Abstract Linear rates of sediment aggradation and fluvial incision are inverse functions of measurement interval, a generic consequence of unsteadiness in the underlying processes. This effect results from a one-dimensional approach–that is, vertical rates determined at a single location–and significantly complicates comparisons of rates at different timescales. Mass conservation imposes an important but underutilized constraint; sediment by-passing or eroded from one location must deposit somewhere else. Over the long term, sediment generation and deposition must balance. In principle, the effects of unsteadiness could be eliminated if the total volume of sediment eroded or deposited over different intervals could be measured. In practice, however, obtaining such three-dimensional data from an individual site is virtually impossible. Here, we advance from one- to two-dimensional rate data. We present two new global compilations of data: denudation rates of fluvial uplands; and lateral migration (progradation) rates of siliciclastic lowland and marine systems, from ripple to shelf-slope scale. Important new findings are: (1) upland denudation rates determined from specific sediment yield show little or no dependence of rate on time interval; (2) in the transfer zone between sediment source and sink, rates of erosion and deposition balance over all scales; and (3) progradation mirrors aggradation over all timescales. The product of progradation and aggradation is independent of timescale, implying that global sediment flux into the world’s oceans has been constant on the order of 10 0 m 2 /yr, from scales of months to tens of millions of years. Results show that global rates of denudation and accumulation are time invariant with appropriate spatial averaging; however, site-specific application remains a daunting challenge.

Abstract Stratigraphic correlation involves three distinct tasks: establishing the temporal sequence of marker events (sequencing task), determining the relative sizes of the intervals between those events (spacing task), and locating the horizons that correspond in age with each event in every section (locating task). Stratigraphic sections do not yield enough information to solve this problem exactly. Instead, stratigraphers must search for the approximation that “best” fits all local stratigraphic observations. The concept of economy of fit, as used in graphic correlation, provides a rigorous definition of “best” and implies the existence of a penalty function that can be used to rank possible solutions. Unfortunately, traditional graphic correlation requires severe simplifying assumptions about accumulation rates because it attempts to solve all three tasks at the same time, and yet it incorporates the local sections into the solution one at a time. Using a penalty function based on economy of fit, an alternative solution technique naturally emerges in the form of constrained optimization. This technique is J dimensional, in the sense that it treats the observations in all J sections simultaneously. It can complete the sequencing task before making assumptions necessary to the spacing task. Constrained optimization eliminates impossible solutions (constraint) and then searches for the best of all the possible ones (optimization). For realistic instances of the problem, it is not feasible to calculate the penalty function for all possible solutions. Instead, we use a probabilistic search procedure termed “simulated annealing” to find very good solutions without an exhaustive search. Simulated annealing does not maintain any memory of the search path or search exhaustively at the local scale. We reject an alternative procedure that incorporates these features because it proved difficult to tallor to produce satisfactory solutions. Our J -dimensional procedure quickly finds solutions for Palmer’s (1954) classical data set (/= 7 sections from the Cambrian of Texas) that are comparable to the solution Shaw (1964) achieved by traditional graphic correlation. The expert judgements that the stratigrapher uses to draw the traditional lines of correlation and which give the appearance of excessive subjectivity, in fact, derive primarily from a knowledge of all the sections. By treating all sections at once, constrained optimization eliminates much of the apparent subjectivity associated with traditional graphic correlation. Constrained optimization still allows the user to explore the consequences of different and genuinely subjective judgements about the relative reliability of different taxa and sections.

ABSTRACT The average rates of unsteady processes decrease progressively for time spans of increasing duration. Sediment accumulation, facies migration, subsidence, sea-level change and accommodation are all unsteady processes. Over 235,000 empirical rate determinations from nearly 2,000 different published sources prove that the expected rates of these processes are different decreasing functions of time span. The shape of the function depends upon the time scales and patterns of unsteadiness. We may inquire about the expected rate for any of these processes, or ask which is the fastest, but the answers vary with time scale. Many features of the stratigraphic record require a critical balance in the rates of two or more unsteady processes; the range of time spans at which such conditions can be met is usually limited and the empirical rate data allow expected limits to be determined.

