## Reverse Time Migration

PGS Reverse Time Migration (RTM) can image steep dips, overhangs and other complex structural provinces that could not be resolved accurately with ray tracing or one-way wavefield extrapolation. Our RTM implementation relies on the advanced Inverse Scattering Imaging Condition (ISIC) that suppresses artifacts, and delivers clean and accurate angle gathers and images.

The RTM algorithm offers our most accurate imaging with full dip fidelity and accurate amplitudes. It is based on a pseudo-analytic solution to the wave equation that allows for very accurate modeling of anisotropic wave propagation, without the artifacts normally associated with other industry solutions.

PGS PSDM wave equation based migrations are designed to handle general data geometries such as NAZ, MAZ, WAZ and FAZ (narrow, multi, wide and full azimuths respectively). They are also designed to work with arbitrary depths to efficiently handle Ocean Bottom Cable (OBC) and Ocean Bottom Node (OBN) data.

**Migration in Time Domain**

RTM is achieved by a forward and reverse time propagation of source and receiver wavefields respectively, followed by the application of an imaging condition. The algorithm handles the source and receiver wavefields separately, performing a correlation between them to form the image. RTM forward models the source in time, and reverse models the receiver wavefield in time. Because RTM propagates the wavefields in time and not depth, there is no dip limitation on the wavefields.

**Computing the Image**

RTM constructs the image from numerically synthesized subsurface incident and reflected wavefields. A representation of the seismic source and the reversed time reflection seismogram are used as boundary conditions in a seismic modeling framework to simulate the time history of these data in the subsurface.

An approximation of the reflectivity of the earth is then generated by appropriately combining these images at locations where these two wavefields are in phase at the time of reflection in the subsurface.

There are a variety of methods for computing the image, but often the method of choice is based on a cross-correlation between the source and receiver wavefields. This is the time integration of the forward and reverse time wavefields, potentially scaled by a normalization factor which corrects for source power, transmission, illumination and acquisition effects.

**Addressing Correlated Noise**

Unfortunately, RTM correlation methods can be negatively affected by backscattered and turning waves in the modeling process, which causes the incident and reflected wavefields to be in phase at locations that are not the reflection points. This results in strongly correlated noise in the seismic image.

Typical means of addressing this correlation noise is to reduce these artifacts by conditioning the modeling process. However, conditioning the model can introduce propagation errors, and thus there is a trade-off between artifact reduction and imaging accuracy. Also, model conditioning typically does not address turning waves or high angle reflections. Post processing of the RTM image with spatial reject filters is often used to attenuate the low wavenumber noise and can reduce the near DC component of the noise. However, these methods need to be assessed and must properly treat the velocity dependent wavenumber variations in the depth image.

**Inverse Scattering Imaging Condition**

PGS offers an improved imaging condition, ISIC, which has been designed to reduce the imaging noise by using directional information computed directly from the data. ISIC is based on a generalized inverse scattering imaging condition in which the backscattered waves are attenuated by using the combination of two separate images: one based on the product of the time derivatives of the incident and reflected wavefields and the other based on the product of the spatial gradients of the incident and reflected wavefields. These images are then combined to produce the final inverse scattering image.

**RTM Provides an Image and Pre-Stack Gathers**

RTM has become a standard method for illumination of complex geologic structures and potential reservoirs. To utilize the angular and azimuthal coverage of the wide azimuth acquisition systems, imaging and velocity estimation methods require adequate treatment of subsurface dip, azimuth, and illumination angle. In PGS' implementation of RTM, not only is the RTM image output but also the option to decompose the data into pre-stack gathers that sample both the azimuth and angular components of the image that can be used for data processing and 3D tomography.

For the decomposition of the data into angle gathers, PGS use a method which is a dynamic binning onto angle and azimuth which is performed at each time step. The method employs the inverse scattering imaging conditions to reduce backscattered noise during propagation which is essential in providing high quality angle gathers.

RTM is a shot based migration method, where each shot is imaged onto the subsurface independently. During the imaging process, the source and receiver angles can be determined from a combination of the source wavefield direction vectors and subsurface dip (or alternatively, the receiver wavefield direction vectors at the source onset time), giving an opening angle computation.

However, angular decomposition of the RTM image requires removal of the backscattered RTM noise at each time step. PGS employs ISIC to generate a backscatter free RTM image that can be decomposed into subsurface angles. At the same time, the RTM image can also be binned onto output azimuth bins - allowing for a direct mapping to angle-azimuth images during RTM imaging. The final RTM angle-azimuth images are then computed by summing the binned images over the entire time and then over all of the resultant shot images.

This dynamic angle-azimuth decomposition of the RTM image is achieved during the RTM computation and angle-azimuth data is saved at each image point. This allows for post migration processing such as residual depth error corrections, angle and azimuth dependent stacking, and 3D tomography. Note that the angular sampling at a specific image point depends directly on the source-receiver geometry of the acquisition system. If regularly sampled angle gathers are required for analysis, as in the case of 3D tomography, some form of specular resampling may be required.