Least-Squares Migration Technique Improves Imaging and Inversion Offshore China

In this paper, the authors propose a least-squares Q migration (LSQM) method that combines the benefits of both LSM and Q prestack depth migration (QPSDM) to improve the amplitude fidelity and image resolution of seismic data.

Seismic images

Least-squares migration (LSM) has become an increasingly important imaging tool. Recently, several case studies have shown that LSM provides greatly improved seismic imaging. However, only a few examples reveal its advantages in both imaging and amplitude-vs.-offset (AVO) inversion. In this paper, the authors propose a least-squares Q migration (LSQM) method that combines the benefits of both LSM and Q prestack depth migration (QPSDM) to improve the amplitude fidelity and image resolution of seismic data.


Seismic data can be considered an outcome of a forward modeling experiment with an unknown Earth velocity model and absorption Q model. Several major factors can affect the resolution and amplitude fidelity of the resulting seismic images, namely the acquisition configuration, absorption of the anelastic Earth, and the complexity of the subsurface velocity model. With regard to the first factor, seismic images can suffer from limited migration aperture and nonuniform illumination. This illumination issue can be addressed through image-domain single-iteration LSM. With regard to the second and third factors, it is important to include Q absorption in the velocity model-building process and the migration algorithm, and to use least-squares means to control the compensation of energy loss through LSQM.

In the South China Sea, complex faulting geology poses a significant challenge to imaging with narrow-azimuth towed streamer data. Over the past decade, Q tomography and Q migration have been developed to tackle the issue with Q absorption. However, because both the Q compensation level and the noise level of seismic data usually increase with travel time and frequency, high-frequency noise and migration swings are often overamplified in Q migration.

The issues with amplitude distortion associated with fault shadows and smeared fault images with a limited usable aperture can be coped with better through the use of LSM, and seismic image resolution can be increased by compensating Q effect with travel time and frequency. The high-frequency noise generated from QPSDM can be attenuated better through LSM if Q can be brought into the process of LSM. To fully exploit the merits of LSM and QPSDM, seismic imaging can be improved through LSQM.

The authors apply LSQM to a narrow-azimuth marine-towed streamer survey acquired over an area with complicated faulting structures and significant absorption in the South China Sea. Using image-domain single-iteration LSQM and reservoir-oriented processing, the authors demonstrate that the previously mentioned problems can be addressed, with the result of improved AVO inversion at the wells.

Imaging Domain LSQM

Image-domain LSQM inverts for a reflectivity model to fit the raw migrated image by solving an optimization problem described in the complete paper. In addition to the common benefits of LSM that compensate for spatial illumination variations and suppress migration-related artifacts, single-iteration LSQM has also been shown to be effective at attenuating random noise, migration swings, and other noise. However, to derive the inverse of the Hessian filter more effectively, an enhanced reflectivity model can be used to guide the derivation of the inverse Hessian filters through single-iteration image-domain LSQM. Ideally, the enhanced reflectivity model should be both noise- and multiple-free. This can be achieved by introducing more comprehensive processing steps guided by a priori AVO knowledge from the wells through further conditioning.


Improved Imaging. The survey is located in a shallow-water area with water depth between 60 and 100 m over a highly faulted area in the South China Sea. The LSQM flow starts with Kirchhoff Q prestack depth migration using a smooth Earth velocity model and a constant Q field. As can be seen in Fig. 1a, the fault imaging of QPSDM looks less focused, and the seismic events are contaminated heavily with random noise and migration swings generated from a sudden change in amplitude at a depth of approximately 1.2 km. Furthermore, amplitude stripes relating to the acquisition footprint can also be seen clearly. This random noise and the migration swings are the artifacts of QPSDM when attempting to improve seismic resolution. However, the noise is likely to affect adversely the quality of seismic inversion and interpretation. LSQM is highly recommended in order to suppress the noise while improving the seismic resolution with Q compensation during migration.

Fig. 1—The shallow part of a line crossing significant faults: (a) QPSDM and (b) LSQM; depth slices at 1200 m: (c) QPSDM; and (d) LSQM in the survey. (e) The amplitude spectra measured over a shallow window on LSQM and QPSDM are very similar except that the energy above 100 Hz is dominated by random noise in QPSDM.


Fig. 1b shows that the fault imaging, as well as signal-to-noise ratio, have been improved by LSQM. Residual random noise, particularly immediately below the water bottom, and migration noise associated with the acquisition footprint also have been reduced significantly after LSQM. The amplitude stripes related to the acquisition of the marine narrow-azimuth towed streamer, seen in Figs. 1a and 1c, have been better attenuated in Fig. 1b and 1d after LSQM. The resolution of the seismic image produced by LSQM looks similar to that generated by QPSDM, but with the signal-to-noise ratio also being improved greatly. The fault imaging at 1200 m looks much sharper, illustrated by much better delineation in Fig. 1d after LSQM.

Amplitude-spectrum analysis in Fig. 1e shows that the frequency bandwidth from QPSDM and LSQM looks similar, which also confirms previous observations. The energy above 100 Hz is dominated mainly by random noise on the QPSDM seismic image.

Improved AVO Inversion. The AVO inversion work flow, including synthetic to seismic tie, AVO curve, AVO attribute, and AVO inversion, are used to quality-control and assess the seismic data after application of the different processing methods described in the complete paper.

AVO inversion is one of the primary uses of the processed seismic data. In AVO inversion, the input multiseismic stacks are modeled by the convolution of the seismic wavelets with the inverted reflection coefficient series. Geological and geophysical constraints are provided to find the best solution from the large number of available mathematical inverted solutions from the inversion. The AVO inversion operates through minimization of a multitrace, multielement cost function. Each element of the cost function is controlled and tested in terms of P-impedance, S-impedance, and density.

High-resolution AVO inversion requires a broad bandwidth of seismic imaging along with a high quality of event characteristics. In this survey, the target reservoir is within a fine layer, and there is one well within the survey area. The gathering at the well location generated by LSQM is much cleaner, with less residual multiple energy and with a more-consistent waveform across the offsets. The corresponding AVO curves, taken at 1900 ms from these gathers, are compared with well synthetics, clearly showing that the AVO curve from LSQM has a good match with that generated from the well data, while QPSDM shows a different AVO class pattern. The AVO behavior of the LSQM stacks has better agreement with the well synthetics than the QPSDM stacks, and correspondingly a more-accurate AVO pattern is defined with LSQM.


QPSDM can improve seismic resolution, but it suffers from migration swings and more random noise, particularly when high frequency is needed for AVO inversion at finer layers. LSQM has proved beneficial in allowing the retention of the benefits of QPSDM. A good reflectivity reference that ties to well synthetics and the AVO curve pattern can be used to guide the generation of an inverse Hessian filter. LSQM can be applied to both Kirchhoff and reverse-time migration. The authors demonstrate that both seismic imaging and AVO inversion results can be improved significantly through image-domain single-iteration least-squares Q Kirchhoff APSDM.

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper IPTC 19285, “Improving Imaging and Inversion Through Least-Squares Q-Kirchhoff APSDM: A Case Study From Offshore China,” by Chenghai Jiao, Jianfeng Yao, and Keat Huat Teng, CGG, et al., prepared for the 2019 International Petroleum Technology Conference, Beijing, 26–28 March. The paper has not been peer reviewed. Copyright 2019 International Petroleum Technology Conference. Reproduced by permission.