Well-lithified Tertiary sedimentary rocks crop out within the San Andreas fault zone south of the San Bernardino Mountains. At the east end of the outcrop is the pre-Pliocene Mill Creek Formation. The diverse compositional facies of the Mill Creek Formation can be explained in terms of a strike-slip basin model. The northern and southern flanks of the basin are characterized by sediments of quite different provevance: garnet- and muscovite-bearing granitoids from the north and Pelona grayschists from the south. Sediments transported into the basin from the southeast are characterized by clasts of volcanic rocks. Conglomeratic sandstone with hornblende- and biotite-bearing granitoid and gneiss clasts entered the basin from the northwest and dominate the axis of the basin. All of the Tertiary outcrop east of the Mill Creek Formation is assigned to the Potato Sandstone, which has much less compositional variety. The two units are separated by a fault that is probably a major strand of the San Andreas fault, the Wilson Creek strand. The composition and paleocurrents of the Potato Sandstone do resemble the axial deposits in the Mill Creek basin that were derived from the northwest, but the rapid facies changes in strike-slip basins make lithostratigraphic correlations rather unreliable. In order to account for the garnet- and muscovite-bearing granitoids on the northern flank of the Mill Creek Basin, we suggest that the basin formed in the active Clemens Well-Fenner-San Francisquito fault zone. This is consistent with the pre-Pliocene age of the basin. The Clemens Well fault formed the southern margin. The fault on the northern margin may have been a very early strand in the San Andreas fault zone. The basement clasts in the Potato Sandstone have affinities with the Little San Bernardino Mountains. This suggests that the Potato Sandstone was deposited to the northwest of the Mill Creek basin, perhaps at a later time.

The Cenozoic Santa Ana basin lies between the San Gorgonio massif and the northern plateau of the San Bernardino Mountains. Cenozoic sediments are considerably thinner on these two upland areas, which are obvious sources only for the Quaternary portion of the basin fill. The Tertiary fill is the Santa Ana Sandstone—an alluvial to lacustrine, preorogenic deposit that includes at least four conglomerate facies with different provenance. Only two of these facies can simply be derived from local basement terrain, and of these only one is compatible with the modern relief. A third facies requires a source of garnet-bearing Pelona Schist, Pelona green-schists and grayschists, greenstones, arkose, and “polka-dot granite” clasts. The distribution of clast sizes suggests a source that lay about 5 km to the south, just across the San Andreas fault. Such a source could have been provided by the Sierra Pelona of the northern San Gabriel Mountains, prior to major offset on the Punchbowl fault zone. The clast suite of the fourth facies was also transported northward, but bears superficial resemblance to the San Gorgonio basement rocks. The reconstruction of the Santa Ana basin requires that the rocks of the San Gabriel Mountains drew alongside before the uplift of the San Bernardino Mountains. At that time the San Gabriel area was relatively high and stood close to the present position of San Gorgonio Mountain. The modern configuration of the Santa Ana basin was acquired during compression of the Santa Ana basin and thrust faulting of its local sources over the northern margin. The fault at the southern margin is obscured by landsliding and superficial deposits, but may deserve inclusion with the San Andreas fault system. The Pelona Schist-bearing facies in the Santa Ana basin is now about 120 km from its inferred sources, separated by the San Andreas fault zone. Unfortunately, the age of that facies is poorly constrained. It is certainly older than the uplift of the northern plateau of the San Bernardino Mountains. In some areas beyond the Santa Ana basin, the uplift appears to have begun by 4.2 Ma; in others it is still undetected by 2.5 Ma. The Pelona Schist-bearing facies is apparently younger than the 15-Ma sediments near the base of the basin fill, and may be younger than 6.2-Ma basalts. This remaining range of age includes possibilities that do not fit well with published reconstructions of the San Andreas fault history.