Microtremor surveys based on rotational seismology: theoretical analysis with focus on separation of Rayleigh and Love waves in general wavefield of microtremors

SUMMARY The applicability of rotational seismology to the general wavefield of microtremors is theoretically demonstrated based on a random process model of a 2-D wavefield. We show the effectiveness of taking the rotations (i.e. spatial differentiation) of microtremor waveforms in separating the Rayleigh and Love waves in a wavefield where waves are simultaneously arriving from various directions with different intensities. This means that a method based on rotational seismology (a rotational method) is capable of separating Rayleigh and Love waves without adopting a specific array geometry or imposing a specific assumption on the microtremor wavefield. This is an important feature of a rotational method because the spatial autocorrelation (SPAC) method, a conventional approach for determining phase velocities in microtremor array surveys, requires either the use of a circular array or the assumption of an isotropic wavefield (i.e. azimuthal averaging of correlations is required). Derivatives of the SPAC method additionally require the assumption that Rayleigh and Love waves are uncorrelated. We also show that it is possible to apply a rotational method to determine the characteristics of Love waves based on a simple three-point microtremor array that consists of translational (i.e. ordinary) three-component sensors. In later sections, we assume realistic data processing for microtremor arrays with translational sensors to construct a theoretical model to evaluate the effects of approximating spatial differentiation via finite differencing (i.e. array-derived rotation, ADR) and the effects of incoherent noise on analysis results. Using this model, it is shown that in a short-wavelength range compared to the distance for finite differencing (e.g. $\lambda < 3h$, where $\lambda $ and $h$ are the wavelength and distance for finite differencing, respectively), the leakage of unwanted wave components can determine the analysis limit. It is also shown that in a long-wavelength range (e.g. $\lambda > 3h$), the signal intensity gradually decreases, and thus the effects of incoherent noise increase (i.e. the signal-to-noise ratio, SNR decreases) and determine the analysis limit. We derive the relation between the SNR and wavelength. Although the analysis results quantitatively depend on the array geometry used for finite differencing, the qualitative understanding supported by mathematical expressions with a physically clear meaning can serve as a guideline for the treatment of data obtained from ADR.

A direct noise attenuation approach in processing of land continuous records

Blended source acquisition has drawn great attention in industry due to its increased efficiency and reduced overall cost for acquiring seismic data. It eliminates the requirement of a minimum time (usually determined by record length) between adjacent shots and allows multiple sources to be activated simultaneously and independently. Conventional processing simply converts continuous records into fixed-length records using the source excitation time and then applies traditional denoising techniques to the fixed-length records. Source excitation time is used to extract fixed-length records that are the equivalent of traditional synchronous recording. Here, we elaborate on the usage of continuous records for land noise attenuation. Compared to conventional common shot/receiver/midpoint/offset domains, continuous records represent the data in the naturally recorded domain. This domain offers flexible and much longer record lengths to work with and, moreover, enables exploiting the characteristics of noise prior to correlation, shot slicing, or other preprocessing. We limit our discussions to the techniques and methods for attenuating coherent environmental and source-generated noise on vibroseis data. We have found that incoherent noise can be handled effectively by traditional noise suppression methods after deblending. We illustrate the effectiveness of noise attenuation in the continuously recorded domain for three different types of noise using field examples from the North Slope of Alaska and the Permian Basin.

Prestack Q compensation with sparse tau-p operators

The application of [Formula: see text] compensation to prestack marine data needs the proper removal of the water-layer time from the total traveltime, a process known as “time referencing.” To obtain the water-layer time, current industry practices use some form of normal moveout equation that requires subsurface velocities. We have derived a more straightforward and accurate formula for time referencing that does not require subsurface velocities and works under the same assumptions. The formula is based on a local angle decomposition via the tau-[Formula: see text] transform. Further complicating the [Formula: see text] compensation task in the prestack domain is the proper treatment of spatially aliased energy and high-frequency noise. We found out how time-slowness sparsity, used as a constraint for [Formula: see text] compensation, gives excellent immunity to incoherent noise and spatial aliasing, and we evaluate its role in accelerating the convergence rate for our iterative inversion algorithm.

Methods of correlation noise minimization and suppression for multisource acquisition in vibroseis survey

The use of several simultaneously operating sources in seismic operations allows one to obtain large amounts of data per unit of time than for classical works with a single source, and also to improve the seismic data recording system. Depending on the type of seismic source used (vibrating or pulsed), different methods of signal separation are used. When working with vibroseismic method, separation of signals becomes possible at the stage of correlative processing of vibrograms. In this paper, we demonstrate methods for constructing noncorrelating signals for use in vibroseis survey (with an example of using such signals on synthetic data) and hyperbolic median filtering to minimize correlation and incoherent noise.