True Amplitude Recovery

Key Takeaways

• Spherical divergence is the primary amplitude decay mechanism for seismic body waves in homogeneous media: as a seismic wavefront expands from a point source, the total energy is conserved but the energy per unit area of wavefront decreases proportionally to the square of the travel distance (the wavefront area increases as the square of the radius), causing amplitude to decay as 1/r where r is the travel distance; in a layered earth where seismic velocity increases with depth, the spherical divergence correction is more complex than simple 1/r because the wavefront propagates faster at depth, with the standard approximation for the divergence correction factor being proportional to v^2 * t, where v is the RMS velocity and t is the two-way travel time; applying this correction to the raw seismic data multiplies each sample by v^2 * t, restoring the relative amplitudes of reflectors at different depths to approximately the values they would have had if spherical spreading had not occurred; for a 3-second two-way time recording in a typical basin with RMS velocity of 2,500 m/s, the spherical divergence amplitude decay factor is approximately 2,500^2 * 3 = 18.75 million (about 145 dB), illustrating why raw seismic records show dramatic amplitude decay from near-surface reflectors to deep reflectors that must be corrected before any quantitative amplitude work is attempted.
• Intrinsic attenuation (Q correction or inverse Q filtering) is the second major true amplitude recovery step, compensating for the anelastic absorption of seismic energy as waves propagate through rocks that are not perfectly elastic: in real Earth materials, a fraction of the mechanical energy in the seismic wave is converted to heat by internal friction at grain boundaries, fluid-solid interfaces, and other imperfection mechanisms, causing the amplitude to decay exponentially with travel time and the higher frequencies to attenuate faster than lower frequencies (the attenuation parameter Q determines the frequency-dependent decay rate, with lower Q meaning more attenuation, with typical Q values of 20 to 50 for unconsolidated near-surface sediments, 50 to 150 for consolidated sandstones and shales, and 200 to 1000 for carbonates and crystalline rocks); the combined effect of frequency-dependent attenuation is that seismic data becomes progressively lower in frequency and lower in amplitude at greater depths, making deeper reflectors appear dimmer and less resolved than shallower reflectors even after spherical divergence correction; inverse Q filtering (Bickel and Toksoz method, or the more stable frequency-domain phase shift approach) applies a time-variant, frequency-dependent amplitude boost that is the inverse of the attenuation operator, restoring the high-frequency content and correcting the amplitude bias caused by Q; accurate Q correction requires a depth or time-velocity model of Q derived from VSP or well log measurements (using the spectral ratio method to measure Q from upgoing and downgoing VSP waves) that is often more uncertain than the velocity model used for spherical divergence correction.
• Surface-consistent amplitude corrections address the amplitude variations between seismic records that arise from factors at the source and receiver locations rather than from subsurface geology: variations in shot energy (imperfect explosive charges or vibrator hydraulic pressure), receiver coupling differences (geophones planted in soft soil versus hard rock, hydrophone groups with varying pressure response), near-surface weathering (the low-Q near-surface layer attenuates more in areas of thick, poorly consolidated soil than in areas of thin weathering), and instrument gain differences between channels contribute systematic amplitude patterns on the shot records and receiver records that, if not corrected, appear as striping or checkered patterns on stacked seismic data; surface-consistent decomposition solves for separate shot, receiver, offset, and midpoint terms in a multiplicative model for each sample amplitude on each trace, using least-squares inversion of the overdetermined system of amplitude equations to separate the surface-related terms from the subsurface reflection amplitude term; after surface-consistent correction, the residual amplitude variations on the stacked data are attributed primarily to subsurface geology (lithology, fluid content, and porosity variations) rather than to acquisition artifacts, enabling reliable quantitative interpretation of amplitude anomalies as seismic direct hydrocarbon indicators.
• Amplitude-versus-offset (AVO) analysis uses true-amplitude-recovered pre-stack seismic gathers to measure how the reflection amplitude varies with the source-receiver offset (or equivalently, the angle of incidence at the reflecting interface), providing information about the elastic properties (P-wave velocity, S-wave velocity, and density) of the rock and fluid at the reflection interface that is not available from the zero-offset amplitude alone: the Aki-Richards linearized approximation of the Zoeppritz equations predicts that the variation of reflection amplitude with angle of incidence depends on the contrasts in Vp, Vs, and density across the interface, with gas sands exhibiting a characteristic "Class II-negative" or "Class III" AVO response (large negative intercept increasing in magnitude with offset due to the low acoustic impedance and low Poisson's ratio of gas-saturated sandstone) distinguishable from brine sands ("Class I" positive intercept decreasing with offset) on a crossplot of AVO intercept versus AVO gradient; because AVO analysis compares the relative amplitude at different offsets, any uncorrected true-amplitude recovery errors that are offset-dependent (such as residual spherical divergence differences between near and far offsets, or NMO stretch amplitude effects) will produce spurious AVO attributes that mimic the lithology/fluid response being sought, making high-quality true amplitude recovery a prerequisite for reliable AVO interpretation.
• Seismic inversion uses true-amplitude-recovered seismic data to compute acoustic impedance or elastic impedance models of the subsurface, directly estimating the rock physical property (impedance = velocity times density) that is the geologically meaningful quantity at each reflector, rather than the reflection coefficient (impedance contrast) that is directly represented by the seismic amplitude: model-based inversion (using a low-frequency model derived from well logs as a starting model and iteratively adjusting it to match the seismic data) and sparse-spike inversion (solving for a minimum-number-of-impedance-change model consistent with the seismic data) both require that the input seismic amplitudes are proportional to the actual reflection coefficients, which is the definition of true amplitude recovery; the quality of the impedance model produced by seismic inversion is limited by the accuracy of the true amplitude recovery applied to the input data, the bandwidth of the seismic wavelet (inversion cannot recover frequencies outside the seismic bandwidth), and the quality of the wavelet estimation from well-to-seismic tie; improvements in true amplitude recovery processing directly improve the reliability of impedance inversion products used for facies mapping, porosity prediction, and fluid substitution modeling in reservoir characterization workflows.