Co-Authors: T. Kaschwich, L. Zühlsdorff (NORSAR)

The oil industry is looking for successively smaller and deeper reservoirs in more complex structures, which are more difficult to illuminate and image using the seismic technique. This poses a challenge to seismic acquisition design and survey evaluation. Seismic surveys need to fit their purpose while balancing today’s acquisition costs with the given survey objectives, which may be as diverse as structural imaging, analysis of anisotropy, analysis of seismic amplitudes versus offset and incident angle, inversion, time-lapse feasibility testing, and many more. All these tasks will have their specific requirements and surely rely on sufficient signal to noise ratio, sufficient spatial sampling, amplitude control, sufficient resolution, and sufficient coverage regarding fold, incident angle range and azimuth range within the full target volume of interest.

Seismic forward modelling is required to determine that the proposed survey will result in seismic data that contain the information required to carry out the proposed analysis and interpretation. This includes the evaluation of survey parameters, but also resolution testing and PSDM simulation. Seismic forward modelling also is required for preparing seismic processing (e.g., by supporting processing parameter selection or generating travel time tables) as well as for seismic interpretation (in terms of event identification, illumination testing, AVO/AVA interpretation and velocity sensitivity analysis).  

Ray-based seismic modelling provides a fast, flexible and computational efficient approach to fulfill these tasks. Especially in cases that require a comparison between many different modelling scenarios, routine application of full wavefield modelling may not be practical or necessary, and advanced ray-based modelling may be an efficient alternative. Moreover, ray-based methods typically add relevant information that is not (or not as easily) available through full wavefield modelling. 

Illumination mapping is the classic application of ray tracing, as the location of reflection points is known. However, advanced ray-based methods go far beyond the classic approaches. Kirchhoff modelling exploits Green’s functions and thus models diffractions, generating synthetic gathers that allow for migration tests (i.e., PSDM simulation) while keeping the flexibility and efficiency of ray-based techniques. The computational effort typically is larger than for conventional ray tracing but still significantly less than expected for full wavefield modelling. A key application is the assessment of the sensitivity of the migrated image to velocity uncertainties. A complex structural model and initial velocity field can be used to generate the synthetic shot gathers, while a perturbed velocity field can be used to migrate the synthetic data, and the image compared with the original structural model to assess shifts in position. 

Using Green’s functions for generating so-called illumination vectors is an even more efficient process. Each illumination vector is representing a valid shot and receiver combination of the survey, and combining all given shots and receivers provides an illumination function dependent on survey, sub-surface model and illumination point. Converting illumination vectors into scattering wavenumbers and combining them with the amplitude spectrum of a given wavelet generates a specific 3D filter that integrates both illumination and resolution properties. The filter can be applied to a representative model volume around the illumination point, acting as a fast-track PSDM simulator directly from a reservoir model. The depth domain representation of the filter is a point-spread function that provides direct access to both vertical and lateral resolution. For the given purpose, the point-spread function is considered as a 3D convolution wavelet that is as efficient but much more realistic and accurate than 1D convolution wavelets, which often are still used when modelling results are required quickly. 

This study shows some examples how sharp lateral velocity variations in the overburden may affect imaging underneath if the migration velocity field is overly smooth. Point-spread functions are used for estimating both lateral and vertical resolution at target level, and fast-track PSDM simulation in combination with illumination analysis indicates illumination limitations due to overburden and survey setup.  

Speaker Biography: Graham Johnson, NORSAR
Graham Johnson has been a representative of NORSAR in North America and user of NORSAR’s software since 1999. Working with NORSAR’s service department, he has completed several illumination studies on various prospects mainly in the Gulf of Mexico. Using NORSAR software, he performed numerous studies for the SMAART II consortium in connection with their physical tank model.

Graham holds a Bachelor of Science degree in Physics from the University of Durham, UK, and Master of Science degree in Geophysics also from Durham. After graduating, he joined the research department at Seismograph Service Ltd in the UK where he developed and maintained signal processing and signature deconvolution software. After five years, he joined GECO as part of a team developing Marine Vibrators for commercial use. He continued with Schlumberger after the merger and worked with land and marine source development, as well as borehole geophysics and general geophysical support. Since 1999, he has been president of Sound Seismic Solutions and, in addition to his NORSAR activities, has continued his involvement in the development of Marine Vibrators and other geophysical projects.