TRUST AGREEMENT OF GULF COAST ULTRA DEEP ROYALTY TRUST

EXHIBIT 10.2

TRUST AGREEMENT

OF

GULF COAST ULTRA DEEP ROYALTY TRUST

TRUST AGREEMENT, dated as of December 18, 2012, among Freeport-McMoRan Copper & Gold Inc., as “Depositor,” Wilmington Trust, National Association, not in its individual capacity but solely as the “Delaware Trustee,” and Kathleen L. Quirk and Douglas N. Currault II, as the “Regular Trustees.” The Delaware Trustee and the Regular Trustees, together with each other person or entity from time to time serving as a trustee hereunder, are collectively referred to herein as the “Trustees” and each, individually, as a “Trustee.” The Depositor and the Trustees hereby agree as follows:

Section 1. The Trust. The trust created hereby shall be known as Gulf Coast Ultra Deep Royalty Trust (the “Trust”), in which name the Trustees, or the Depositor to the extent provided herein, may conduct the business of the Trust, make and execute contracts, and sue and be sued.

Section 2. The Trust Estate. The Depositor hereby assigns, transfers, conveys and sets over to the Trust the sum of Ten Dollars ($10.00), which amount shall constitute the initial trust estate. The Trustees hereby declare that they will hold the trust estate in trust for the Depositor. It is the intention of the parties hereto that the Trust created hereby constitute a statutory trust under Chapter 38 of Title 12 of the Delaware Code, 12 Del. C. §§ 3801 et seq. (the “Statutory Trust Act”), and that this document constitutes the governing instrument of the Trust. The Trustees are hereby authorized and directed to execute and file a certificate of trust with the Delaware Secretary of State in the form attached hereto as Exhibit A.

Section 3. Amended and Restated Trust Agreement. Prior to the first issuance of beneficial interests in the Trust pursuant to the Registration Statement (as defined below), the Depositor and the Trustees will enter into an amended and restated Trust Agreement, in a form satisfactory to each such party, to provide for the contemplated operation of the Trust created hereby and the issuance of beneficial interests therein. Prior to the execution and delivery of such amended and restated Trust Agreement, the Trustees shall not have any duty or obligation hereunder or with respect to the trust estate, except as otherwise required by applicable law or as may be necessary to obtain prior to such execution and delivery any licenses, consents or approvals required by applicable law or otherwise. Notwithstanding the foregoing, each Regular Trustee is authorized on behalf of the Trust to execute and deliver, and to cause the Trust to perform its obligations under, any documents and to take any actions that such Trustee determines to be necessary or appropriate in connection with the formation and operation of the Trust.

Section 4. Certain Authorizations. The Depositor and the Trustees hereby authorize the Depositor (i) to prepare, execute and file on behalf of the Trust with the Securities and Exchange Commission (the “Commission”) a Registration Statement on Form S-4 (the “Registration Statement”), including any pre-effective and/or post-effective amendments to such Registration Statement (including the prospectus and the exhibits contained therein), relating to the registration under the Securities Act of 1933, as amended, of beneficial interests in the Trust; (ii) to prepare, execute and file on behalf of the Trust with The Nasdaq Stock Market, the New

York Stock Exchange or any other national stock exchange, in any case, as the Depositor shall determine in its sole discretion (each, an “Exchange”), one or more listing applications and all other applications, statements, certificates, agreements and other instruments as shall be necessary or desirable to cause the beneficial interests in the Trust to be listed or approved for quotation on any of such Exchanges; (iii) to prepare, execute and file on behalf of the Trust such applications, reports, surety bonds, irrevocable consents, appointments of attorney for service of process and other papers and documents as shall be necessary or desirable to register the beneficial interests in the Trust under any state securities or “blue sky” laws, as the Depositor, on behalf of the Trust, may deem necessary or desirable; and (iv) to prepare and execute on behalf of the Trust letters or documents, or instruments for filing with, a depository relating to beneficial interests in the Trust. In the event that any filing referred to in clauses (i) through (iv) above is required by the rules and regulations of the Commission, an Exchange or any state securities or “blue sky” laws to be executed on behalf of the Trust by the Trustees, in their capacities as Trustees of the Trust, the Trustees are hereby authorized and directed to join in any such filing and to execute on behalf of the Trust any and all of the foregoing, it being understood that no Trustee shall be required to join in any such filing or execute on behalf of the Trust any such document unless required by the rules and regulations of the Commission, an Exchange or any state securities or blue sky laws, and in such case, only to the extent required.

