD t ) 
                 2ΔC b  = 2ΔD t   
               
               
                 −Q 
                   
                   
                 C + ΔC t   
                 D − ΔD b   
                 −(C + ΔC b ) + (D −ΔD t ) 
                 −2ΔC t  = −2ΔD b   
               
               
                 N + Q 
                 A + ΔA b   
                 B − ΔB t   
                 C + ΔC b   
                 D − ΔD t   
                 (A + ΔA b ) − (B − ΔB t ) + 
                 2ΔA b  + 2ΔC b  = 
               
               
                   
                   
                   
                   
                   
                 (C + ΔC b ) − (D − ΔD t ) 
                 2ΔB t  + 2ΔD t   
               
               
                 −(N + Q) 
                 A + ΔA t   
                 B − ΔB b   
                 C + ΔC t   
                 D − ΔD b   
                 −(A + ΔA t ) + (B −ΔB b ) − 
                 −2ΔA t  − 2ΔC t  = 
               
               
                   
                   
                   
                   
                   
                 (C + ΔC t ) + (D − ΔD b ) 
                 −2ΔB b  − 2ΔD b   
               
               
                 N − Q 
                 A + ΔA b   
                 B − ΔB t   
                 C + ΔC t   
                 D − ΔD b   
                 (A + ΔA b ) − (B − ΔB t ) − 
                 2ΔA b  − 2ΔC b  = 
               
               
                   
                   
                   
                   
                   
                 (C + ΔC b ) + (D − ΔD t ) 
                 2ΔB t  − 2ΔD t   
               
               
                 −(N − Q) 
                 A + ΔA t   
                 B − ΔB b   
                 C + ΔC b   
                 D − ΔD t   
                 −(A + ΔA t ) + (B − ΔB b ) + 
                 −2ΔA t  + 2ΔC t  = 
               
               
                   
                   
                   
                   
                   
                 (C + ΔC t ) − (D − ΔD b ) 
                 −2ΔB b  + 2ΔD b   
               
               
                   
               
             
          
         
       
     
     In another embodiment, the A and B servo bursts are written by the servo track writer and have fixed but different WRO contributions than the C and D servo bursts. As a result, there is no WRO correction for the A and B servo bursts, and the WRO is caused only by the edge errors of the C and D servo bursts. 
     Table III illustrates eight track following modes that use two combinations of the top and bottom edge errors for the C and D servo bursts. 
     
       
         
               
               
               
               
               
               
               
             
           
               
                 TABLE III 
               
               
                   
               
               
                 Mode 
                 A 
                 B 
                 C 
                 D 
                 PES 
                 WRO 
               
               
                   
               
             
             
               
                 N 
                 A + ΔA b   
                 B + ΔB t   
                   
                   
                 (A + ΔA b ) − (B + ΔB t ) 
                 0 
               
               
                 N − Q 
                 A + ΔA b   
                 B + ΔB t   
                 C + ΔC t   
                 D + ΔD b   
                 (A + ΔA b ) − (B + ΔB t ) − 
                 −ΔC t  + ΔD b   
               
               
                   
                   
                   
                   
                   
                 (C + ΔC b ) + (D + ΔD t ) 
               
               
                 −Q 
                   
                   
                 C + ΔC t   
                 D + ΔD b   
                 −(C + ΔC b ) + (D + ΔD t ) 
                 −ΔC t  + ΔD b   
               
               
                 −(N + Q) 
                 A + ΔA t   
                 B + ΔB b   
                 C + ΔC t   
                 D + ΔD b   
                 −(A + ΔA t ) + (B + ΔB b ) − 
                 −ΔC t  + ΔD b   
               
               
                   
                   
                   
                   
                   
                 (C + ΔC t ) + (D + ΔD b ) 
               
