Introduction to structural inversion

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Seismic Data Analysis
Series Investigations in Geophysics
Author Öz Yilmaz
ISBN ISBN 978-1-56080-094-1
Store SEG Online Store

A recorded seismic wavefield represented by a shot gather has two components — traveltimes and amplitudes. Direct inversion of a seismic wavefield to estimate elastic parameters of the earth demands numerically intensive computations. Instead, most practical methods of inversion are applied to seismic traveltimes and amplitudes, separately. In earth modeling in depth, we discussed methods of layer velocity estimation — Dix conversion, stacking velocity inversion, and coherency inversion, which essentially are based on inversion of traveltimes. In earth imaging in depth, we discussed prestack Kirchhoff migration, which again, essentially is based on computing diffraction traveltimes. Traveltime inversion thus yields a structural model of the earth represented by a set of layer velocities and reflector geometries, which can then be used to derive a structural image of the earth by depth migration. The term structural inversion may be appropriately used to describe the process of structural modeling and imaging by way of inversion of traveltimes.

In reservoir geophysics, we shall discuss poststack amplitude inversion to estimate an acoustic impedance model of the earth and prestack amplitude inversion to derive the amplitude variation with offset (AVO) attributes. Amplitude inversion thus yields a stratigraphic model of the earth represented by a combination of acoustic impedance and AVO attribute changes within the layers themselves. The term stratigraphic inversion may be appropriately used to describe the processes of estimating the acoustic impedance and AVO attributes by way of inversion of amplitudes.

In this chapter, we shall discuss case studies in structural inversion of 2-D and 3-D seismic data. These case studies relate to structural complexities caused by

  1. extensional tectonism as in the cases of salt diapirs of the North Sea and the Gulf of Mexico,
  2. compressional tectonism as in the cases of overthrust belts of the Middle East and Rocky Mountains, and
  3. wrench tectonism as in the cases of the pull-apart basins of offshore Indonesia and Venezuela.

Results from inversion of a 2-D seismic data set must be evaluated within the bounds of 2-D imaging, and 3-D effects must always be kept in mind (introduction to earth imaging in depth). A structural inversion project can be a futile exercise if the 2-D data set has not been recorded along a dominant dip direction with minimal 3-D effects.

The first 2-D case study is from the Southern Gas Basin of the North Sea. The North Sea Basin has been subjected to extensional tectonics, primarily in the northeast-southwest direction with some rotational component. As a result, salt diapiric structures were formed and the overlying strata were subjected to faulting. Continuing extensional tectonics and salt movements caused further faulting of the overlying strata, thus forming collapsed structures especially above the apexes of the salt diapirs. Common structural targets in the North Sea are Permian sands of the Rotliegendes and Carboniferous substrata below the Zechstein diapiric formation. We want to obtain an accurate depth structure map of the top Rotliegendes formation in the survey area. This requires an estimate of the velocity-depth model above the Zechstein diapiric formation and removal of its deleterious effect on the underlying Permian sands of Rotliegendes and deeper targets.

The second 2-D case study is from the Gulf of Mexico. The basin in the Gulf of Mexico has been subjected to extensional tectonics, primarily in the north-south direction. As a result, the Jurassic salt loaded by the overburden sand-shale sequence began to be deformed first in the edges of the basin, forming diapiric structures. The extensional tectonism also gave rise to a series of growth faults, often enveloped by major listric faults and sometimes accompanied by counter-regional faults. As the sand-shale deposition of Miocene and subsequent ages increased the overburden pressure, some diapirs took dike-like forms and some formed overhangs. Additionally, some of the salt diapirs were squeezed along the fault planes and some even were moved laterally as far up as the water bottom, eventually detaching themselves from the source salt layer situated within the deeper strata and forming tabular salt bodies. Some of these tabular bodies joined together to form salt canopies. The subsequent deposition on top then deformed the shape of the salt canopies, giving rise to a rugose geometry along the top and the base. The target zones are, for some cases, immediately below the base-salt, and for some other cases, somewhat deeper, they are below an overpressured zone.

The third 2-D case study deals with irregular water-bottom topography associated with a reef body. The reef causes severe distortions of reflection travel-times associated with underlying target horizons. The fourth 2-D case study deals with imaging beneath a volcanic layer. Finally, the fifth 2-D case study is from the Gulf of Thailand. Shallow gas anomalies cause difficulty in imaging multileveled reservoirs along faults that are abundant in the area.

The first 3-D case study is from the Southern Gas Basin of the North Sea. The objective is to delineate the geometry of the base-Zechstein layer which forms a three-dimensionally complex diapiric structure. The second 3-D case study is from the Central North Sea. We demonstrate the use of the combination of the inversion methods listed in Table 9-1 to estimate layer velocities and delineate reflector geometries within the overburden above the Zechstein formation. The third 3-D case study is from offshore Indonesia. The objective is to image the complex fault blocks caused by pull-apart tectonism. In this case study, we also demonstrate structural and stratigraphic interpretation of the image volume derived from 3-D prestack depth migration. Finally, the fourth 3-D case study is from Northeast China. With this case study, we demonstrate a complete time-and-depth sequence for processing, inversion, and interpretation that involves both 3-D prestack time and depth migrations.

Table 9-1. A set of inversion procedures for earth modeling in depth to estimate layer velocities and delineate reflector geometries.
Layer Velocities Reflector Geometries
Dix conversion of rms velocities vertical-ray time-to-depth conversion (vertical stretch)
stacking velocity inversion image-ray time-to-depth conversion (map migration)
coherency inversion poststack depth migration
image-gather analysis prestack depth migration

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