Relative efficiency of four parameter-estimation methods in steady-state and transient ground-water flow models

M. C. Hill

Home/Archive/USGS

USGS · 70015892

Relative efficiency of four parameter-estimation methods in steady-state and transient ground-water flow models

M. C. Hill

View original source ↗Export metadata ↓

Abstract

Parameters in numerical ground-water flow models have been successfully estimated using nonlinear-optimization methods such as the modified Gauss-Newton (GN) method and conjugate-direction methods. This paper investigates the relative efficiency of GN and three conjugate-direction parameter-estimation methods on two-dimensional, steady-state and transient ground-water flow test cases. The steady-state test cases are included to compare the performance of the algorithm with published examples. The three conjugate-direction methods are the Fletcher-Reeves (FR) and quasi-Newton (QN) regression methods, and combination Fletcher-Reeves quasi-Newton (FR-QN). All three are combined with Newton's method of calculating step size. The numerical ground-water flow model is described by McDonald and Harbaugh.

Explore related subjects

Conference Paper

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

M. C. Hill. 1990. Relative efficiency of four parameter-estimation methods in steady-state and transient ground-water flow models. https://pubs.usgs.gov/publication/70015892

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related USGS reports

USGS2026

Time-to-depth conversion of seismic-reflection data from eastern Lake Superior and implications for the eastern arm of the Midcontinent Rift

Seismic-reflection data were acquired in the mid 1980s along several lines across eastern Lake Superior by industry and the Great Lakes International Multidisciplinary Program on Crustal Evolution (GLIMPCE) (Fig. 1). The lines form part of a larger network of crossing lines over the entire lake, which can be used to develop three-dimensional geologic models of the Mesoproterozoic Midcontinent Rift that lies below. To better interpret these lines, we developed velocity models to convert seismic reflections versus two-way travel time (TWTT) to reflections versus depth. In addition, the velocity models themselves provide insights into the structure of the Midcontinent Rift by recognizing common velocity ranges for certain rock types (Grauch, 2023).

eastern Lake Superior↗

USGS2026

Revisiting the utility of regional-scale, high-quality geophysical data in mineral exploration - A case study featuring the Mammoth Magnetic Anomaly, Pinal County, Arizona

Regional aeromagnetic surveys passively measure the total magnetic intensity (TMI) and are a foundational tool used in mineral exploration (Airo, 2015). With the increased global demand and the number of critical mineral resources required for manufacturing high-tech devices, developing high-quality, regional-scale geophysical surveys could aid critical mineral exploration efforts and geologic mapping. In 2019, the U. S. Geological Survey launched the Earth Mapping Resources Initiative (Earth MRI) to modernize the geologic and geophysical mapping of regions that have the potential to contain critical mineral resources within the United States. In support of planning Earth MRI geophysical surveys, Drenth and Grauch (2019) defined five aeromagnetic data quality rankings (rank 1 through rank 5) applying them to the airborne geophysical survey inventory of the United States (Johnson et al., 2021). Rank 1 aeromagnetic surveys are of the highest quality, meeting modern standards and allowing best practices for qualitative and quantitative interpretation; whereas rank 5 aeromagnetic surveys are of the lowest quality, being useful only for qualitative interpretation of broad features. Through the Earth MRI effort, 48 high-quality, regional-scale rank 1 and 2 airborne magnetic and radiometric geophysical surveys have been planned, collected, or publicly release through May 2025 (U. S. Geological Survey, 2025). Here, a portion of a rank 1 Earth MRI aeromagnetic survey in southeast Arizona is presented and compared to a legacy rank 5 aeromagnetic survey over the Mammoth Magnetic Anomaly (MMA), demonstrating how modern, high-quality aeromagnetic data improves our view of crustal geology, aiding mineral exploration.

Arizona↗

USGS2026

Early Miocene volcanic rocks and associated tectonics, Lava Hills and southern Bristol Mountains, California

Volcanic rocks of latest Oligocene to early Miocene age form an east-west belt across part of the central eastern Mojave Desert from the Whipple Mountains on the east to the Rosamond Hills on the west. We term this the central belt because it is separated from northern and southern belts by swaths with no volcanic rocks. Limited geochronologic data indicate that much of the belt is latest Oligocene and early Miocene in age, about 24 to 19 Ma, a finding that is consistent with these rocks being overlain by the 18.8 Ma Peach Spring Tuff in many places. We describe Miocene geology in a central area of the belt, in the Lava Hills, southern Bristol Mountains, and southern Old Dad Mountains. Sedimentary basins formed coeval with early andesite to rhyolite volcanism, progressing from fluvial and lacustrine tuffaceous sandstone to volcanic lavas, tuffs, and breccias, indicating that early basins formed proximal to volcanic edifices. Higher strata are fluvial and lacustrine with lavas punctuating the sequence. Although basins may partly have been formed within topographic lows bounded by volcanic domes, plateaus, and stratovolcanoes, consistent stratigraphic sections over wide areas indicate that tectonic basin evolution affected broad areas. The volcanic section is capped by local basalt flows and the regional Peach Spring Tuff. Limited data on normal faults support interpretations of early extensional basin development caused by northeast-southwest oriented stretching. Later extension caused stratal rotations, tilting early deposits down to the southwest. This tilted and subsequently beveled basin architecture was overlain by the youngest volcanic deposits, primarily rhyolite and basalt. The Peach Spring Tuff, 18.8 Ma, lies within this upper unit. Similar stratigraphic and structural relations are exposed in the nearby Marble Mountains and Van Winkle Mountain sections, reinforcing that a broad area underwent similar volcanism and tectonism. In our study area the upper unit is only very gently tilted except near dextral strike-slip faults of the eastern California shear zone. These late Miocene to Recent faults are represented as four main fault zones spaced about 5 km apart, representing distributed shear north of the Bristol Lake basin.

California↗