               
                 −N 
                 A + ΔA t   
                 B + ΔB b   
                   
                   
                 −(A + ΔA t ) + (B + ΔB b ) 
                 0 
               
               
                 −(N − Q) 
                 A + ΔA t   
                 B + ΔB b   
                 C + ΔC b   
                 D + ΔD t   
                 −(A + ΔA t ) + (B + ΔB b ) + 
                 ΔC b   − ΔD t   
               
               
                   
                   
                   
                   
                   
                 (C + ΔC t ) − (D + ΔD b ) 
               
               
                 Q 
                   
                   
                 C + ΔC b   
                 D + ΔD t   
                 (C + ΔC b ) − (D + ΔD t ) 
                 ΔC b   − ΔD t   
               
               
                 N + Q 
                 A + ΔA b   
                 B + ΔB t   
                 C + ΔC b   
                 D + ΔD t   
                 (A + ΔA b ) − (B + ΔB t ) + 
                 ΔC b   − ΔD t   
               
               
                   
                   
                   
                   
                   
                 (C + ΔC b ) − (D + ΔD t ) 
               
               
                   
               
             
          
         
       
     
       FIG. 5  shows a flowchart  100  of self-servo writing that removes WRO to prevent compound errors. The flowchart  100  includes the steps of: 
     1. Writing servo bursts in a STW track using a servo track writer (step  102 ); 
     2. Performing (optionally) embedded run-out correction to remove RRO from the servo bursts in the STW track (step  104 ); and then self-servo writing by 
     3. Moving the head a fraction of a track width to position the read element to read servo bursts from the STW track and the write element to write servo bursts to a SSW track (step  106 ); 
     4. Reading servo bursts from the STW track and using the associated PES to position the head while self-servo writing servo bursts to the SSW track (step  108 ); 
     5. Repeating steps (2) to (4) to self-servo write the remaining servo bursts to the SSW track (step  110 ); 
     6. Moving the head a fraction of a track width to position the read element to read servo bursts from the previous SSW track and the write element to write servo bursts to the next SSW track (step  112 ); 
     7. Reading servo bursts from the previous SSW track and using the associated PES to position the head while self-servo writing servo bursts to the next SSW track (step  114 ); 
     8. Repeating steps (6) to (7) to self-servo write the remaining servo bursts to the next SSW track (step  116 ); and 
     9. Repeating steps (6) to (8) to self-servo write the remaining tracks on the disk (step  118 ). 
     Thus, the flowchart  100  includes servo writing using a servo track writer (step  102 ) and then self-servo writing (steps  106  to  118 ). 
       FIG. 6  shows a logic diagram for servo writing that removes WRO to prevent compound errors. At head position block  120 , the head  14  is positioned at a target position for writing servo bursts to a next track and reading servo bursts from a previously written track. At mode switch block  122 , the servo bursts on the previous track that are used to generate the PES are selected. At target position block  124 , the target position for the head  14  is selected. At memory block  126 , the eight edge errors from the previous track are retrieved from memory. At mode switch block  128 , the edge errors are selected according to the relations in Tables I, II or III. At WRO block  130 , the WRO is determined based on the selected edge errors. At compensation junction  132 , the PES is adjusted by the target position and the WRO to obtain an adjusted PES to position the head  14  for writing the servo bursts to the next track according to the relation:
   PES (Without  WRO )=Target Head Position− WRO    
     The track following modes listed in Tables I, II and III have a linear range of N, Q, (N+Q) and (N−Q). The mode switch blocks  122 ,  128  stitch the eight linear track segments to cover a full track range. 
       FIG. 7  shows the head  14  with a single track offset relative to the disk  12 . The disk  12  includes an inner diameter (ID) and an outer diameter (OD). The head  14  includes a magneto-resistive read element  40  and a write element  42 . The read and write elements  40 ,  42  have a circumferential separation  44  and a radial separation  46  therebetween. The circumferential separation  44  extends in the circumferential direction (parallel to the track centerline  34 ), and the radial separation  46  extends in the radial direction (normal to the track centerline  34 ). Furthermore, the circumferential separation  44  and the radial separation  46  provide a track offset  48  of one track width on the disk  12 . As a result, the read element  40  can read servo bursts from track N while the write element  42  writes servo bursts to adjacent track N+1. 