Section 5. Trustees. The number of Trustees initially shall be three (3) and thereafter the number of Trustees shall be such number as shall be fixed from time to time by a written instrument signed by the Depositor (or fixed by the amended and restated Trust Agreement referenced above) that may increase or decrease the number of Trustees; provided, however, that to the extent required by the Statutory Trust Act, one Trustee shall either be a natural person who is a resident of the State of Delaware or, if not a natural person, an entity that has its principal place of business in the State of Delaware and otherwise meets the requirements of applicable Delaware law. Subject to the foregoing, the Depositor is entitled to appoint or remove with or without cause any Trustee at any time. A Trustee may resign upon thirty (30) days’ prior written notice to the Depositor; provided, however, that no resignation of the Delaware Trustee shall be effective until a successor Delaware Trustee has been appointed and has accepted such appointment by instrument executed by such successor Delaware Trustee and delivered to the Trust, the Depositor and the resigning Delaware Trustee.

Section 6. Delaware Trustee. Wilmington Trust, National Association, in its capacity as Delaware Trustee, shall not have any of the powers or duties of the Trustees set forth herein (except as may be required under the Statutory Trust Act) and shall be a Trustee of the Trust for the sole purpose of satisfying the requirements of Section 3807(a) of the Statutory Trust Act. Any business entity into which the Delaware Trustee may be merged or converted or with which it may be consolidated, or any entity resulting from any merger, conversion or consolidation to which the Delaware Trustee shall be a party, or any entity succeeding to all or substantially all of the corporate trust business of the Delaware Trustee, shall be the successor of the Delaware Trustee hereunder, without the execution or filing of any paper or any further act on the part of any of the parties hereto.

Section 7. Indemnification. To the full extent permitted by applicable law, the Depositor agrees (a) to indemnify (i) the Trustees, (ii) any affiliate of the Delaware Trustee and (iii) any officers, directors, partners, employees, representatives, nominees, custodians or

agents of the Delaware Trustee (each of the persons or entities in (i) through (iii) being referred to as an “Indemnified Person”) for, and to hold each Indemnified Person harmless against, any loss, liability or expense incurred without gross negligence, willful misconduct or bad faith on its part, arising out of or in connection with the acceptance or administration of the trust hereunder, including the costs and expenses (including reasonable legal fees and expenses) of defending itself against, or investigating, any claim or liability in connection with the exercise or performance of any of its powers or duties hereunder and (b) to advance costs and expenses (including reasonable legal fees and expenses) incurred by an Indemnified Person in defending itself against, or investigating, any such claim or liability in connection with the exercise or performance of any of its powers or duties hereunder, upon receipt by the Depositor of an undertaking by or on behalf of such Indemnified Person to repay such amount if it shall be determined that such Indemnified Person is not entitled to be indemnified under this Section 7. The obligation to indemnify and advance as set forth in this Section 7 shall survive the resignation or removal of a Trustee and the termination of this Trust Agreement.

Section 8. Termination. The Trust may terminate without issuing any beneficial interests at the election of the Depositor.

Section 9. Governing Law. This Trust Agreement shall be governed by, and construed in accordance with, the laws of the State of Delaware (without regard to conflict of laws principles); provided, however, that there shall not be applicable to the parties hereunder or this Trust Agreement any provision of the laws (common or statutory) of the State of Delaware pertaining to trusts that relate to or regulate, in a manner inconsistent with the terms hereof, (a) the filing with any court or governmental body or agency of trustee accounts or schedules of trustee fees and charges, (b) affirmative requirements to post bonds for trustees, officers, agents or employees of a trust, (c) the necessity for obtaining court or other governmental approval concerning the acquisition, holding or disposition of real or personal property, (d) fees or other sums payable to trustees, officers, agents or employees of a trust, (e) the allocation of receipts and expenditures to income or principal, (f) restrictions or limitations on the permissible nature, amount or concentration of trust investments or requirements relating to the titling, storage or other manner of holding or investing trust assets or (g) the establishment of fiduciary or other standards of responsibility or limitations on the acts or powers of trustees that are inconsistent with the limitations or authorities and powers of the trustee hereunder as set forth or referenced in this Trust Agreement. Section 3540 of Title 12 of the Delaware Code shall not apply to the Trust.

Section 10. Counterparts. This Trust Agreement may be executed in one or more counterparts.

Section 11. Amendments. This Trust Agreement may be amended at any time by (i) an instrument in writing (or by the amended and restated Trust Agreement referenced above) signed by all of the Trustees or (ii) adoption by the Trustees acting unanimously of a resolution specifying the amendment. Any such amendment hereto shall be effective immediately upon such execution or adoption.

[Signature page follows.]

IN WITNESS WHEREOF, the parties hereto have caused this Trust Agreement to be duly executed as of the day and year first above written.