Least-squares joint imaging of multiples and primaries

Abstract

INTRODUCTIONMy Least-squares Joint Imaging of Multiples and Primaries (LSJIMP) algorithm (Brown, 2003b) separates pegleg multiples and primaries. LSJIMP computes separate images of the peglegs and primaries, and then uses the mutual consistency of the images to discriminate against unwanted noise types in each image. The images must be consistent in two respects: kinematics and amplitudes. A companion paper (Brown, 2003a) paper addresses the amplitude issue. In this paper, I address the kinematics. Kinematically, the events must be correctly positioned in time and flat with offset. To this end, I derive new time imaging operator, "HEMNO" (Heterogeneous Earth Multiple NMO Operator).To correctly image primary or multiple reflections in a heterogeneous earth, migration reigns supreme, although its computational cost may be nontrivial over complex geology, in 3-D, or when a "true amplitude" image is required. My previously presented (Brown, 2002a) joint imaging technique used normal moveout (NMO), because of NMO's speed and its amplitude predictability, despite its inability to account for nonflat geology. HEMNO correctly accounts for moderate subsurface structure but retains the speed and amplitude advantages of NMO. I show that the 2-D and 3-D pegleg moveout equations for two dipping planes derived by Levin and Shah (1977) and Ross et al. (1999), respectively, reduce to HEMNO in the small dip angle limit.When used in conjunction with LSJIMP, I show that HEMNO produces improved results on the moderately complex Mississippi Canyon 2-D multiples test dataset, relative to a flatearth NMO operator. Nevertheless, the real value of HEMNO lies in 3-D. Guitton (2003) demonstrates that the "Delft method" (Verschuur et al., 1992) (plus advanced multiple subtraction technology), almost perfectly separates surface-related multiples from 2-D data with complex 2-D structure. However, in real-world 3-D situations, acquisition and computational constraints diminish the method's applicability. I demonstrate that in a simple, yet realistic, 3-D synthetic example that HEMNO can accurately image pegleg multiples from a seabed that dips in both directions. In the future, HEMNO should prove a useful advance in 3-D multiple separation. S201G S102GA first-order pegleg multiple consists of two unique arrivals: the event with a multiple bounce over the source, and the event with a bounce over the receiver. Figure 1 shows that in a flat earth, both "legs" of a pegleg (denoted S102G and S201G) arrive simultaneously; when the reflector geometry varies with position, they generally do not. In some cases, pegleg multiples are actually observed to "split", though humans rarely observe the phenomenon unambiguously in field data, unless the reflector geometry is uniformly dipping over a large distance (see (Morley, 1982), for a good example).The practical non-observation of split peglegs notwithstanding, geologic heterogeneity is a first-order effect in the accurate modeling of their kinematic and amplitude behavior. Mild variations in reflector d...

Recursive imaging with multiply scattered waves using partial image regularization: A North Sea case study

“…Even with the added complication of regularization and use of two-pass, one-way methods, it is still faster to make an image in this way than to use reverse-time methods. An added advantage of the ability to separate images made with singly, doubly, and triply scattered waves is that these separate images can be used to identify artifacts from crosstalk (as discussed in detail by Brown and Guitton [2005]), allowing an interpreter to assess the likely artifacts in each image separately. By using an image, rather than including the interface directly in the velocity model, one can still use discontinuous or poorly imaged structures to estimate and thus exploit multiply scattered waves.…”

“…Similar to methods discussed by Brown and Guitton (2005), imaging with multiply scattered waves requires the separation of these multiples from primaries. Although a method such as that suggested by Brown and Guitton would likely result in a cleaner image with fewer artifacts, we have found that much simpler procedures are adequate, in particular for doubly scattered waves.…”

“…Beginning with the work of Reiter et al (1991), who proposed a method for imaging with water-column multiples in a Kirchhoff scheme, and continuing through the recent work of Berkhout and Verschuur (2003, in which surfacerelated multiples are converted into primaries, surface-related multiples have been shown to provide added information for imaging. Brown and Guitton (2005) discuss a unified framework to image with primaries and surface-related multiples, focusing on removing crosstalk between the different images. There are also several discussions for particular acquisition configurations, such as VSP (Jiang, 2006) and ocean bottom cable (Muijs et al, 2007), as well as more in-depth inversion procedures, such as that suggested by Métivier et al (2009).…”

Elastic P- and S-wave autofocus imaging with primaries and internal multiples

“…Youn and Zhou (2001) devised a prestack depth migration method that used a model-based estimate of the internal multiples. Data-driven methods for imaging using internal multiples include least squares migration (Brown and Guitton, 2005), interferometric imaging (Jiang et al, 2005), one-way wave equation migration (Malcolm et al, 2009), full wavefield migration (Berkhout, 2012), RTM for internal multiples (Liu et al, 2011;Fleury, 2013) and generalized internal multiple imaging (Zuberi and Alkhalifah, 2014).…”

Correlation-based seismic velocity inversion

“…This motivates us to take a look at the data-domain, where, in principle, we can include multiples by using the full wave-equation to model the data. It should be mentioned that some attempts have been made to use multiples in migration (see, for example, Youn & Zhou, 2001;Brown & Guitton, 2005;Jiang et al, 2007). Data-domain methods come in various shapes and sizes, however, we will focus on waveform inversion.…”