
<PAGE>   1


                       SECURITIES AND EXCHANGE COMMISSION
                              WASHINGTON, DC 20549

                                  SCHEDULE 13G

                    Under the Securities Exchange Act of 1934
                               (Amendment No. 4 )*



                       PETROLEUM HELICOPTERS INCORPORATED
             ------------------------------------------------------
                                (Name of Issuer)


               NON-VOTING COMMON STOCK, $0.10 PAR VALUE PER SHARE
             ------------------------------------------------------
                         (Title of Class of Securities)


                                   716604 10 3
             ------------------------------------------------------
                                 (CUSIP Number)


                                DECEMBER 31, 2000
             ------------------------------------------------------
             (Date of Event Which Requires Filing of this Statement)


     Check the appropriate box to designate the rule pursuant to which this
Schedule is filed:

          |_|  Rule 13d-1(b)

          |X|  Rule 13d-1(c)

          |_|  Rule 13d-1(d)

     * The remainder of this cover page shall be filled out for a reporting
person's initial filing on this form with respect to the subject class of
securities, and for any subsequent amendment containing information which would
alter the disclosures provided in a prior cover page.

     The information required in the remainder of this cover page shall not be
deemed to be "filed" for the purpose of Section 18 of the Securities Exchange
Act of 1934 ("Act") or otherwise subject to the liabilities of that section of
the Act but shall be subject to all other provisions of the Act (however, see
the Notes).


<PAGE>   2



-------------------------                                  ---------------------
  CUSIP No. 716604 10 3               13G                    Page 2 of 6 Pages
-------------------------                                  ---------------------

--------------------------------------------------------------------------------
  1   Names of Reporting Persons/I.R.S. Identification Nos. of Above Persons
      (entities only)

      WOODBOURNE PARTNERS, L.P.
--------------------------------------------------------------------------------
  2   Check the Appropriate Box if a Member of a Group*                  (a) |_|
                                                                         (b) |_|
--------------------------------------------------------------------------------
  3   SEC Use Only

--------------------------------------------------------------------------------
  4   Citizenship or Place of Organization

      MISSOURI
--------------------------------------------------------------------------------
   Number of        5   Sole Voting Power

     Shares             -0-
                 ---------------------------------------------------------------
  Beneficially      6   Shared Voting Power

    Owned by            -0-
                 ---------------------------------------------------------------
      Each          7   Sole Dispositive Power

   Reporting            -0-
                 ---------------------------------------------------------------
  Person With       8   Shared Dispositive Power:

                        -0-
--------------------------------------------------------------------------------
  9   Aggregate Amount Beneficially Owned by Each Reporting Person

      390,500
--------------------------------------------------------------------------------
  10  Check if the Aggregate Amount in Row (9) Excludes Certain Shares
      (See Instructions)                                                     |_|

--------------------------------------------------------------------------------
  11  Percent of Class Represented by Amount in Row (9)

      16.4%
--------------------------------------------------------------------------------
  12  Type of Reporting Person

      PN
--------------------------------------------------------------------------------


<PAGE>   3


-------------------------                                  ---------------------
  CUSIP No. 716604 10 3               13G                    Page 3 of 6 Pages
-------------------------                                  ---------------------

--------------------------------------------------------------------------------
  1   Names of Reporting Persons/I.R.S. Identification Nos. of Above Persons
      (entities only)

      CLAYTON MANAGEMENT COMPANY
--------------------------------------------------------------------------------
  2   Check the Appropriate Box if a Member of a Group*                  (a) |_|
                                                                         (b) |_|
--------------------------------------------------------------------------------
  3   SEC Use Only

--------------------------------------------------------------------------------
  4   Citizenship or Place of Organization

      MISSOURI
--------------------------------------------------------------------------------
   Number of        5   Sole Voting Power

     Shares             390,500
                 ---------------------------------------------------------------
  Beneficially      6   Shared Voting Power

    Owned by            -0-
                 ---------------------------------------------------------------
      Each          7   Sole Dispositive Power

   Reporting            390,500
                 ---------------------------------------------------------------
  Person With       8   Shared Dispositive Power:

                        -0-
--------------------------------------------------------------------------------
  9   Aggregate Amount Beneficially Owned by Each Reporting Person

      390,500
--------------------------------------------------------------------------------
  10  Check if the Aggregate Amount in Row (9) Excludes Certain Shares
      (See Instructions)                                                     |_|

--------------------------------------------------------------------------------
  11  Percent of Class Represented by Amount in Row (9)

      16.4%
--------------------------------------------------------------------------------
  12  Type of Reporting Person

      CO
--------------------------------------------------------------------------------


<PAGE>   4


-------------------------                                  ---------------------
  CUSIP No. 716604 10 3               13G                    Page 4 of 6 Pages
-------------------------                                  ---------------------

--------------------------------------------------------------------------------
  1   Names of Reporting Persons/I.R.S. Identification Nos. of Above Persons
      (entities only)