       FIG. 8  shows the head  14  with a multiple track offset relative to the disk  12 . The read element  40  is positioned on a previously written track N and reads the servo bursts from the previously written track N to generate a PES for servoing the head  14 , while the write element  42  writes servo bursts to non-adjacent track N+i, where the integer i is greater than one and based on factors such as track density, skew angle and head geometry. Thus, the track offset  48  is multiple tracks rather than a single track. For example, the integer i can be 2 to 8 such that the write element  42  is two to eight tracks in advance of the read element  40  in the propagation direction from the outer diameter to the inner diameter of the disk  12 . 
       FIG. 9  shows a flowchart  150  of self-servo writing that removes WRO to prevent compound errors while the track offset  48  is eight tracks. The flowchart  150  includes the steps of: 
     1. Moving the head a fraction of a track width to position the read element to read servo bursts from track N and the write element to write servo bursts to track N+8 (step  152 ); 
     2. Reading servo bursts from the track N and using the associated PES to position the head while self-servo writing servo bursts to the track N+8 (step  154 ); 
     3. Repeating steps (1) to (2) to self-servo write the remaining servo bursts to the track N+8 (step  156 ); and 
     4. Repeating steps (1) to (3) to self-servo write the remaining tracks on the disk (step  158 ). 
     The process steps and logic blocks can be implemented in firmware in the servo loop, or in other logic elements in the disk drive  10  such as the controllers  24  and/or  26  or separate components. The firmware can include diagnostics such as reading the edge errors for verification before and after the self-servo writing. 
     The head  14  can read the servo bursts from the previous track to generate the PES while the head  14  is at a radial position relative to the disk  12  and write the servo bursts to the next track using the PES to position the head  14  while the head  14  remains at the radial position. In other words, the radial position is a propagation step that includes PES corrections. In addition, the head  14  can read the servo bursts from the previous track to generate the PES during a revolution of the disk  12  and write the servo bursts to the next track using the PES during the same or a subsequent revolution of the disk  12 . For instance, the PES for each servo sector on the track can be stored in the memory  28  as the head  14  reads the servo bursts from the previous track during a first revolution of the disk  12  and then retrieved from the memory  28  to position the head  14  as the head  14  writes the servo bursts to the next track during a second revolution of the disk  12 . 
     The memory  28  can be allocated for storing the PES of the track that the head  14  is servoing on, and reused from track-to-track in the propagation steps as the self-servo writing proceeds. The memory  28  can be sized to store the number of servo burst edges in a servo sector multiplied by the number of servo sectors on a track. The memory  28  can also be reused after the self-servo writing is completed. 
     The embedded run-out correction can remove RRO from the STW tracks as well as electronic noise that causes residual WRO during the self-servo writing. For instance, the embedded run-out correction can be applied to adjust the PES if the WRO exceeds a threshold during self-servo writing. Embedded run-out correction is described in the U.S. application Ser. No. 09/753,969, filed on Jan. 2, 2001, which is incorporated herein by reference. 
     The selected combination of edge errors is a unique combination of edge errors relative to the other combinations of edge errors. The selected combination of edge errors is a function of the track following mode. Furthermore, the selected combination of edge errors can be a single edge error (such as 2 ΔA b  for mode N in Table II) or multiple edge errors (such as 2 ΔA b −2 ΔC b  for mode N−Q in Table II). 
     The present invention is applicable to servo burst patterns with more than four servo bursts or less than four servo bursts, and is not limited to the A, B, C and D servo bursts described herein. Furthermore, different track following modes can be used with corresponding calculations to determine WRO to prevent compound errors. 
     The present invention has been described in considerable detail with reference to certain preferred versions thereof, however other versions are possible. Therefore, the spirit and scope of the appended claims should not be limited to the description of the preferred versions contained herein.