Structure Using Wave Field Continuation of P Waves

Wave field continuation transforms seismic record section data directly into velocity-depth space, simultaneously providing an estimate of model nonuniqueness. This inversion, previously used for reflection and refraction data, converts readily to spherical earth problems through simple adjustments in each of the two linear transformations: the slant stack and downward continuation. Because the time resolution inherent in the data transforms to depth resolution in the model space, this method is extremely useful for analysis of data compatibility with preexisting models and direct comparison between data sets, as well as the complete inversion of raw data for structure. Wave field inversion demands densely sampled, digital data, and assumes source coherency and lateral homogeneity along the profile. We test this technique for upper mantle analysis using a previously studied, large, array-recorded data set representative of structure beneath the Gulf of California. We compare slant stacks and downward continuations of both synthetic and data record sections to illustrate the method's resolution capability. Wave field continuation proves particularly useful in comparing entire data sets to various models; even subtle structural differences are resolvable given good data quality. INTRODUCTION Numerous studies in the geophysical literature document the upper mantle velocity structure of tectonically interesting regions. Assembly of a detailed global map of the upper mantle would be very useful in enlarging our understanding of plate tectonics and mantle convection. Such a project requires comparison of many models derived with differing techniques and multiple data types; the uncertainties associated with the velocity-depth profiles become very important in assessing regional differences. Quantification of the uncertainties in upper mantle models is a pervasive problem, since many of the published models were achieved through trial-and-error methods with various combinations of data constraints. One way to estimate the nonuniqueness of such models is through an extension of the trial-and-error concept: the Monte Carlo method (Wiggins, 1969). This computer intensive scheme generates a large number of random models and tests them for consistency with the data, thereby mapping an acceptable region in velocity-depth space. If only travel-time data are available, the tau method (Bessonova et al., 1974, 1976) is capable of inverting large data sets and estimating the associated extremal bounds on the uncertainty. Upper mantle researchers utilizing array data (e.g., England et al., 1978; Walck, 1984a) have used this type of inversion extensively. The extremal envelope is clearly a maximum error estimate, since each envelope boundary is not itself an acceptable model. Often, additional data types such as ray parameter and amplitude information are used to constrain the models. The uncertainties in these data are not generally used in calculating the extremal bounds, although Wiggins et al. (1973) have provided a method for including ray parameter uncertainties. If still more data are included, such as waveform constraints derived 1703 1704 MARIANNE C. WALCK AND ROBERT W. CLAYTON from forward modeling with synthetic seismograms, the uncertainty envelope should be even more restrictive. Quantitative description of the uncertainty reduction obtained through this process, however, is not straightforward. Another approach is to abandon forward modeling in favor of more formalized inversions. The series of papers by Backus and Gilbert (1967, 1968, 1970) outlines general techniques for obtaining inverses for geophysical problems with accompanying estimates of model resolution and uniqueness. More recently, Given (1984) and Shaw (1983) develop inversion schemes based on comparisons of waveform data and synthetic seismograms. Because of high computational costs, only limited data can be included in these algorithms. For large, densely sampled data sets, wave field continuation (Clayton and McMechan, 1981) provides direct estimates of the data uncertainty in the slownessdepth domain. The entire wave field, in the form of a record section (7, A) is transformed to the (T, p), or intercept time-ray parameter, domain through the inverse Radon transform or slant stack. This process forms the T p curve directly, without any travel-time picks. Downward continuation with a prespecified velocity model carries the stacked data to the slowness-depth (p, z) plane. Both of these processes are linear, and the final result contains all the information present in the original data set. The width of the slowness-depth image is governed by the data's coherency, quality, and inherent time resolution. Important in application of the method are the underlying assumptions of densely sampled data and lateral homogeneity (see McMechan et al., 1982 for details). Also, the presence of a velocity reversal in the generating structure will result in an offset in T for fixed p. A priori knowledge of the existence of the low velocity zone is necessary to properly image it using the downward continuation process. In previous work, wave field continuation was applied to flat-earth problems involving reflection and refraction data (Schultz and Claerbout, 1978; Clayton and McMechan, 1981; McMechan et al., 1982). Through a simple substitution this method is adaptable to problems requiring spherical geometry such as upper mantle modeling. Because of the necessity of dense spatial sampling, wave field analysis is most applicable to data collected at seismic arrays. Since seismograms from several earthquakes at various distances from an array are required to assemble an upper mantle record section, we apply some preprocessing of the data to simulate a single source. Static shifts due to receiver structure are removed, and source wavelet equalization is attempted through a simple deconvolution procedure. We test the wave field technique's usefulness for upper mantle data with analysis of synthetic record sections, and then compare the synthetic results to those for real data representing Gulf of California upper mantle structure. THEORY Wave field continuation consists of two linear transformations of the data: the slant stack and downward continuation (see Clayton and McMechan, 1981, for a detailed discussion). The slant stack transforms a seismic record section P(t, x) from the (t, x) domain to the (% p) domain through the relation (e.g., McMechan and Ottolini, 1980)