      JOHN D. WEIL
--------------------------------------------------------------------------------
  2   Check the Appropriate Box if a Member of a Group*                  (a) |_|
                                                                         (b) |_|
--------------------------------------------------------------------------------
  3   SEC Use Only

--------------------------------------------------------------------------------
  4   Citizenship or Place of Organization

      MISSOURI
--------------------------------------------------------------------------------
   Number of        5   Sole Voting Power

     Shares             390,500
                 ---------------------------------------------------------------
  Beneficially      6   Shared Voting Power

    Owned by            -0-
                 ---------------------------------------------------------------
      Each          7   Sole Dispositive Power

   Reporting            390,500
                 ---------------------------------------------------------------
  Person With       8   Shared Dispositive Power:

                        -0-
--------------------------------------------------------------------------------
  9   Aggregate Amount Beneficially Owned by Each Reporting Person

      390,500
--------------------------------------------------------------------------------
  10  Check if the Aggregate Amount in Row (9) Excludes Certain Shares
      (See Instructions)                                                     |_|

--------------------------------------------------------------------------------
  11  Percent of Class Represented by Amount in Row (9)

      16.4%
--------------------------------------------------------------------------------
  12  Type of Reporting Person

      IN
--------------------------------------------------------------------------------


<PAGE>   5


-------------------------                                  ---------------------
  CUSIP No. 716604 10 3               13G                    Page 5 of 6 Pages
-------------------------                                  ---------------------


                         AMENDMENT NO. 3 TO SCHEDULE 13G

     The Reporting Person reported the acquisition of shares of Non-Voting
Common Stock, par value $.10 per share ("Stock"), of Petroleum Helicopters
Incorporated, a Delaware corporation ("Issuer"), 113 Borman Drive, P.O. Box
23502, Lafayette, LA 70508, in an initial filing of this Schedule 13G on April
16, 1998, as amended by Amendment No. 1 filed on February 16, 1999, Amendment
No. 2 filed on April 8, 1999, and Amendment No. 3 filed on February 14, 2000. In
this regard, Item 4 is hereby amended as follows. All other items are unchanged
from the initial filing, as amended.


ITEM 4. OWNERSHIP.

<TABLE>
<CAPTION>
                                                                                                      WEIL
                                                                                CLAYTON         (sole director and
                                                                           (general partner       shareholder of
                                                           WOODBOURNE       of Woodbourne)           Clayton)
                                                          ------------     ----------------     ------------------
<S>                                                         <C>                 <C>                  <C>
(a)  Amount beneficially owned:                             390,500             390,500              390,500

(b)  Percent of Class:                                        16.4%               16.4%                16.4%

(c)  Number of Shares as to which the person has:

     (i)   Sole power to vote or direct the vote:               -0-             390,500              390,500

     (ii)  Shared power to vote or direct the vote:             -0-                 -0-                  -0-

     (iii) Sole power to dispose or to direct the
           disposition of:                                      -0-             390,500              390,500

     (iv)  Shared power to dispose or to direct the
           disposition of:                                      -0-                 -0-                  -0-
</TABLE>


ITEM 10. CERTIFICATION.

     By signing below I certify that, to the best of my knowledge and belief,
the securities referred to above were not acquired and are not held for the
purpose of or with the effect of changing or influencing the control of the
issuer of the securities and were not acquired and are not held in connection
with or as a participant in any transaction having that purpose or effect.


     Dated: February 14, 2001           WOODBOURNE PARTNERS, L.P.,


                                        by its General Partner, CLAYTON
                                        MANAGEMENT COMPANY


                                                    /s/ John D. Weil
                                        ----------------------------------------
                                        John D. Weil, President


     Dated: February 14, 2001           CLAYTON MANAGEMENT COMPANY


                                                    /s/ John D. Weil
                                        ----------------------------------------
                                        John D. Weil, President



     Dated: February 14, 2001                       /s/ John D. Weil
                                        ----------------------------------------
                                        John D. Weil



<PAGE>   6


-------------------------                                  ---------------------
  CUSIP No. 716604 10 3               13G                    Page 6 of 6 Pages
-------------------------                                  ---------------------


                            EXHIBIT A TO SCHEDULE 13G
                            -------------------------

                     AGREEMENT PURSUANT TO RULE 13D-1(K)(1)

     The undersigned persons, on February 14, 2001, agree and consent to the
joint filing on their behalf of this Amendment No. 4 to Schedule 13G in
connection with their beneficial ownership of the Stock of Petroleum Helicopters
Incorporated.

                                        WOODBOURNE PARTNERS, L.P.,

                                        by its General Partner, CLAYTON
                                        MANAGEMENT COMPANY



                                                    /s/ John D. Weil
                                        ----------------------------------------
                                        John D. Weil, President


                                        CLAYTON MANAGEMENT COMPANY



                                                    /s/ John D. Weil
                                        ----------------------------------------
                                        John D. Weil, President



                                                    /s/ John D. Weil
                                        ----------------------------------------
                                        John D. Weil
