FORM 6-K

SECURITIES AND EXCHANGE COMMISSION

Report of Foreign Private Issuer
Pursuant to Rule 13a- 16 or 15d- 16 of
the Securities Exchange Act of 1934

For the month of October, 2004

GENERAL COMPANY OF GEOPHYSICS

1, rue Léon Migaux, 91341 MASSY FRANCE (address of principal executive offices)

Indicate by check mark whether the registrant files or will file annual reports under cover Form 20-F or Form 40-F.

Form 20-F þ Form 40-F o

Indicate by check mark whether the registrant by furnishing the information contained in this Form is also thereby furnishing the information to the Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934.

Yes o No þ

If “Yes” is marked, indicate below the file number assigned to the registrant in connection with Rule 12g3-2(b): 82 ________

COMPAGNIE GENERALE DE GEOPHYSIQUE
(ISIN : 0000120164 — NYSE : GGY)

CGG withdraws its offer to PGS

Paris, 5^th October 2004

On September 1, 2004, CGG made an offer to the Board of Directors of PGS for the acquisition of the PGS seismic business for a total consideration of $900 million, including $800 million in cash and $100 million in CGG shares.

Following the immediate rejection of this offer by PGS, CGG and its counsel have sought clarification from PGS on the main issues which it believed justified this negative response, with a view to the possibility of addressing such concerns by means of adequately adjusted proposals.

The conclusion of this exchange is that, unfortunately, the gap existing between the two parties, in particular concerning the valuation of the transaction under consideration and further exacerbated by the perception of recently improving seismic markets, is far in excess of what can be reasonably expected to be bridged under a final negotiation process.

As a consequence, CGG has decided to withdraw its offer of a potential combination with PGS seismic services, and will continue to pursue strategic alternatives aimed at creating value for its shareholders.

The Compagnie Generale de Geophysique group is a global participant in the oilfield services industry, providing a wide range of seismic data acquisition, processing and geoscience services and software to clients in the oil and gas exploration and production business. It is also a global manufacturer of geophysical equipment.

Contacts:

Internet: www.cgg.com

Page 2

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

Page 3