Method and system for simultaneous acquisition of pressure and pressure derivative data with ghost diversity

1. A marine streamer spread for acquiring seismic data, the spread comprising:

a streamer having a first portion and a second portion;

the first portion including both first pressure sensors and pressure derivative sensors for acquiring first pressure wave-fields and pressure derivatives wave-fields; and

the second portion including only second pressure sensors for acquiring second pressure wave-fields,

wherein the first portion is configured to have a variable-depth profile so that notches of a pressure amplitude spectrum of the acquired first and second pressure wave-fields are filled with energy from a pressure derivative amplitude spectrum of the acquired pressure derivatives wave-fields.

2. The streamer spread of claim 1 , wherein the second portion has a flat or variable-depth profile and is free of pressure derivative sensors.

3. The streamer spread of claim 1 , wherein the first pressure sensors and the pressure derivative sensors are co-located on the first portion, which is curved.

4. The streamer spread of claim 1 , wherein the acquired first and second pressure wave-fields exhibit ghost diversity, which is associated with different times necessary for ghost wave-fields to reach corresponding first pressure sensors, distributed along the variable-depth profile, after their corresponding primary wave-fields have been recorded by the corresponding first pressure sensors.

5. The streamer spread of claim 1 , wherein the acquired pressure derivatives wave-fields exibit polarity diversity, which is associated with an orientation of a measured pressure derivative wave-field relative to a given axis.

6. The streamer spread of claim 1 , wherein a part of the seismic data associated with the first portion has both ghost diversity and polarity diversity while another part of the seismic data associated with the second portion has no diversity.

7. The streamer spread of claim 1 , wherein a first part of the seismic data associated with the first portion has both ghost diversity and polarity diversity, a second part of the seismic data associated with the first portion has only ghost diversity and a third part of the seismic data associated with the second portion has neither diversity.

8. A method for processing input seismic data d, the method comprising:

receiving the input seismic data d recorded in a first domain by seismic sensors that travel in water, the input seismic data d including up-going and down-going wave-fields;

generating a model p in a second domain to describe the input seismic data d; and

processing with a processor the model p to obtain an output seismic dataset indicative of a surveyed subsurface,

wherein the input seismic data d includes (1) first pressure wave-fields acquired with first pressure sensors located on a first portion of a streamer, (2) pressure derivative wave-fields acquired with pressure derivative sensors located on the first portion of the streamer, and (3) second pressure wave-fields acquired with second pressure sensors located on a second portion of the streamer, and

wherein the first portion is configured to have a variable-depth profile so that notches of a pressure amplitude spectrum of the first and second pressure wave-fields are filled with energy from a pressure derivative amplitude spectrum of the pressure derivatives wave-fields.

9. The method of claim 8 , wherein the first pressure sensors and the pressure derivative sensors are co-located on the first portion.

10. The method of claim 8 , wherein the second portion has a curved profile or a flat profile.

11. The method of claim 8 , wherein the acquired first and second pressure wave-fields exhibit ghost diversity, which is associated with different times necessary for ghost wave-fields to reach corresponding first pressure sensors, distributed along the variable-depth profile, after their corresponding primary wave-fields have been recorded by the corresponding first pressure sensors.

12. The method of claim 8 , wherein the acquired pressure derivatives wave-fields exibit polarity diversity, which is achieved with the pressure derivative sensors and the polarity diversity associated with an orientation of a measured pressure derivative wave-field relative to a given axis.

13. The method of claim 8 , wherein the first domain is a time-space domain and the second domain is one of a radon domain, frequency-wave number domain, tau-p domain, parabolic domain, shifted hyperbola domain, singular value decomposition, rank reduction and curvelet domain.

14. The method of claim 8 , wherein the input seismic data d includes a first seismic dataset acquired at a first time and a second seismic dataset acquired, over the same surveyed subsurface, at a second time.

15. The method of claim 8 , wherein the step of processing includes a step of redatuming the output seismic dataset.

16. The method of claim 8 , wherein the step of processing uses pre-stack wave-fields.

17. A non-transitory computer readable medium including computer executable instructions, wherein the instructions, when executed by a processor, implement instructions for processing input seismic data d, the instructions comprising:

receiving the input seismic data d recorded in a first domain by seismic sensors that travel in water, the input seismic data d including up-going and down-going wave-fields;

generating a model p in a second domain to describe the input seismic data d; and

processing with a processor the model p to obtain an output seismic dataset indicative of a surveyed subsurface,

wherein the input seismic data d includes (1) first pressure wave-fields acquired with first pressure sensors located on a first portion of a streamer, (2) pressure derivatives wave-fields acquired with pressure derivative sensors located on the first portion of the streamer, and (3) second pressure wave-fields acquired with second pressure sensors located on a second portion of the streamer, and

wherein the first portion is configured to have a variable-depth profile so that notches of a pressure amplitude spectrum of the first and second pressure wave-fields are filled with energy from a pressure derivative amplitude spectrum of the pressure derivatives wave-fields.